Methods for identifying interdependencies

Abstract

To efficiently and accurately specify interdependence between objects about events by simply and accurately calculating a mutual information amount between the events with a small calculation amount even in the case of using data for handing the events including multiple criteria.SOLUTION: A method for specifying interdependence between a first object and a second object includes a step for using a data set composed of a plurality of pieces of data for handling a first event including a plurality of criteria about the first object and handling a second event including a plurality of criteria about the second object to calculate a mutual information value between a specific value of the first event and a specific value of the second event. A combination of the specific value of the first event and the specific value of the second event is selected with a frequency of the combination in the data set as an index.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to a method for identifying interdependencies, which includes a step of calculating mutual information; a computer program for performing the method; and a calculation device for calculating the mutual information. [Background technology]

[0002] With the recent advancements in computer technology, data is being collected through various means, resulting in the accumulation of vast amounts of data containing different types of information. These large datasets are expected to contain useful information, and if they can be comprehensively and uniformly used as random variables across a large range for analysis, it is expected that the characteristics of the target subject related to these random variables can be identified with greater accuracy.

[0003] Mutual information between multiple random variables is a quantity used in information theory to represent the interdependence between two random variables, and is used to represent the interdependence between objects with respect to those random variables. By calculating the mutual information between multiple random variables, it is possible to identify the interdependence between the objects of those random variables, and thereby it is expected that the characteristics of those objects can be identified. Techniques for analyzing large amounts of data using mutual information are used in the processing of diverse information such as documents, audio, images, location, life, astronomy, finance, and sales. As an algorithm for analyzing life information, for example, ARACNE is known (Non-Patent Literature 1).

[0004] While mutual information is suitable for handling large amounts of data, it has the drawback of being difficult to perform statistical analysis based on probability theory and difficult to compare between many random variables. To overcome this, the inventors have developed a method for calculating mutual information using statistical methods for data represented in a 2x2 contingency table (Patent Document 1). However, it was difficult to apply this method to data on multiple events consisting of a large number of criteria, that is, data represented in an mxn contingency table. This was because the statistical method used in this method was Fisher's exact probability, which is specialized for 2x2 contingency tables, and because calculating mutual information from data represented in an mxn contingency table requires an enormous amount of computation, similar to when calculating mutual information using conventional methods.

[0005] The mutual information MI between two discrete random variables X and Y is a measure of the amount of information shared between X and Y, and the following formula is known for its calculation.

[0006]

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[0007] In the above equation, p(x i ,y j ) is the joint probability of X and Y, p(x i ) and p(y j These are the marginal probabilities of X and Y, respectively.

[0008] Furthermore, the following formula is known for calculating the mutual information I(X;Y) between two continuous random variables X and Y.

[0009]

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[0010] In the above equations, p(x,y) is the joint probability density function of X and Y, and p(x) and p(y) are the marginal probability density functions of X and Y, respectively. These equations mean that mutual information is calculated by calculating the expected value of the joint probability of the two variables over all possible data ranges and then summing them up. Thus, since mutual information is calculated by summing the expected values ​​of the joint probability of the two variables, the amount of computation required increases dramatically as the number of possible values ​​of the variables increases. For this reason, calculating mutual information between random variables that take many values ​​in order to identify the interdependence between subjects was not practical from the standpoint of computation time and computation cost. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] WO2018 / 181988 [Non-patent literature]

[0012] [Non-Patent Document 1] NATURE REVIEWS CANCER,VOLUME 17,FEBRUARY 2017,116-130 [Overview of the project] [Problems that the invention aims to solve]

[0013] The present invention aims to accurately calculate the mutual information between random variables with minimal computational effort, even when using data that deals with random variables that take on a large number of values, and to efficiently and accurately identify the interdependence between objects with respect to the random variables. [Means for solving the problem]

[0014] The inventors, through diligent research, found that the mutual information MI between a first random variable that takes m values ​​and a second random variable that takes n values ​​can be approximated as the sum of the individual mutual information between a specific value of the first random variable and a specific value of the second random variable. Furthermore, the frontier mutual information (MI), which is the individual mutual information with the largest absolute value among them, is... front Using the formula m × n × MI front We found that mutual information can be approximately calculated using / log(m×n-1). And so, the Frontier Mutual Information MI front We found that the frequency of the aforementioned combination in the dataset can be used as an indicator to identify it. Based on these findings, we developed a method to identify the mutual information between two events by using the relative frequencies of the two events as the first and second random variables.

[0015] In other words, the present invention provides the following: [1] A method for identifying the interdependence of a first event and a second event, wherein the first event includes m criteria and the second event includes n criteria, and the method includes a sample count aggregation step of aggregating the sample counts in all cells into an m × n frequency distribution table with respect to a cell consisting of one criterion selected from the first event and one criterion selected from the second event; a relative frequency aggregation step of calculating simultaneous relative frequencies from the sample counts in all cells of the frequency distribution table and aggregating them into an m × n contingency table; an individual mutual information determination step of determining the individual mutual information of each cell based on the simultaneous relative frequencies in all cells; a mutual information calculation step of calculating the mutual information of the first event and the second event from the individual mutual information; and a mutual dependency determination step of determining the interdependence of the first event and the second event based on the values ​​of the mutual information. The aforementioned m and n are each integers of 2 or greater, and at least one of them is 3 or greater, and the simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The individual mutual information amount determination step includes, for each cell, (a) a conversion step of converting the m×n contingency table into a 2×2 contingency table including binary data for the criteria in each of the first and second events based on the simultaneous relative frequency of one cell, the marginal relative frequency for the criterion in the first event of that cell, and the marginal relative frequency for the criterion in the second event of that cell, and (b) a calculation step of calculating the strength of the correlation between the criteria in the first and second events as the individual mutual information amount using the multi-dimensional mutual information amount, Fisher's exact probability, or the hypergeometric distribution from the 2×2 contingency table, The mutual information amount calculation step includes (i) a direct calculation step of calculating the mutual information amount from the individual mutual information amount based on Equation (I) [Number] (where MI represents the mutual information amount and MI kl represents the individual mutual information amount) and includes, or (ii) a frontier mutual information amount selection step of comparing the individual mutual information amounts with each other and selecting the individual mutual information amount with the largest absolute value as the frontier mutual information amount, and a frontier mutual information amount utilization step of calculating the mutual information amount based on the frontier mutual information amount. The calculation of the mutual information amount in the frontier mutual information amount utilization step is performed by Equation (II) [Number] (where MI represents the mutual information amount and MI front represents the frontier mutual information amount) The method as described above. [2] The method according to [1], wherein the calculation using the multi-dimensional mutual information amount is performed based on the following Equation (III). [Number] (where MI kl represents the individual mutual information amount of the cell composed of the k-th criterion of the first event and the l-th criterion of the second event, and X k′This indicates the k'-th criterion of the first event in the 2x2 contingency table, Y l′ This indicates the l'-th criterion of the second event in the 2x2 contingency table, and p(X k′ ,Y l′ ) is standard X k′ and reference Y l′ This shows the simultaneous relative frequency of cells consisting of p(X k′ ) is standard X k′ The marginal relative frequencies for p(Y) are shown, and p(Y l′ ) is the reference Y l′ (This shows the relative frequency of the margins.) [3] The method according to [1] or [2], wherein at least one of m and n is 100 or more. [4] The method according to any one of [1] to [3], wherein the total number of samples is 1000 or more. [5] The method according to any one of [1] to [4], further comprising a confidence interval calculation step for determining the confidence interval of the mutual information after the mutual information calculation step. [6] The method according to any one of [1] to [5], wherein the determination step includes an integration step of integrating the mutual information amounts with one or more different contingency tables by meta-analysis. [7] The method according to any one of [1] to [6], wherein each of the processes and steps is performed by a computer. [8] A method for comparing the expected values ​​of each cell in a first event and a second event, wherein the first event includes m criteria and the second event includes n criteria, and the method includes a sample count aggregation step of aggregating the sample counts in all cells into an m × n frequency distribution table with respect to a cell consisting of one criterion selected from the first event and one criterion selected from the second event; a relative frequency aggregation step of calculating simultaneous relative frequencies from the sample counts in all cells of the frequency distribution table and aggregating them into an m × n contingency table; an individual mutual information determination step of determining the individual mutual information of each cell based on the simultaneous relative frequencies in all cells; and an expected value calculation step of converting the individual mutual information into an expected value according to a probability distribution in at least one of the cells; an expected value comparison step of comparing the expected values ​​between multiple different cells; and a cell ranking determination step of determining the ranking of each cell based on the magnitude of the expected value from the comparison results. The aforementioned m and n are each integers of 2 or greater, and at least one of them is 3 or greater, and the simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The individual mutual information determination step includes, for each cell, (a) a conversion step of converting the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the marginal relative frequency of the cell with respect to the criterion in the first event, and the marginal relative frequency of the criterion in the second event; and (b) a calculation step of calculating the strength of the interrelationship between the criteria in the first and second events as the individual mutual information from the 2 × 2 contingency table using multidimensional mutual information, Fisher's exact probability, or a hypergeometric distribution. The probability density function of the aforementioned probability distribution is given by equation (IV).

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[0016]

[10] A device for calculating mutual information between a first event and a second event, wherein the first event includes m criteria and the second event includes n criteria, and the device includes a sample count aggregation unit that aggregates the number of samples in all cells into an m × n frequency distribution table with respect to a cell consisting of one criterion selected from the first event and one criterion selected from the second event; a relative frequency aggregation unit that calculates simultaneous relative frequencies from the number of samples in all cells of the frequency distribution table and aggregates them into an m × n contingency table; an individual mutual information determination unit that determines the individual mutual information of each cell based on the simultaneous relative frequencies in all cells; and a mutual information calculation unit that calculates the mutual information between the first event and the second event from the individual mutual information. The aforementioned m and n are each integers of 2 or greater, and at least one of them is 3 or greater, and the simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The determination by the individual mutual information determination unit is performed, for each cell, by (a) converting the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the marginal relative frequency of the criterion in the first event of that cell, and the marginal relative frequency of the criterion in the second event, and (b) calculating the strength of the interrelationship between the criteria in the first and second events as the individual mutual information from the 2 × 2 contingency table using multidimensional mutual information, Fisher's exact probability, or hypergeometric distribution. The calculation by the mutual information calculation unit is performed by (i) calculating the mutual information from the individual mutual information using formula (I)

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[11] A program for processing mutual information of a first event and a second event, wherein the first event includes m criteria and the second event includes n criteria, and the program provides a computer with respect to a cell consisting of one criterion selected from the first event and one criterion selected from the second event, a sample count aggregation step of aggregating the sample counts in all cells into an m × n frequency distribution table; a relative frequency aggregation step of aggregating simultaneous relative frequencies from the sample counts in all cells of the frequency distribution table into an m × n contingency table; and aggregating simultaneous relative frequencies in all cells The system is configured to perform an individual mutual information determination step, which determines the individual mutual information of each cell based on relative frequencies; an expected value calculation step, which, when calculating an expected value, converts the individual mutual information of at least one of the cells into an expected value according to a probability distribution; a mutual information calculation step, when not calculating an expected value, which calculates the mutual information of the first event and the second event from the individual mutual information; and an interdependence determination step, which determines the interdependence of the first event and the second event based on the values ​​of the mutual information. The aforementioned m and n are each integers of 2 or greater, and at least one of them is 3 or greater, and the simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The individual mutual information determination step includes, for each cell, (a) a conversion step of converting the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the marginal relative frequency of the cell with respect to the criterion in the first event, and the marginal relative frequency of the criterion in the second event; and (b) a calculation step of calculating the strength of the interrelationship between the criteria in the first and second events as the individual mutual information from the 2 × 2 contingency table using multidimensional mutual information, Fisher's exact probability, or a hypergeometric distribution. The aforementioned mutual information calculation step involves (i) calculating the mutual information from the individual mutual information amounts using formula (I)

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[0017] According to the present invention, the mutual information between random variables can be accurately calculated without having to calculate the expected value of the joint probability for all possible combinations of values ​​that the random variables can take. Furthermore, according to the present invention, the expected value of any joint probability can be calculated based on the mutual information. [Brief explanation of the drawing]

[0018] [Figure 1] This is a schematic diagram showing an example configuration of the mutual information calculation device (1). [Figure 2] This figure shows an example of the software configuration for a mutual information calculation device. [Figure 3] This flowchart shows the steps for identifying interdependencies and comparing the expected values ​​of each cell. [Figure 4] This flowchart shows the details (S0110 and S0111) of the individual mutual information amount determination process (S0103). [Figure 5] This flowchart shows the details (S0112-S0114) of the mutual information calculation process (S0104) in the method for identifying interdependencies. [Figure 6] This graph shows the relationship between mutual information (MI), Fisher's exact probability (PF), and the probability obtained from the chi-squared distribution (Pχ) in a 2x2 contingency table. In the figure, LogP represents the common logarithm of probability P, R² for Fisher's exact probability represents the coefficient of determination, and N represents the total sample size. [Figure 7] This graph shows the relationship between mutual information (MI), Fisher's exact probability (PF), and the probability obtained from the chi-squared distribution (Pχ) in a 2x2 contingency table. In the figure, LogP represents the common logarithm of probability P, R² for Fisher's exact probability represents the coefficient of determination, and N represents the total sample size. [Figure 8-1] This diagram shows the magnitude of the frequency in each cell of a 10x10 contingency table. (A) The intensity of the color indicates the magnitude of the absolute difference between the frequency and the mean of each cell. (B) The frequency of each cell is shown. [Figure 8-2] This diagram shows the magnitude of the individual mutual information in each cell of a 10x10 contingency table. (A) The magnitude of the individual mutual information value in each cell is indicated by the intensity of the color. (B) The individual mutual information of each cell is shown. [Figure 9] This graph shows the relationship between the individual mutual information and the simultaneous relative frequency of each cell in an m×n contingency table. The left panel of each graph shows the relationship between the individual mutual information and the simultaneous relative frequency, and the right panel shows the relationship between the individual mutual information and the logarithmic value of the simultaneous relative frequency. (A) shows the case when m=n=10. (B) shows the case when m=n=100. In the graph, MIkl represents the individual mutual information, p is the simultaneous relative frequency of each cell, and Log(p) is the common logarithm of the simultaneous relative frequency p. [Figure 10] This graph shows the relationship between the individual mutual information and the simultaneous relative frequency of each cell in an m×n contingency table. The left panel of each graph shows the relationship between the individual mutual information and the simultaneous relative frequency, while the right panel shows the relationship between the individual mutual information and the logarithmic value of the simultaneous relative frequency. (A) shows the case when m=n=1,000. (B) shows the case when m=n=10,000. In the graph, MIkl represents the individual mutual information, p is the simultaneous relative frequency of each cell, and Log(p) is the common logarithm of the simultaneous relative frequency p. [Figure 11] This graph shows the individual mutual information and simultaneous relative frequency of each cell in an m×n contingency table. In the figure, MIkl represents the individual mutual information, and p represents the simultaneous relative frequency of each cell. [Modes for carrying out the invention]

[0019] In this specification, the "×" symbol in mathematical formulas is sometimes omitted. The present invention provides a method for identifying the interdependence between a first event and a second event. As shown in Figure 3, the method of the present invention includes a sample counting step (S0101), a relative frequency counting step (S0102), an individual mutual information determination step (S0103), a mutual information calculation step (S0104), and an interdependence determination step (S0105).

[0020] Here, an example of an event is a state that is observed and perceived as an object. Examples of objects include genes and words. Other examples of objects include documents, sounds, images, locations, life, astronomy, finance, and sales. An example of a state is that it differs from the average properties of the aforementioned object. Examples of events include changes in genes, epigenetic changes, and increases or decreases in stock prices. Other examples of events include the use of multiple words in the same sentence and the inclusion of sales of a specific product in sales figures.

[0021] Examples of gene changes include mutations in gene sequences, changes in gene expression products, and changes in gene modifications. Examples of gene sequence mutations include mutations in the base sequence of a gene, changes in the copy number of a gene on a chromosome, and changes in gene modifications. Examples of gene base sequence mutations include point mutations, addition of base sequences to a gene, and deletion of base sequences in a gene. Examples of gene expression products include proteins, mRNA, and miRNA (microRNA). Examples of changes in gene expression products include changes in the expression level of a gene expression product, changes in the expression site of a gene expression product, formation of a complex of gene expression products, and degradation of a complex of gene expression products. Examples of gene modifications include DNA methylation and histone modifications. Examples of histone modifications include acetylation, methylation, ubiquitination, phosphorylation, and SUMOylation. Furthermore, examples of gene modifications include post-translational modifications. Examples of post-translational modifications include functional group addition, addition of proteins or peptides, transformation of the chemical properties of amino acids, and structural transformation. Examples of functional group addition include acylation, acetylation, alkylation, amidation, biotinylation, formylation, γ-carboxylation, glutamylation, glycosylation, glycylation, heme, hydroxylation, iodation, isoprenylation, lipoylation (prenylation, GPI anchor formation, myristoylation, farnesylation, geranylgeranylation, etc.), covalent addition to nucleotides or derivatives (ADP-ribosylation, FAD bonding, etc.), redox reactions, polyethylene glycolation, phosphatidylinositol, phosphopantetheinylation, phosphorylation, pyroglutamic acid formation, racemization, tyrosine sulfate, and selenoylation. Examples of protein or peptide addition include ISG formation, SUMO formation, and ubiquitination. Examples of transformation of the chemical properties of amino acids include citrullination or deaminement and deamide formation. Examples of structural transformation include disulfide and protease formation.

[0022] Examples of genes include those of mammals such as humans, monkeys, mice, and rats. Examples of epigenetic changes include changes that are inherited through cell division and are independent of changes in the DNA base sequence.

[0023] In the first and second events, "first" and "second" are symbols used to distinguish between the first and second events, and do not limit their order. Here, the first and second events may be the same state for different objects, or different states for the same object. For example, the first event may be a mutation in the base sequence of gene A, and the second event may be a mutation in the base sequence of gene B. Alternatively, for example, the first event may be a mutation in the sequence of gene A, and the second event may be a change in the expression level of the expression product of gene A. Here, gene A and gene B refer to different genes.

[0024] Common examples of subjects include those derived from living organisms, those derived from humans, those derived from humans with diseases, those derived from humans with cancer, and those derived from humans with a specific type of cancer. Examples of subjects include cells, organs, and other biological samples of living organisms such as humans.

[0025] Examples of specific types of cancer include leukemia, lymphoma, Hodgkin's disease, non-Hodgkin lymphoma, multiple myeloma, brain tumors, breast cancer, endometrial cancer, cervical cancer, ovarian cancer, esophageal cancer, stomach cancer, appendiceal cancer, colorectal cancer, liver cancer, hepatocellular carcinoma, gallbladder cancer, bile duct cancer, pancreatic cancer, adrenal cancer, gastrointestinal stromal tumors, mesothelioma, head and neck cancer, laryngeal cancer, oral cancer, floor of the mouth cancer, gingival cancer, tongue cancer, buccal mucosa cancer, salivary gland cancer, paranasal sinus cancer, maxillary sinus cancer, frontal sinus cancer, ethmoid sinus cancer, sphenoid sinus cancer, thyroid cancer, kidney cancer, lung cancer, osteosarcoma, prostate cancer, testicular cancer, renal cell carcinoma, bladder cancer, rhabdomyosarcoma, skin cancer, and anal cancer.

[0026] Because organisms suffering from disease, particularly cancer, exhibit amplified interactions between genes, cells, organs, and other biological samples derived from diseased organisms are suitable as samples for identifying interdependencies between different genes.

[0027] Examples of events include those that can be expressed as presence or absence, and those that can be expressed numerically. Examples of events that can be expressed numerically include those that can be expressed as discrete quantities greater than 2, and those that can be expressed as continuous quantities. The first and second events may be expressed differently; for example, the first event may be expressed as presence or absence, and the second event may be expressed as discrete quantities greater than 2.

[0028] When the event concerns a gene, examples of interdependencies to be identified include those relating to the gene's molecular and cellular function, physiological function, disease association, and biological pathway, as well as interactions between cell surface molecules, metabolic pathways, molecular functional pathways, and drug targeting. Examples of disease associations include the onset and progression of cancer, immune and allergic diseases, neuropsychiatric disorders, and congenital anomalies.

[0029] In this invention, even when the sample used is derived from a patient with cancer, it is possible to identify interdependencies between genes that are not related to cancer. Examples of genes that are not related to cancer include those related to the nervous system, immune system, metabolism, and endocrine system. Conversely, in this invention, even when the sample used is derived from a patient who does not have cancer, it is possible to identify interdependencies between genes that are related to cancer. By using the interdependencies identified in this invention, it is possible to identify target molecules and drugs for diseases. Furthermore, by using the interdependencies identified in this invention, it is possible to search for ligands for orphan receptors.

[0030] When the event concerns a word, for example, when the event is the use of a particular word in a particular sentence, an example of the specific interdependence to be identified is the meaning of the word.

[0031] In the method of the present invention, information about each event can be used regardless of its type. Even when the process is repeated for different events, the method of the present invention allows for processing using a common technique, thus enabling simple and unified analysis. Therefore, the method of the present invention is suitable for using data containing information about multiple events, for example, multiple genes, in a unified manner to identify the interdependencies between those events.

[0032] In the method of the present invention, a dataset is used that consists of relative frequencies for a first event containing multiple criteria and a second event containing multiple criteria. The relative frequencies are positive values ​​and have a sum of 1.

[0033] In a dataset, for example, each of the N samples contains information about a first event and information about a second event. Here, examples of event information include (1) if the event is represented by presence or absence, information about whether the event occurred or not for that sample; and (2) if the event is represented by a numerical value, a numerical value for that sample.

[0034] In the method of the present invention, the data is first compiled into an m × n contingency table. Specifically, this is done in two steps: a sample size calculation step (S0101) and a relative frequency calculation step (S0102).

[0035] The sample count aggregation step (S0101) is a step in which the sample count for all cells consisting of one criterion selected from the first event and one criterion selected from the second event is aggregated into an m × n frequency distribution table.

[0036] The relative frequency calculation process (S0102) is a process in which the simultaneous relative frequency is calculated from the sample size for all cells in the frequency distribution table and then aggregated into an m × n contingency table. Here, the simultaneous relative frequency refers to the proportion of the number of samples corresponding to a particular cell to the total number of samples.

[0037] The counting of samples from the aforementioned dataset into a contingency table can be done, for example, by aggregating the sample counts a, b, c, and d in Table 1 below, which correspond to the conditions in each column, using a 2x2 contingency table where both the data for the first event and the data for the second event are represented as presence or absence. The sum of a to d is the total number of samples N included in the aforementioned dataset.

[0038] [Table 1]

[0039] In aggregating into a contingency table, it is not necessary to use a table, as long as the number of samples corresponding to a, b, c, and d, which are the number of samples that meet the aforementioned conditions, is aggregated. In this example, for example, it can be done as follows: First, set the conditions: (1) the first event exists and the second event exists; (2) the first event exists and the second event does not exist; (3) the first event does not exist and the second event exists; and (4) the first event does not exist and the second event does not exist. Next, determine which of conditions (1) to (4) each of the N samples meets, and classify each of the N samples into the respective condition. Repeat this for all N samples and aggregate the number of samples classified into each condition. In this case, (1)a is the number of samples out of all N samples in which the first event is "present" and the second event is "present", (2)b is the number of samples out of all N samples in which the first event is "present" and the second event is "absent", (3)c is the number of samples out of all N samples in which the first event is "absent" and the second event is "present", and (4)d is the number of samples out of all N samples in which the first event is "absent" and the second event is "absent".

[0040] Alternatively, instead of the sample size described above, relative frequencies may be directly aggregated and used in the method of the present invention, or data expressed as relative frequencies may be used as is in the method of the present invention. In this case, the aggregation can be performed by carrying out the relative frequency aggregation step (S0102) simultaneously with the sample size aggregation step (S0101), or by carrying out the relative frequency aggregation step (S0102) alone.

[0041] The criteria included in each event may include, for example, the presence or absence of a certain phenomenon, its type, or the properties of individual events when the event is expressed as a difference in the nature of a particular phenomenon, or a numerical range divided by a threshold when the event is expressed numerically, but are not limited to these. When using the aforementioned threshold, for example, the event can be classified according to the criteria based on whether the numerical value is greater than or equal to the threshold, or less than the threshold.

[0042] The criteria may be set in a way that includes samples that do not fall into any of the criteria. For example, when an event is expressed numerically, it is not necessary to set a threshold for all possible values ​​of the sample and classify them accordingly; instead, a certain range can be defined, and the criteria can be set within that defined range. Here, in the case of a numerical range, the certain range can be, for example, a range excluding outliers, a range divided by percentiles, a range divided by the magnitude of the standard deviation from the mean, or a range divided by any other arbitrary numerical value, or a range divided by an indicator that can be used in general statistical methods. In other cases, the range can be arbitrarily set according to various purposes, for example, to include the main phenomenon or to make the phenomenon of interest clearer.

[0043] The criteria included in a single event may consist of only one phenomenon or property, or it may be a combination of criteria relating to multiple different phenomena or properties. Furthermore, when using combinations, all possible combinations may be used as criteria, or only some of them may be used as criteria.

[0044] The criteria for the first event and the criteria for the second event may be the same or different. For example, if the two events are represented by numerical values, the threshold for the first event and the threshold for the second event may be the same or different.

[0045] Conventionally, calculating the mutual information between events containing a vast number of criteria has been extremely difficult in practice due to the exponential increase in computational complexity. According to the present invention, as described later, the more criteria included in an event increase, the more accurately the mutual information can be approximated, and even when using such events, the mutual information can be accurately calculated with less computational complexity.

[0046] Let the number of criteria included in the first event be m, where m is an integer greater than or equal to 2. Let the number of criteria included in the second event be n, where n is an integer greater than or equal to 2 and may be the same as or different from m. Furthermore, at least one of m and n must be 3 or greater. The magnitudes of m and n are not particularly limited, but for example, at least one of them could be 10 or greater, 50 or greater, 100 or greater, 500 or greater, 1,000 or greater, 5,000 or greater, 10,000 or greater, 50,000 or greater, or 100,000 or greater. Let the number of data points in the dataset, i.e., the total number of samples, be N, where N is an integer greater than or equal to 2. There are no particular limitations, but examples of N include values ​​such as 10 or greater, 50 or greater, 100 or greater, 500 or greater, 1,000 or greater, 5,000 or greater, 10,000 or greater, 50,000 or greater, or 100,000 or greater. The larger m and n are, the more accurately the interdependence between the first and second events can be identified.

[0047] As the inventors have found, the mutual information MI between a first event containing m criteria and a second event containing n criteria can be calculated based on the individual mutual information between a specific value of the first event and a specific criterion of the second event. Specifically, it can be calculated by the sum of these, or by the frontier mutual information MI with the largest absolute value among them. frontUsing the formula m × n × MI front The mutual information (MI) can be approximated by / log(m×n-1).

[0048] The calculation of mutual information is performed in two steps: the individual mutual information determination step (S0103) and the mutual information calculation step (S0104). The calculation of mutual information is usually performed after aggregation. However, for example, part or all of the calculation of mutual information may be started before the aggregation is completed.

[0049] The individual mutual information determination step (S0103) is a step in which the individual mutual information of each cell is determined for all cells based on the simultaneous relative frequencies.

[0050] The mutual information calculation step (S0104) is a step in which the mutual information of the first event and the second event is calculated from the individual mutual information.

[0051] Normally, the mutual information calculation step (S0104) is performed after the individual mutual information determination step (S0103). However, for example, if the frontier mutual information described later is not used in the mutual information calculation step (S0104), it is not necessary to perform the mutual information calculation step (S0104) after determining the individual mutual information of all cells in the individual mutual information determination step (S0103). For example, the calculation of mutual information may be started sequentially from the determined individual mutual information. Also, even when using frontier mutual information, the selection of frontier mutual information may be started during the individual mutual information determination step (S0103).

[0052] Here, mutual information is a quantity used in information theory to represent the interdependence of two random variables. Mutual information is a measure of the amount of information shared between the first random variable X and the second random variable Y. In general, the mutual information MI of two discrete random variables X and Y can be calculated, for example, by the following formula.

[0053]

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[0054] In the above equation, p(x i ,y j ) is the joint probability of X and Y, p(x i ) and p(y j These are the marginal probabilities of X and Y, respectively.

[0055] Furthermore, the mutual information I(X;Y) between two continuous random variables X and Y can be calculated, for example, by the following formula.

[0056]

number

[0057] In the above equation, p(x,y) is the joint probability density function of X and Y, and p(x) and p(y) are the marginal probability density functions of X and Y, respectively.

[0058] In the above example, where MI is the mutual information of an m×n contingency table relating two events X and Y, if k is one criterion for event X and l is one criterion for event Y, then the mutual information of a 2×2 contingency table centered on the cell (k,l), which is a combination of these, is defined as the individual mutual information MI. kl The individual mutual information of each cell is determined based on the simultaneous relative frequencies.

[0059] The individual mutual information determination process (S0103) includes two steps, as shown in Figure 4: a conversion step (S0110) and a calculation step (S0111).

[0060] For each cell, the transformation step (S0110) is the step of transforming the m × n contingency table for each cell into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, respectively.

[0061] The calculation step (S0111) is a step in which, for each cell, the strength of the interrelationship between the criteria in the first and second events is calculated as individual mutual information from a 2x2 contingency table.

[0062] The calculation step (S0111) can usually be performed after the conversion step (S0110). Here, for example, the conversion step (S0110) may be performed for all cells before the calculation step (S0111), or the conversion step (S0110) and the calculation step (S0111) may be performed for each cell.

[0063] In the conversion step described above (S0110), a 2x2 contingency table can be converted based on the simultaneous relative frequency of a cell, the marginal relative frequency of that cell with respect to the criterion in the first event, and the marginal relative frequency of the criterion in the second event. Here, the marginal relative frequency refers to the sum of the simultaneous relative frequencies in a single column or a single row.

[0064] Specifically, in an m×n contingency table relating the two events X and Y described above, the simultaneous relative frequency of cell (k,l) is p(X k ,Y l Let ) be the marginal relative frequencies of column k and row l, respectively, and p(X k ) and p(Y l Let's assume that the 2x2 contingency table centered on cell (k,l) is represented as shown in the following table.

[0065] [Table 2]

[0066] The individual mutual information of each cell is calculated in calculation step (S0111). The method used here is not particularly limited, but for example, it can be calculated using multidimensional mutual information, Fisher's exact probability, or a hypergeometric distribution.

[0067] An example of a method using multidimensional mutual information is the method performed based on the following equation (III).

[0068]

number

[0069] Methods using Fisher's exact probability include, for example, using Fisher's exact probability as is or with modifications. An example of a method using Fisher's exact probability with modifications is the calculation using -log(P) / N (where P represents Fisher's exact probability).

[0070] One example of a method using the hypergeometric distribution is the main term P of Fisher's exact probability, which will be discussed later in the section on the application of meta-analysis. main One method is to use [this method].

[0071] The mutual information calculation process (S0104), as shown in Figure 5, includes the following two procedures depending on whether or not frontier mutual information is used (E0103): (i) If the Frontier Mutual Information is not used, the mutual information calculation step includes a direct calculation step (S0112); (ii) When frontier mutual information is used, the mutual information calculation step includes a frontier mutual information selection step (S0113) and a frontier mutual information utilization step (S0114).

[0072] In the direct calculation step (S0112), the mutual information is calculated from the individual mutual information using equation (I)

number

[0073] As shown below, when m and n are sufficiently large, the right-hand side of equation (I) approaches the left-hand side, and equation (I) can be considered an equality.

[0074] Sufficiently large means, for example, 50 or more, 100 or more, 500 or more, 1,000 or more, 5,000 or more, or 10,000 or more.

[0075] The following describes the case where frontier mutual information is used. As shown below, the inventors have found that by using the individual mutual information with the largest absolute value (frontier mutual information) as a representative value showing the interdependence between the first and second events, mutual information can be easily and accurately calculated with minimal computation.

[0076] In the frontier mutual information selection step (S0113), the individual mutual information is compared with each other, and the individual mutual information with the largest absolute value is selected as the frontier mutual information.

[0077] In the Frontier Mutual Information Utilization Step (S0114), mutual information is calculated based on the selected Frontier mutual information. Here, this calculation is performed using the following equation (II).

[0078]

number

[0079] As shown below, when m and n are sufficiently large, the right-hand side of equation (II) approaches the left-hand side, and equation (II) can be considered an equality. The values ​​of sufficiently large m and n are the same as those described for formula (I) above.

[0080] Whether or not to use the Frontier Mutual Information can be appropriately determined depending on the magnitudes of m and n, the performance of the computer used, and other conditions and purposes. For example, the Frontier Mutual Information can be used when both m and n are sufficiently large.

[0081] Here, "sufficiently large" means, for example, 100 or more, 500 or more, 1,000 or more, 5,000 or more, 10,000 or more, 50,000 or more, or 100,000 or more.

[0082] The calculated mutual information can be used to determine the interdependence between the first and second events. This determination is performed in the interdependence determination step (S0105). This determination can usually be performed after the calculation of the mutual information.

[0083] In this process, interdependence is determined based on the magnitude of the mutual information value. Specifically, for example, a larger value indicates a greater interdependence between the first and second events. One or more thresholds may be set for the mutual information value to determine the magnitude of interdependence in stages. Alternatively, the mutual information value may be evaluated by comparing it with the value for another contingency table.

[0084] Below are mutual information (MI) and the individual mutual information (MI) mentioned above. kl and Frontier Mutual Information (MI) front The inventors present their findings regarding the relationship between the two random variables. While the following describes the mutual information between the two random variables due to the need for mathematical formulas, this can be directly applied to the method for identifying interdependencies of the present invention by replacing these random variables with events.

[0085] Let MI be the mutual information of an m×n contingency table for two random variables X and Y. Let k be one value that the random variable X can take, and l be one value that the random variable Y can take. The mutual information of a 2×2 contingency table centered on a cell (k,l), which is a combination of these values, is the individual mutual information MI. kl Let's assume that the simultaneous relative frequency of cell (k,l) is p(X k ,Y l Let ) be the marginal relative frequencies of column k and row l, respectively, and p(X k ) and p(Y l Let's assume that the MI between random variables X and Y and the MI in all cells are then... kl The difference from the sum is expressed by the following formula:

[0086]

number

[0087] Each cell in an m×n contingency table is divided into h uniform parts for both rows and columns, and the MI is applied to all divided cells. kl When the sum is taken, the following formula is obtained.

[0088]

number

[0089] Let the left-hand side of the above equation be defined as Δ(h). Using L'Hôpital's rule, we calculate the limit of each term on the right-hand side as h approaches infinity. Then, the limits of both the first and second terms are p(X k ,Y l ) The third term approximates as follows:

[0090]

number

[0091] Terms 4 and 5 approximate the following:

[0092]

number

[0093] These limits and p(X k ,Y l The sum of ) and p(X k The sum of ) and p(Y l Using the fact that the sums of ) are equal, it can be shown that the limit of the right-hand side is zero. Therefore, the following holds:

[0094]

number

[0095] Therefore, when m and n are sufficiently large, the following equation (I) holds.

[0096]

number

[0097] Next, according to the inventors' findings, the individual mutual information quantity MI is the mutual information quantity of a 2x2 contingency table centered on cell (k,l). kl It follows an exponential distribution. This is shown below.

[0098] First, the mutual information of an m × n contingency table is defined as follows, where k and l are between 1 and m, and between 1 and n, respectively.

[0099]

number

[0100] Furthermore, the sum of the expected values ​​of each random variable is 1, as shown below.

[0101]

number

[0102] The individual mutual information for a cell (k,l) is defined as follows:

[0103]

number

[0104] By the way, as shown in equation (I) above, when m and n are sufficiently large, the following holds true.

[0105]

number

[0106] The following holds for the probability p(MI) that the mutual information between X and Y is MI.

[0107]

number

[0108] MI related to k and l kl The sum of the second, third, and fourth terms on the right-hand side converges to 0. Therefore, MI kl This becomes more independent of the simultaneous relative frequencies of other cells. When X and Y follow a uniform distribution, the marginal relative frequencies of column k and row l asymptotically approach 1 / m and 1 / n, respectively, and as m and n increase, their dependence on the marginal relative frequencies of other rows and columns decreases. Therefore, when m and n are sufficiently large, from a microscopic standpoint, X and Y can be expressed as X k and Y l By doing so, MI kl The above formula for p(MI) can also be applied to this.

[0109] In other words, MI kl It follows an exponential distribution. On the other hand, from a macroscopic perspective, MI kl The average value of x is MI / (m×n) from the above formula. That is, x = MI kl The probability density function p(x) is expressed by the following equation:

[0110]

number

[0111] Here, λ is the mutual information MI kl It is the reciprocal of the mean value. mutual information MI kl As mentioned above, it follows an exponential distribution. Therefore, j is MI kl If we consider the rank of the absolute value, then the following holds:

[0112]

number

[0113] Here x1 is MI kl At its maximum value, here we have the Frontier Mutual Information (MI). front It is called [this]. The following holds true regarding this.

[0114]

number

[0115] Therefore MI front This includes the overall MI and the average MI. kl It is approximately proportional to both. Therefore, the overall MI is MI front The following is calculated from this:

[0116]

number

[0117] As described above, when n and m are sufficiently large, the mutual information MI between a first event containing m criteria and a second event containing n criteria is the frontier mutual information MI, which is the largest absolute value among the mutual information between a specific value of the first event and a specific value of the second event. front m × n × MI calculated using front It can be approximated by / log(m×n-1).

[0118] The method for identifying interdependence of the present invention may further include a confidence interval calculation step (S0106) after the mutual information calculation step (S0104) when evaluating mutual information (E0102), in which the confidence interval of the mutual information is determined. This step allows for evaluation of the accuracy of the mutual information calculated in the mutual information calculation step (S0104).

[0119] Any method known in the art can be used for the calculation. The method is not particularly limited, but for example, the distribution of the maximum values ​​of a sample extracted from an exponential distribution can be used.

[0120] There are no specific limitations on the width of the confidence interval. For example, it could be 90%, 95%, 99%, or 99.5%.

[0121] Specifically, for example, the 95% confidence interval for mutual information can be calculated using the following formula. Generally, it is known that as the values ​​of m and n increase, the confidence interval narrows, and the accuracy of mutual information improves.

[0122]

number

[0123] The interdependency determination step (S0105) may include an integration step. In this step, mutual information is integrated between one or more different contingency tables by meta-analysis.

[0124] Meta-analysis allows for the integration and analysis of multiple mutual information quantities calculated from data obtained under different conditions, such as data from different types of samples.

[0125] Various methods are known for integration using meta-analysis. For example, Rosenthal, R. (1984). Meta-analytic procedures for social research. Beverly Hills, CA: Sage describes integrating p-values ​​obtained under multiple different study conditions. overall The method for calculating this is explained. Furthermore, it is possible to compare the mutual information of one or more different contingency tables and rank them. For example, by unifying one event in all contingency tables, it is possible to identify events that have a high interdependence with that event.

[0126] Typically, meta-analysis is only applicable to metrics in the field of probability theory; therefore, it could not be applied to mutual information, which is included in information theory. However, the inventors of this invention have discovered that, despite mutual information being a metric in information theory, meta-analysis, a method of analysis in probability theory, is applicable to it, as described below. The details are described below.

[0127] As described above, the individual mutual information between a specific value of the first random variable and a specific value of the second random variable can be calculated according to the following formula.

[0128]

number

[0129] More specifically, this can be done by the following method: Let k be the selected value for the first random variable, and l be the selected value for the second random variable. Then, determine the relative frequencies in the dataset (frequency divided by the total sample size N) according to the following 2x2 contingency table.

[0130] [Table 3]

[0131] Using the relative frequencies X0 to X3 in Table 3 above, the individual mutual information (MI) is calculated using the following formula. klCalculate it.

[0132]

Number

[0133] What the inventors have found is that the individual mutual information amount MI kl has the following relationship with the Fisher's exact probability P Fkl using the total number of samples N. This approximate formula can be treated as an equation that holds when the total number of samples N is sufficiently large.

[0134] Here, when the total number of samples N is sufficiently large, for example, it means that N is 20 or more, 50 or more, 100 or more, 500 or more, 1,000 or more, 5,000 or more, 10,000 or more. Also, for example, the average number of samples per cell may be 1 or more, 5 or more, 10 or more, 50 or more, 100 or more, 500 or more, 1,000 or more, 5,000 or more.

[0135]

Number

[0136] This is shown below. The individual mutual information amount MI kl is expressed by the above formula using X0 to X3. On the other hand, the main term P Fkl of the Fisher's exact probability P main is as follows.

[0137]

Number

[0138] Here, taking the logarithm on both sides, it becomes as follows.

[0139]

Number

[0140] Using Stirling's formula, we approximate log(N!) with N×log(N)-N, and then apply the relationship X0+X1+X2+X3=1 to obtain the above approximation formula as follows.

[0141]

number

[0142] Thus, mutual information MI kl This is the total sample size N and Fisher's exact probability P. Fkl A predetermined relationship was shown between the two. Fisher exact probability P Fkl These can be integrated using meta-analysis. Therefore, as described above, by using the above formula and meta-analysis, p-values ​​obtained under multiple different study conditions can be integrated, and mutual information can be calculated based on datasets obtained under multiple different study conditions (i.e., multiple contingency tables).

[0143] The present invention further provides a method for comparing the expected values ​​of each cell in a first event and a second event.

[0144] In this method, the steps prior to the individual mutual information determination step, specifically the sample count aggregation step (S0101), the relative frequency aggregation step (S0102), and the individual mutual information determination step (S0103), are the same as the interdependence identification method described above. In addition to these three steps, this method includes an expected value calculation step (S0107), an expected value comparison step (S0108), and a cell ranking determination step (S0109), as shown in Figure 3.

[0145] The expected value calculation step (S0107) is a step in which the individual mutual information in at least one cell is converted into an expected value according to the probability distribution. The probability density function of the probability distribution used here is given by equation (IV).

number

[0146] Here, Equation (IV) is the relational expression <MI kl in the formula of number 28 showing the probability density function p(x) of x = MI kl >= MI / (m × n) is reflected.

[0147] The number of cells for which the expected value is calculated is not limited. It can be determined according to the purpose and the computer equipment used, etc. For example, it may be at least two cells, at least one column, at least one row, or all cells.

[0148] The expected value comparison step (S0108) is a step of comparing the expected values between a plurality of different cells. The cells to be compared are not particularly limited as long as they are different cells. For example, they may be different cells in the same contingency table, or cells in different contingency tables. The number of cells to be compared is also not particularly limited.

[0149] Usually, the expected value comparison step (S [0108) is performed after the expected value calculation step (S0107), but it is not necessary to perform the expected value comparison step (S0108) after calculating the expected values for all the cells of the purpose. For example, comparison with the already calculated expected values may be performed every time a new expected value is calculated.

[0150] The cell ranking determination step (S0109) is a step of determining the rank of each cell based on the magnitude of the expected value from the comparison result. Specifically, for example, ranking can be performed in descending order or ascending order of the expected value. One or more thresholds may be set and ranking may be performed by classifying the expected values into a plurality of groups.

[0151] The cell ranking determination step (S0109) can be performed simultaneously with or after the expected value comparison step (S0108).

[0152] In this specification, the various mathematical formulas shown as usable in the method may be modified in any way, as long as it does not impair the objective achieved by the method. For example, constant terms may be added to the formulas, or arbitrary coefficients or exponents may be added, or roots of the formulas may be used.

[0153] Furthermore, according to our findings, the Frontier Mutual Information Quantity (MI) is as follows: front Cells that provide mutual information can be selected using the frequency of the cell in the dataset as an indicator. Therefore, in some cases, in the individual mutual information determination step (S0103), specific cells can be selected, the individual mutual information can be determined only for those cells, and the mutual information can be calculated in the mutual information calculation step (S0104) using the frontier mutual information. This method allows for the calculation of mutual information more simply than the method of identifying interdependencies described above.

[0154] The selection of specific cells is based on the cell's frequency or simultaneous relative frequency in the dataset, using MI as an indicator. front This can be done by estimating the cells that provide the result. Multiple cells may be selected. In that case, the individual mutual information (MI) can be calculated for each cell as appropriate. kl Calculate the MI with the largest value among them. kl The cell that shows MI front You may select a cell that can provide the value. Alternatively, you can make a selection based on its deviation from the mean. For example, you can compare the simultaneous relative frequency of one cell with the simultaneous relative frequencies of other cells and select the cell whose simultaneous relative frequency is more deviated from the mean. In this case, for example, you may select based on the deviation of the simultaneous relative frequency p(x,y) from the mean, p(x,y)-1 / (m×n). In this case, for example, you can select the cell with the largest absolute value of the deviation.

[0155] Furthermore, the cell with the highest or lowest frequency or simultaneous relative frequency is MI frontSince it is expected to be a cell that gives, the selection may be made using as an index that the frequency or the simultaneous relative frequency is the maximum or the minimum. For example, both the cell with the maximum frequency and the cell with the minimum frequency are selected, and their MI kl is compared, or by comparing their deviations, the cell that can give MI front may be further selected.

[0156] In the case where N < (m × n), a cell with a frequency of 0 appears. In any method of the present invention, the cell with a frequency of 0 may be included or excluded from the calculation. When these cells are included, for example, the maximum value of MI kl may identify either or both of the cell with the maximum p(x,y) or the cell with the minimum p(x,y) (that is, the cell where p(x,y) = 0). In this case, as a result, the cell with the maximum p(x,y) is often selected as the cell that can give MI front For a sufficiently large total sample size N, it is as described above in the section on the integration step.

[0157] ]> The findings discovered by the present inventors are shown below. When the joint distribution density function p(x,y) of the random variables x and y is a uniform distribution, its mean Mean is Mean = 1 / (m × n), and the standard deviation SD is the square root of the variance 1 / (N × m × n). The ratio Ratio(XSD) of the value of MI kl when p(x,y) is Mean - X × SD to the value of MI kl when p(x,y) is Mean + X × SD is represented as follows.

[0158]

Equation

[0159] In the formula, each σ represents the following respectively.

[0160]

Equation

[0161] Then, when N is sufficiently large, the following holds true.

[0162]

number

[0163] Thus, when N is sufficiently large, mutual information MI kl The mean value of 1 / mn is almost symmetrical on both sides.

[0164] Therefore, if N is sufficiently large, mutual information MI kl Assuming that it is symmetrical around the mean value 1 / mn, p(X k ,Y l Select a combination of kl that results in a higher or lower value for MI kl This allows for the calculation of MI more efficiently. front It can lead to this.

[0165] Here, a sufficiently large total sample size N means, for example, that it is 100 or more, 500 or more, 1,000 or more, 5,000 or more, 10,000 or more, 50,000 or more, or 100,000 or more. Alternatively, for example, the average sample size per cell may be 10 or more, 50 or more, 100 or more, 1,000 or more, 5,000 or more, 10,000 or more, 50,000 or more, or 100,000 or more.

[0166] Even when calculating mutual information for events involving a vast number of criteria, the mutual information between events can be accurately calculated easily with minimal computation, and the interdependencies between subjects can be accurately identified. Therefore, since the present invention allows for large-scale analysis using the entire dataset consisting of diverse data, the method of the present invention is suitable for implementation by computer. In the present invention, any of the above methods may be performed by a calculation device including a computer, or by a computer program for executing the method.

[0167] As an apparatus, for example, a device for calculating the mutual information amount between a first event and a second event can be used.

[0168] Figure 1 is a schematic diagram showing an example configuration of the calculation device. The device includes a computer (10). The computer (10) is configured, for example, with a CPU (Central Processing Unit) (101), volatile memory (102), non-volatile memory (103), input / output control unit (104), display control unit (105), display (106) (display unit), keyboard (107), and mouse (108). The CPU (101) is a central processing unit that controls the overall operation of the calculation program.

[0169] Volatile memory (102) is a memory device such as RAM that temporarily stores the results of program calculations, etc.

[0170] Non-volatile memory (103) is a storage device that does not require external power supply to maintain its contents. Examples of non-volatile memory (103) include ROM, hard disk drives, and flash memory. For example, multiple types of non-volatile memory can be included, such as storing various data necessary for executing a program in ROM and storing the data set to be analyzed and the individual mutual information amounts of each cell in the contingency table in the hard disk drive. Programs stored in non-volatile memory (103) include, for example, a program for calculating mutual information amounts.

[0171] The input / output control unit (104) is a control unit that controls the input of data and commands from an input device and the output of various data from a processing unit. Examples of input devices that can be used in the present invention include a keyboard (107) and a mouse (108), and an example of a processing unit is a CPU (101).

[0172] The display control unit (105) is a control unit that controls the information presented to the user via the display unit. In this invention, for example, it is responsible for display control when displaying the execution screen of the aforementioned program on the display (106).

[0173] As shown in FIG. 2, the computer (10) includes, as a software configuration realized by a program, a sample number aggregating unit (121), a relative frequency aggregating unit (122), an individual mutual information amount determining unit (123), and a mutual information amount calculating unit (124).

[0174] The sample number aggregating unit (121) is a part that aggregates the sample numbers in all cells regarding a cell composed of one criterion selected from the first event and one criterion selected from the second event according to a user's input from a data set to be analyzed into an m×n frequency distribution table. For example, it is composed of a CPU (101), a volatile memory (102), a non-volatile memory (103), an input / output control unit (104), a keyboard (107), and a mouse (108). In this part, according to a user input signal (a signal instructing the start of calculation) from the keyboard (107) or the mouse (108) obtained via the input / output control unit (104), the data to be analyzed stored in the non-volatile memory (103) is aggregated into an m×n frequency distribution table and stored in the volatile memory (102).

[0175] The relative frequency aggregating unit (122) is a part that calculates the simultaneous relative frequency from the sample numbers in all cells of the frequency distribution table stored in the sample number aggregating unit (121) and aggregates it into an m×n contingency table. For example, it is composed of a CPU (101), a volatile memory (102), and a non-volatile memory (103). In this part, the simultaneous relative frequency is calculated as the ratio of the sample number corresponding to each cell to the total sample number from the frequency distribution table data stored in the volatile memory (102), aggregated into an m×n contingency table, and stored in the volatile memory (102).

[0176] The individual mutual information determination unit (123) is the part that determines the individual mutual information of each cell based on the simultaneous relative frequencies. For example, it is composed of a CPU (101), volatile memory (102), and non-volatile memory (103). In this part, the individual mutual information of each cell is determined based on the simultaneous relative frequencies from the frequency distribution table data stored in the volatile memory (102), and stored in the non-volatile memory (103). When a user requests the calculation of individual mutual information, the data of the individual mutual information of each cell is displayed on the display (106) via the display control unit (105) in a way that is visually recognizable.

[0177] The mutual information calculation unit (124) is the part that calculates the mutual information of the first event and the second event from the individual mutual information amounts. For example, it is composed of a CPU (101), volatile memory (102), and non-volatile memory (103). In this part, the mutual information amounts of the first event and the second event are calculated based on the values ​​from the individual mutual information data stored in the non-volatile memory (103), and stored in the non-volatile memory (103). When a user requests the calculation of mutual information amounts, the data of the mutual information amounts of the first event and the second event are displayed on the display (106) via the display control unit (105) in a way that is visually recognizable.

[0178] The apparatus of the present invention may include further software components. For example, it may include a confidence interval calculation unit that calculates a confidence interval for the mutual information calculated by the mutual information calculation unit (124).

[0179] By including further software components, the device can be configured to output other information. For example, by further including an interdependence determination unit that determines the interdependence between a first event and a second event from the interdependence amount calculated by the interdependence amount calculation unit (124), the device can be configured to be an interdependence determination device.

[0180] Alternatively, for example, the device can be made into an expected value calculation device by including an expected value calculation unit that converts the individual mutual information calculated by the individual mutual information determination unit (123) in at least one cell into an expected value according to a probability distribution.

[0181] For example, by further including an expected value comparison unit that compares the expected values ​​calculated by the expected value calculation unit among multiple different cells, and a cell ranking determination unit that determines the ranking of each cell based on the magnitude of the expected value from the comparison results, it can be made into an expected value comparison device.

[0182] If the necessity of a process or step needs to be selected according to the user's requirements, this instruction is given by user input from the keyboard (107) or mouse (108), and the signal is transmitted to each software part via the input / output control unit (104). The method of requesting this instruction input from the user is not particularly limited, but for example, it can be requested from the user collectively in one part or separately for each part.

[0183] The present invention further provides a program for processing the mutual information of a first event and a second event.

[0184] As shown in Figure 3, this program is configured to have the computer perform the following steps: sample count aggregation (S0101), relative frequency aggregation (S0102), and individual mutual information determination (S0103). If the user requests the identification of interdependencies, this program is configured to have the computer perform a mutual information calculation step (S0104) and an interdependency determination step (S0105).

[0185] The details of each step performed by the program of the present invention are described in detail in the methods for identifying interdependencies and comparing expected values.

[0186] This program is configured to execute a conversion step (S0110) and a calculation step (S0111) as an individual mutual information determination step (S0103), as shown in Figure 4.

[0187] Furthermore, this program is configured to either execute a direct calculation step (S0112) or a frontier mutual information selection step (S0113) and a frontier mutual information utilization step (S0114) as a mutual information calculation step (S0104), as shown in Figure 5. Here, whether or not to execute the frontier mutual information selection step (S0113) and the frontier mutual information utilization step (S0114) is selected depending on whether or not the use of frontier mutual information is required (E0103). Whether or not the use of frontier mutual information is required depends, for example, whether or not the user requests the use of frontier mutual information. Alternatively, it may be configured to be selected according to the type of data to be processed. For example, it may be configured to select the use of frontier mutual information when n and m of the data to be processed are of sufficient size.

[0188] This program is configured to cause the computer to perform an expected value calculation step (S0107) if the user requests the calculation of the expected value (E0101).

[0189] The program of the present invention may be configured to perform further steps. For example, after the expected value calculation step (S0107), it may include an expected value comparison step (S0108) for comparing expected values ​​among several different cells, and a cell ranking determination step (S0109) for determining the ranking of each cell based on the magnitude of the expected value from the comparison results.

[0190] The program of the present invention may be configured to prompt the user for further instructions. For example, it can be configured to prompt the user for instructions regarding whether or not to evaluate mutual information (E0102), and if evaluation is performed, a confidence interval calculation step (S0106) for determining the confidence interval of mutual information can be executed after the mutual information calculation step (S0104).

[0191] There are no particular limitations on the timing or frequency of requests for instructions from the user. For example, all instructions may be requested at once initially, or instructions may be requested multiple times as needed.

[0192] The program of the present invention may be configured to perform some of the above steps, as long as it processes individual mutual information or mutual information. For example, a program that includes only the sample counting step (S0101), the relative frequency counting step (S0102), and the individual mutual information determination step (S0103) can be treated as an individual mutual information calculation program.

[0193] Furthermore, for example, the program of the present invention may be configured to omit the sample counting step (S0101) depending on the type of data to be processed or according to the user's request. For example, if the sum of the frequencies of the data to be processed is 1, the sample counting step (S0101) can be omitted.

[0194] The program of the present invention can also be configured to perform all steps and then request instructions from the user, outputting only the requested information, if the equipment has sufficient performance. In this case, for example, it is also possible to perform all steps and output all information without requesting instructions from the user.

[0195] The program of the present invention may be configured to further include, as appropriate, additional steps detailed in the method for identifying interdependencies.

[0196] Computer programs may be stored on a recording medium. Examples of recording media include optical reading means such as CD-ROMs and DVDs, and information storage means such as semiconductor memory, flexible disks, and hard disks. [Examples]

[0197] Test Example 1: Ten points were randomly spotted on a 2x2 table, the frequency of each spot in each cell was tallied, and the simultaneous relative frequency was calculated for each cell. The MI was then calculated using the following formula (III) in the resulting contingency table.

[0198]

number

[0199] Furthermore, for the same contingency table, Fisher's exact probability (P F ), p-value (P) calculated using the chi-square method χ The common logarithm of ) was calculated. This trial was performed 1000 times, and the results plotted against MI and log(p) are shown in Figure 6. The results of a similar experiment using a total of 1000 points are shown in Figure 7. From Figures 6 and 7, the relationship between MI and P F It was found that there is a proportional relationship, and it was confirmed that the variability decreases as the number of points increases. On the other hand, P χ This line deviates from P FThe relationship with [the other factor] was also not constant. From this, it was found that MI is a more accurate indicator that is more consistent with Fisher's exact probability than the chi-squared method.

[0200] Test Example 2: Points were randomly spotted on an n×m table until the average number of points per cell reached 10,000, and the frequency of the spots in each cell was tallied. Figure 8-1 illustrates the case where n=m=10. In Figure 8-1A, cells with frequencies that deviate more significantly from the mean are shown in darker colors. Furthermore, after calculating the simultaneous relative frequency for each cell, the individual mutual information was calculated based on a 2×2 contingency table centered on each cell. Figure 8-2 shows the individual mutual information calculated in the example of Figure 8-1. In Figure 8-2A, cells with larger individual mutual information are shown in darker colors. It was found that the magnitude of each cell's contribution to the mutual information, which was not clear from the frequency alone, becomes clear when using the individual mutual information. Furthermore, the individual mutual information MI calculated for each cell is also shown. kl The relationship between the simultaneous relative frequencies p and each of these is shown in Figures 9 and 10. In each figure, the right panel shows the common logarithm of p log(p) and MI kl This figure shows the relationship between log(p) and MI. Figure 9A shows the case when n=m=10, Figure 9B shows the case when m=n=100, Figure 10A shows the case when m=n=1,000, and Figure 10B shows the case when m=n=10,000. From these results, log(p) and MI kl It was confirmed that there is a linear relationship between them, and that this trend becomes more pronounced as n and m increase. From this, MI kl It was confirmed that it follows an exponential distribution.

[0201] Test Example 3: The same method as in Test Example 2 was used, with m=n=47 and N=10×m×n, and the simultaneous relative frequency p and individual mutual information MI were obtained for each cell. kl The result was calculated.

[0202] Figure 11 shows p on the horizontal axis and MI on the vertical axis. klThe graph shows this relationship. The mean value of p, 1 / (m×n), is 0.45×10^(-3), and as shown in Figure 11, when p has this value, MI kl It takes a minimum value of 0. The graph is nearly symmetrical around the mean 1 / mn, and MI is found in the cell where the simultaneous relative frequency p is most skewed. kl This reached its maximum value.

[0203] Here, the variance SD^2 of the simultaneous relative frequencies is 1 / (N×m×n), so SD = 0.14×10^(-3). Here, 95% of the cells have p distributed within the range of mean ± 2SD, i.e., 0.31×10^(-3) to 0.59×10^(-3). From Figure 11, in this interval, p and MI kl It was found that the relationship between the two is almost symmetrical around the mean value.

[0204] Next, the same method was used to perform the analysis with m=n=10 and N=100. At that time, the MI of cells where p is mean -1SD was kl And the MI of cells where p is mean + 1SD kl These values ​​were approximately 6.34 × 10⁻⁵ and approximately 6.02 × 10⁻⁵, respectively, and their ratio was 1.05. Also, the MI of cells with mean -2SD was calculated. kl And the MI of the cell where p is mean + 2SD kl These values ​​were approximately 2.61 × 10⁻⁴ and 2.35 × 10⁻⁴, respectively, and their ratio was approximately 1.11. From this, it can be seen that, in this case as well, p and MI are related, as in the case described above. kl It was found that the relationship is almost symmetrical around the mean value.

[0205] Furthermore, the same method was used to perform the analysis with m=n=100 and N=1,000. MI of cells where p is mean -1SD kl And the MI of cells where p is mean + 1SD kl These values ​​were approximately 5.16 × 10⁻⁸ and 5.05 × 10⁻⁸, respectively, and their ratio was approximately 1.02. Also, the MI of cells with mean -2SD was calculated. kl (mean-2SD) and the MI of the cell where p is mean+2SD klThese values ​​were approximately 2.08 × 10⁻⁷ and 2.00 × 10⁻⁷, respectively, and their ratio was approximately 1.04.

[0206] From the above, p and MI kl It was found that the relationship is almost symmetrical around the average of 1 / (m×n).

[0207] Example 1: Data from 6,664 cancer patients was downloaded from the US Cancer Genome Atlas (TCGA) (http: / / cancergenome.nih.gov / ). This data contained information on approximately 20,000 genes.

[0208] First, mRNA expression data for the ASXL1 (ASXL Transcriptional Regulator 1) gene in each cancer patient was combined with DNA copy number and mutation data to obtain a one-dimensional random variable. Similar one-dimensional random variables were then created for approximately 20,000 other genes.

[0209] The ASXL1 gene is empirically known to encode a chromatin-binding protein involved in DNA methylation and mitochondrial function. It is also known to be involved in maintaining the suppression of homeotic genes and oncogenes in disease-related contexts.

[0210] The values ​​of the one-dimensional random variable for the ASXL1 gene and the random variable values ​​for each of the other genes were compiled into a 47 × 47 contingency table (containing a total of 47 criteria, which combine 7 criteria obtained by dividing the mRNA expression value range from Mean-3SD to Mean+3SD into 7 equal parts for the ASXL1 gene and each of the other genes, 5 criteria obtained by combining the DNA copy number value range from 0 to 4, and 2 criteria for the presence or absence of mutation). The individual relative frequencies were then calculated for each contingency table. The cell with the highest relative frequency was selected, and the individual mutual information of that cell was calculated using MI. front This MI was calculated as follows. front Using mnMIfront The total mutual information was calculated according to the formula / log(mn-1). The mutual information obtained from each contingency table was sorted in order of magnitude, and a list of genes with high mutual information with the ASXL1 gene was created. Since the values ​​of m and n were common to each contingency table, this list is MI front The list was the same as the one sorted in order of size. The top 2000 genes with the largest mutual information values ​​between them and the calculated ASXL1 gene, along with the ASXL1 gene itself, a total of 2001 genes, were subjected to canonical pathway analysis using Qiagen's Ingenuity Pathway Analysis (IPA) (registered trademark) analysis software. The results for the top 5 canonical pathways in IPA, along with the p-values ​​obtained from IPA, are shown in Table 4 below.

[0211] [Table 4]

[0212] The first standard pathway predicted by IPA was oxidative phosphorylation. Oxidative phosphorylation is one of the major functions of mitochondria. Thus, the standard pathway predicted based on the gene list created solely from gene expression level information was in remarkably good agreement with that of the empirically known ASXL1 gene.

[0213] This demonstrates that by using only a list of specific genes and genes that show high mutual information with them, the function of a gene can be identified with high accuracy. Furthermore, the same list shows that the frontier mutual information (MI) is high. front Since it was created using the above mutual information, the Frontier Mutual Information (MI) is similar to the mutual information mentioned above. front It was shown that the interdependencies of the subjects can be identified using this method.

[0214] Example 2: Similar to Example 1, a gene list was created for the UHRF1 (Ubiquitin like with PHD and Ring Finger domains 1) gene, consisting of 2000 genes with a large mutual information amount with the calculated UHRF1 gene, plus the UHRF1 gene itself, for a total of 2001 genes. This list was then analyzed using IPA® analysis software.

[0215] The UHRF1 gene is empirically known to encode a protein involved in histone H3 ubiquitination modification and DNA replication.

[0216] The top five results for the standard pathway, along with the p-values ​​obtained from IPA, are shown in Table 5 below. Note that for all items in Table 5, the total sample size N for the corresponding data is 6664, as in Example 1.

[0217] [Table 5]

[0218] The top predictors of the standard pathway by IPA included numerous items related to the cell cycle. The cell cycle is closely related to DNA replication and DNA methylation. Thus, the standard pathway predicted based on the gene list was in remarkably good agreement with that of the empirically known UHRF1 gene.

[0219] This indicates that, similar to Example 1, it is possible to accurately predict the function of other genes by using only a list of genes that have a large amount of mutual information with a specific gene.

[0220] Example 3: Similar to Example 1, a gene list was created for the CLSTN3 (Calsyntenin 3) gene consisting of 2000 genes with a large mutual information amount with the calculated CLSTN3 gene, plus the CLSTN3 gene itself, for a total of 2001 genes, and this list was analyzed using IPA (registered trademark) analysis software.

[0221] The CLSTN3 gene is empirically known to encode a protein that localizes to the postsynaptic cell membrane and is involved in synapse formation. It has also recently been reported to be involved in insulin resistance.

[0222] The top five results for the standard pathway, along with the p-values ​​obtained from IPA, are shown in Table 6 below. Note that for all items in Table 6, the total sample size N for the corresponding data is 6664, as in Example 1.

[0223] [Table 6]

[0224] Protein kinase A is a protein closely related to the reward system, memory formation, and the insulin pathway. SNARE is a protein involved in synaptic vesicle secretion. Furthermore, GNRH is a neurotransmitter. In addition to these items shown in Table 6, many other items related to neuronal signaling and insulin were found among the top predictors of the standard pathway predicted by IPA. Thus, the standard pathway predicted based on a gene list created from information that does not include signaling pathway information such as gene expression levels showed remarkably good agreement with that of the empirically known CLSTN3 gene.

[0225] This indicates that, similar to Example 1, it is possible to accurately predict the function of genes related to nerve function, in addition to genes involved in epigenetic regulation, simply by looking at a list of genes that have a large amount of mutual information with a specific gene.

Claims

1. A method for identifying the interdependence between a first event and a second event, wherein each process and step is performed by a computer, The first event includes m criteria, and the second event includes n criteria. A sample count aggregation step is performed for a cell consisting of one criterion selected from the first event and one criterion selected from the second event, and for all cells, the sample counts in all cells are aggregated into an m × n frequency distribution table. A relative frequency aggregation process is performed in which the simultaneous relative frequency is calculated from the sample size in all cells of the frequency distribution table and aggregated into an m x n contingency table. A process for determining the individual mutual information amount of each cell based on the simultaneous relative frequency for all cells, A mutual information calculation step for calculating the mutual information amounts of the first event and the second event from the individual mutual information amounts, and Interdependence determination step, which determines the interdependence between the first event and the second event based on the value of the mutual information amount. Includes, The aforementioned m and n are each integers of 2 or more, and at least one of them is 3 or more. The aforementioned simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The aforementioned individual mutual information amount determination process is: For each cell, (a) A transformation step of transforming the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the peripheral relative frequency of that cell with respect to the criterion in the first event, and the peripheral relative frequency of the criterion in the second event, and (b) A calculation step in which the strength of the interrelationship between the criteria in the first and second events is calculated as the individual interrelationship from the 2x2 contingency table using multidimensional interrelationship, Fisher's exact probability, or hypergeometric distribution. Includes, The aforementioned mutual information calculation process is: (i) From the individual mutual information quantities, the mutual information quantity is given by formula (I) [Math 1] (In the formula, MI represents the mutual information amount, MI ｋｌ (This indicates the individual mutual information amount.) This includes a direct calculation step that calculates based on, or (ii) A frontier mutual information selection step in which the individual mutual information quantities are compared with each other and the individual mutual information quantity with the largest absolute value is selected as the frontier mutual information quantity, and The process includes a frontier mutual information utilization step that calculates the mutual information based on the aforementioned frontier mutual information, The calculation of the mutual information in the aforementioned frontier mutual information utilization step is given by equation (II). [Math 2] (In the formula, MI represents the mutual information amount, MI ｆｒｏｎｔ (This indicates the mutual information of the frontiers.) This is done by The aforementioned method.

2. The method according to claim 1, wherein the calculation using the multidimensional mutual information is performed based on the following formula (III). [Math 3] (In the formula, MI ｋｌ This represents the individual mutual information quantity of a cell consisting of the k-th criterion of the first event and the l-th criterion of the second event. X ｋ′ This indicates the k'-th criterion of the first event in the 2x2 contingency table, Y ｌ′ This indicates the l'-th criterion of the second event in the 2x2 contingency table, p(X ｋ′ , Y ｌ′ ) indicates the simultaneous relative frequency of cells consisting of reference X ｋ′ and reference Y ｌ′ , and p(X ｋ′ ) indicates the marginal relative frequency for reference X ｋ′ . p(Y ｌ′ ) is the reference Y ｌ′ (This shows the relative frequency of the margins.)

3. The method according to claim 1 or 2, wherein at least one of m and n is 100 or more.

4. The method according to any one of claims 1 to 3, wherein the total number of samples is 1,000 or more.

5. After the mutual information calculation step, Confidence interval calculation step for determining the confidence interval of the mutual information amount The method according to any one of claims 1 to 4, further comprising:

6. The interdependence determining step The method according to any one of claims 1 to 5, comprising an integration step of integrating the mutual information between one or more different contingency tables by meta-analysis.

7. A method for comparing the expected values ​​of each cell in a first event and a second event, wherein each process and step is performed by a computer, The first event includes m criteria, and the second event includes n criteria. A sample count aggregation step is performed for a cell consisting of one criterion selected from the first event and one criterion selected from the second event, and for all cells, the sample counts in all cells are aggregated into an m × n frequency distribution table. A relative frequency aggregation process is performed in which the simultaneous relative frequency is calculated from the sample size in all cells of the frequency distribution table and aggregated into an m x n contingency table. A process for determining the individual mutual information amount of each cell based on the simultaneous relative frequency for all cells, and An expected value calculation step in which, in at least one of the cells, the individual mutual information amounts are converted into expected values ​​according to a probability distribution. An expected value comparison step of comparing the expected values ​​between multiple different cells, and A cell ranking determination process in which the rank of each cell is determined based on the magnitude of the expected value from the comparison results. Includes, The aforementioned m and n are each integers of 2 or more, and at least one of them is 3 or more. The aforementioned simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The aforementioned individual mutual information amount determination process is: For each cell, (a) A transformation step of transforming the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the peripheral relative frequency of that cell with respect to the criterion in the first event, and the peripheral relative frequency of the criterion in the second event, and (b) A calculation step in which the strength of the interrelationship between the criteria in the first and second events is calculated as the individual interrelationship from the 2x2 contingency table using multidimensional interrelationship, Fisher's exact probability, or hypergeometric distribution. Includes, The probability density function of the aforementioned probability distribution is given by equation (IV). [Math 4] (In the formula, p(x) represents the expected value when the individual mutual information quantity is x, <MI ｋｌ > indicates the average value of the individual mutual information amounts. Represented by, The aforementioned method.

8. A device for calculating the mutual information amount of a first event and a second event, The first event includes m criteria, and the second event includes n criteria. A sample count aggregation unit that aggregates the sample counts in all cells into an m × n frequency distribution table with respect to a cell consisting of one criterion selected from the first event and one criterion selected from the second event. A relative frequency aggregation unit calculates simultaneous relative frequencies from the sample size in all cells of the frequency distribution table and aggregates them into an m x n contingency table. In all cells, an individual mutual information determination unit determines the individual mutual information amount of each cell based on the simultaneous relative frequency, and Mutual Information Calculation Unit that calculates the mutual information amounts of the first event and the second event from the individual mutual information amounts. Includes, The aforementioned m and n are each integers of 2 or more, and at least one of them is 3 or more. The aforementioned simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The determination by the individual mutual information determination unit is: For each cell, (a) Based on the simultaneous relative frequency of one cell, the peripheral relative frequency of that cell with respect to the criterion in the first event, and the peripheral relative frequency of the criterion in the second event, the m × n contingency table is transformed into a 2 × 2 contingency table containing binary data for the criterion in each of the first and second events. (b) Using the 2x2 contingency table, the strength of the interrelationship between the criteria in the first and second events is calculated as the individual interrelationship using multidimensional interrelationship, Fisher's exact probability, or hypergeometric distribution. This is done by The calculation performed by the aforementioned mutual information calculation unit is as follows: (i) From the individual mutual information quantities, the mutual information quantity is given by formula (I) [Math 5] (In the formula, MI represents the mutual information amount, MI ｋｌ (This indicates the individual mutual information amount.) This includes calculating based on, or (ii) Comparing the individual mutual information quantities with each other and selecting the individual mutual information quantity with the largest absolute value as the frontier mutual information quantity, and This includes calculating the mutual information amounts in the first and second events based on the aforementioned frontier mutual information amounts, The calculation of the mutual information is given by equation (II). [Math 6] (In the formula, MI represents the mutual information amount, MI ｆｒｏｎｔ (This indicates the mutual information of the frontiers.) This is done by The aforementioned device.

9. A program for processing the mutual information of a first event and a second event, The first event includes m criteria, and the second event includes n criteria. On the computer, A sample count aggregation step is performed for a cell consisting of one criterion selected from the first event and one criterion selected from the second event, and for all cells, the sample counts in all cells are aggregated into an m × n frequency distribution table. A relative frequency aggregation process is performed in which the simultaneous relative frequency is calculated from the sample size in all cells of the frequency distribution table and aggregated into an m x n contingency table. A process for determining the individual mutual information amount of each cell based on the simultaneous relative frequency for all cells, and When calculating the expected value, In at least one of the cells, an expected value calculation step is performed to convert the individual mutual information quantities into expected values ​​according to a probability distribution. If the expected value is not calculated, A mutual information calculation step for calculating the mutual information amounts of the first event and the second event from the individual mutual information amounts, and A dependency determination step is performed to determine the interdependence between the first event and the second event based on the value of the mutual information amount. Configured to execute, The aforementioned m and n are each integers of 2 or more, and at least one of them is 3 or more. The aforementioned simultaneous relative frequency is the ratio of the number of samples corresponding to a certain cell to the total number of samples. The aforementioned individual mutual information amount determination process is: For each cell, (a) A transformation step of transforming the m × n contingency table into a 2 × 2 contingency table containing binary data for the criteria in the first and second events, based on the simultaneous relative frequency of one cell, the peripheral relative frequency of that cell with respect to the criterion in the first event, and the peripheral relative frequency of the criterion in the second event, and (b) A calculation step in which the strength of the interrelationship between the criteria in the first and second events is calculated as the individual interrelationship from the 2x2 contingency table using multidimensional interrelationship, Fisher's exact probability, or hypergeometric distribution. Includes, The aforementioned mutual information calculation process is: (i) From the individual mutual information quantities, the mutual information quantity is given by formula (I) [Number 7] (In the formula, MI represents the mutual information amount, MI ｋｌ (This indicates the individual mutual information amount.) This includes a direct calculation step that calculates based on, or (ii) A frontier mutual information selection step in which the individual mutual information quantities are compared with each other and the individual mutual information quantity with the largest absolute value is selected as the frontier mutual information quantity, and The process includes a frontier mutual information utilization step that calculates the mutual information based on the aforementioned frontier mutual information, The calculation of the mutual information in the aforementioned frontier mutual information utilization step is given by equation (II). [Number 8] (In the formula, MI represents the mutual information amount, MI ｆｒｏｎｔ (This indicates the mutual information of the frontiers.) It was done by The probability density function of the aforementioned probability distribution is given by equation (IV). [Number 9] (In the formula, p(x) represents the expected value when the individual mutual information quantity is x, <MI ｋｌ > indicates the average value of the individual mutual information amounts. Represented by, The aforementioned program.

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