Program, information processing device, and data analysis method

Abstract

It provides statistically reliable estimates of differences in the relationships between a set of variables between two different data sets. [Solution] A receiving means 111 receives operations from a user via an operation unit 14. An acquisition means 112 acquires journal data and stores it in a journal DB 121. A preprocessing means 113 reads the journal data from the journal DB 121, performs preprocessing, generates a matrix that is an accounting dataset, and stores it in a matrix DB 122. An estimation means 114 reads two different accounting datasets from the matrix DB 122, and estimates a first precision matrix corresponding to the first dataset and a second precision matrix corresponding to the second dataset based on the read first dataset and second dataset so as to minimize a predetermined information criterion.

Description

[Technical Field]

[0001] The present invention relates to a method for analyzing the homogeneity of two data sets. [Background technology]

[0002] Audit work places a heavy burden on people because it requires detecting fraudulent records and abnormal transactions from a vast amount of complex accounting information. Therefore, attempts are being made to utilize artificial intelligence (AI) in this audit work. The use of AI in audit work is expected not only to reduce the burden on people through automation, but also to improve detection capabilities, such as finding things that would be difficult to find manually.

[0003] Patent Document 1 describes an accounting information processing device that uses training data to perform regression analysis using a graphical lasso while discretely changing an L1 regularization term to obtain a trained model, and then uses this trained model to calculate the degree of anomaly of records contained in an unknown data set and detect records that are highly likely to be fraudulent. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 6667865 Summary of the Invention [Problem to be solved by the invention]

[0005] However, the technology described in Patent Document 1 analyzes the relationships between variables in a single data set. On the other hand, even if the accounting information of the same entity is analyzed over different time periods, there is a possibility that changes in the business environment, accounting policies, etc. have occurred. Objectively evaluating the homogeneity of data between such time periods and efficiently identifying the locations (change points) where structural changes have occurred can be important in audits. However, the technology described in Patent Document 1 has difficulty in supporting period comparison analysis using such two data sets.

[0006] Furthermore, it has been pointed out that the parameter estimation process for the multivariate normal distribution, which introduces an L1 regularization term into the objective function employed in the method described in Patent Document 1, is not theoretically guaranteed to have good statistical properties, and therefore there may remain issues with the statistical reliability of the estimation results obtained.

[0007] The present invention has been made in consideration of the above circumstances, and one of its objects is to provide a program, an information processing device, and a data analysis method that perform statistically reliable estimation of differences in the relationships between groups of variables between two different data sets. [Means for solving the problem]

[0008] In one aspect, the present invention provides a program that causes a computer to execute: an acquisition step of acquiring a first dataset and a second dataset different from the first dataset; an estimation step of estimating the first precision matrix and the second precision matrix based on the first dataset and the second dataset acquired in the acquisition step, so as to minimize an information criterion defined based on: a likelihood term based on a first likelihood for the first dataset and a second likelihood for the second dataset, and a penalty term that evaluates sparsity indicated by the number of non-zero elements in at least one of a first precision matrix in the first dataset, a second precision matrix in the second dataset, and a difference between the first precision matrix and the second precision matrix; and an output step of outputting information indicating a difference in relationships between sets of variables between the first dataset and the second dataset, based on the first precision matrix and the second precision matrix estimated in the estimation step. [Effects of the Invention]

[0009] The present invention allows for statistically reliable estimation of differences in the relationships between sets of variables between two different data sets. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram showing an example of the configuration of an information processing device 1. [Figure 2] FIG. 10 is a diagram showing an example of a journal entry DB 121. [Figure 3] FIG. 2 is a diagram showing an example of the configuration of a matrix DB 122. [Figure 4] FIG. 2 is a diagram showing an example of the functional configuration of the information processing device 1. [Figure 5] FIG. 10 is a flowchart showing an example of the flow of pre-processing operations. [Figure 6] FIG. 10 is a flowchart showing an example of the flow of an operation for outputting difference information. [Figure 7] FIG. 10 is a flowchart showing an example of the operation flow of an estimation process. [Figure 8] An example of output that shows the differences in the relationships between groups of variables using a graph structure. DETAILED DESCRIPTION OF THE INVENTION

[0011] <Embodiment> <Configuration of information processing device> Fig. 1 is a diagram showing an example of the configuration of an information processing device 1. The information processing device 1 shown in Fig. 1 includes a processor 11, a memory 12, a communication unit 13, an operation unit 14, and a display unit 15. These components are connected to each other via, for example, a bus so that they can communicate with each other.

[0012] The processor 11 reads and executes a program stored in the memory 12 to control each part of the information processing device 1. The processor 11 is, for example, a CPU (Central Processing Unit).

[0013] The operation unit 14 is equipped with operation buttons, a keyboard, a touch panel, a mouse, and other operators for issuing various instructions, and receives operations and sends signals according to the operation content to the processor 11. These operations include, for example, pressing a button or making a gesture on a touch panel.

[0014] The display unit 15 has a display screen such as a liquid crystal display, and displays images under the control of the processor 11. A transparent touch panel of the operation unit 14 may be placed on top of the display screen.

[0015] The communication unit 13 is a communication circuit that connects the information processing device 1 to an external device or the like so that the information processing device 1 can communicate with the external device or the like via a wired or wireless connection.

[0016] The memory 12 is a storage means for storing an operating system, various programs, data, etc. that are loaded into the processor 11. The memory 12 includes a RAM (Random Access Memory) and a ROM (Read Only Memory). The memory 12 may also include a solid state drive, a hard disk drive, etc. The memory 12 also stores a journalization DB 121 and a matrix DB 122.

[0017] <Journal entry DB configuration> 2 is a diagram showing an example of the journalization DB 121. The journalization DB 121 is a database that stores journalization information related to a plurality of accounting transactions. The journalization DB 121 shown in FIG.

[0018] The journal entry ID list 1211 is a list that stores journal entry IDs for uniquely identifying individual journal entries in association with information about the journal entries. Each journal entry ID listed in the journal entry ID list 1211 is associated with one journal entry table 1212.

[0019] The journal table 1212 is a table or record that stores specific journal data corresponding to a journal ID. The journal data includes essential fields, such as a debit account title, a debit amount, a credit account title, and a credit amount. Furthermore, the journal table 1212 may include fields indicating information indicating the transaction subject, such as a department code, a division code, or a person in charge code; information indicating the transaction counterparty, such as a customer code or a supplier code; and additional information, such as a summary. The journal table 1212 may also include fields or data that distinguish whether the account titles "accounts receivable" and "accounts payable" are generated through normal transactions or through the purchase and sale of fixed assets or securities. The memory areas associated with these fields store codes indicating account titles, character strings indicating names, and numerical values ​​indicating amounts. The journal DB 121 stores journal data. However, if the information processing device 1 analyzes accounting data (accounting data), it may have a database that stores accounting data instead of the journal DB 121. Here, accounting data refers to all data that records the economic activities of a company or organization, and specifically refers to data that forms the basis for creating financial statements, such as sales, purchases, expenses, assets, liabilities, and capital.

[0020] <Matrix DB configuration> 3 is a diagram showing an example of the configuration of the matrix DB 122. The matrix DB 122 is a database that stores matrix-format data (also referred to as an "accounting dataset") generated by the preprocessing means 113, which will be described later, based on the journal entry data stored in the journal entry DB 121. In this matrix-format data, each column corresponds to a variable to be analyzed, such as an account item, and each row corresponds to an individual sample, such as an observed value or aggregated value for a specific period or transaction unit.

[0021] The matrix DB 122 shown in Fig. 3 has a matrix ID list 1221 and a matrix element value group 1222. The matrix ID list 1221 is a list that manages matrix IDs for uniquely identifying matrices that indicate each accounting data set. Examples of matrix IDs are "X1" and "X2." Each matrix ID listed in the matrix ID list 1221 is associated with one matrix element value group 1222.

[0022] The matrix element value group 1222 is an area that stores the values ​​of each element (component) of matrix data corresponding to a matrix ID in association with its row index and column index. For example, the matrix element value group 1222 shown in Fig. 3 stores each component value of an accounting data set (size n1 x d) corresponding to the matrix ID "X1".

[0023] The matrix DB 122 may be secured as a specific area in the memory 12, or may be implemented as a table on a relational database management system (RDBMS).

[0024] Furthermore, the matrix DB 122 may be stored as a file in the memory 12 or an external storage device in a specific file format such as CSV format or Parquet format.

[0025] Furthermore, the matrix DB 122 may store a plurality of accounting data sets as independent tables or files, or may store them together in a single table or the like together with information indicating the period information and the data set classification.

[0026] <Functional configuration of information processing device> Fig. 4 is a diagram illustrating an example of the functional configuration of the information processing device 1. The processor 11 of the information processing device 1 illustrated in Fig. 4 executes a program stored in the memory 12, thereby functioning as a receiving means 111, an acquiring means 112, a preprocessing means 113, an estimating means 114, and an output means 115.

[0027] The accepting means 111 accepts operations from the user via the operation unit 14. These operations include, for example, an operation to instruct input of journal data, an operation to instruct execution of preprocessing to generate a matrix, an operation to instruct selection of matrices representing two different accounting data sets and estimation of the difference in the relationship between the sets of variables between the two, an operation to instruct output of the estimation results, etc.

[0028] For example, when the reception means 111 receives an operation from a user via the operation unit 14 instructing the input of journal data, the acquisition means 112 acquires the input journal data and stores it in the journal DB 121. In addition, for example, when the reception means 111 receives an operation specifying a source from which to obtain journal data, the acquisition means 112 acquires journal data from the specified source via the communication unit 13 and stores it in the journal DB 121.

[0029] For example, when the reception means 111 receives an operation from the user via the operation unit 14 to instruct execution of preprocessing for generating a matrix, the preprocessing means 113 reads journal data from the journalization DB 121, executes the instructed preprocessing, and generates a matrix that is an accounting data set. Then, the preprocessing means 113 stores the generated matrix in the matrix DB 122.

[0030] For example, when the reception means 111 receives from the user via the operation unit 14 a selection of a matrix indicating two different accounting data sets (a first data set and a second data set) and an instruction to estimate the difference in the relationship between them, the estimation means 114 reads out the two corresponding accounting data sets from the matrix DB 122.

[0031] Then, based on the read first and second data sets, the estimation means 114 estimates a first precision matrix corresponding to the first data set and a second precision matrix corresponding to the second data set so as to minimize a predetermined information criterion. Details of this estimation process will be described later. Note that the first and second data sets described above are both matrices generated by performing preprocessing on the journal data read from the journalization DB 121. In other words, these two data sets whose precision matrices are estimated by the estimation means 114 are examples of the first and second data sets generated based on journal data.

[0032] For example, when the receiving means 111 receives an operation from a user instructing output of an estimation result, the output means 115 generates information indicating differences in the relationships between the first dataset and the second dataset based on the first precision matrix and the second precision matrix estimated by the estimation means 114. This information is, for example, a list of variable pairs that have changed over different periods, or a graph structure indicating structural changes (differences) in the relationships. Then, the output means 115 outputs the generated information, for example, by displaying it on the display unit 15 or transmitting it to an external device via the communication unit 13.

[0033] Therefore, the information processing device 1 shown in FIG. 4 is an example of an information processing device having: an acquisition means for acquiring a first dataset and a second dataset different from the first dataset; an estimation means for estimating the first precision matrix and the second precision matrix based on the first dataset and the second dataset acquired by the acquisition means so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first dataset and a second likelihood for the second dataset, and a penalty term evaluating sparsity indicated by the number of non-zero elements in at least one of the first precision matrix in the first dataset, the second precision matrix in the second dataset, and the difference between the first precision matrix and the second precision matrix; and an output means for outputting information indicating a difference in the relationship between the sets of variables between the first dataset and the second dataset based on the first precision matrix and the second precision matrix estimated by the estimation means.

[0034] <Estimation processing algorithm> The algorithm of the estimation process executed by the estimation means 114 in this embodiment will be described.

[0035] Equation (1) shows that the accounting dataset follows a multivariate normal distribution determined by the precision matrix Λ. Note that in this example, the accounting dataset is pre-centered through preprocessing. In other words, the accounting dataset is pre-processed to convert each sample into a deviation from the sample mean. Since the accounting dataset is assumed to follow a multivariate normal distribution in which the population mean vector is approximated by the sample mean vector, the population mean vector in equation (1) is a zero vector.

[0036]

number

[0037] In this formula, x is a sample vector corresponding to one row of the dataset X, and if X has d variables, the number of dimensions is d.

[0038] Equation (2) is the amount of information Rules The objective function EIC based on the standard is shown below. Rules The standard is a method for evaluating the quality and validity of a statistical model. Rules It is defined based on, for example, AIC (Akaike Information Criterion), BIC (Bayes Information Criterion), etc. Rules The information criterion is defined based on either AIC or BIC. Rules The information criterion is an example of an information criterion defined based on the Akaike information criterion or the Bayes information criterion. Rules The criteria are not limited to the AIC and BIC mentioned above, but also include other information criteria such as DIC (Deviance Information Criterion). Rules It may be standard.

[0039] Objective function E IC is the first precision matrix Λ corresponding to the first data set X1(1) and Λ, the second precision matrix corresponding to the second data set X2. (2) It is a function with variables L and R. L is the likelihood term, and R is the penalty term. The likelihood term is an index that shows how well the model fits the data. The penalty term is a term that penalizes the complexity of the model, such as the number of parameters and degrees of freedom.

[0040]

number

[0041] Equation (3) shows the likelihood term. The likelihood term is a term obtained by multiplying the sum of the log-likelihood functions of the first data set X1 and the second data set X2 by a negative coefficient (here, −1). Note that in equation (3), p(X k |Λ (k) ) denotes the first likelihood for the first data set when k=1, and the second likelihood for the second data set when k=2. Thus, this likelihood term is an example of a likelihood term based on the first likelihood for the first data set and the second likelihood for the second data set.

[0042]

number

[0043] Equation (4) and equation (5) described later show examples of specific forms of the penalty term. The penalty term is expressed as a first precision matrix Λ (1) The sparsity of the second precision matrix Λ (2) The penalty term is configured as a term that evaluates at least one of the sparsity of the first precision matrix in the first data set, the sparsity related to the difference between the first precision matrix and the second precision matrix. Here, the sparsity is evaluated based on the number of non-zero elements (L0 norm). That is, this penalty term is an example of a penalty term that evaluates the sparsity indicated by the number of non-zero elements of at least one of the first precision matrix in the first data set, the second precision matrix in the second data set, and the difference between the first precision matrix and the second precision matrix.

[0044] For example, R, which is an example of the penalty term shown in equation (4), A is that the first term is Λ (1) The L0 norm of the second term is Λ (1) and Λ (2) and Λ (2) The Hadamard product is the L0 norm of the Hadamard product of two matrices of the same size. The Hadamard product is a matrix product determined by multiplying each matrix element by element. This form of penalty term is an example of a penalty term that includes a first penalty term based on the number of nonzero elements in the first precision matrix, and a second penalty term based on the number of nonzero elements in the Hadamard product of the difference between the first and second precision matrices and the second precision matrix.

[0045] Here, λ1 and λ in equation (4) d2 , and λ1, λ2, λ in equation (5) described later d is a positive constant that adjusts the weight of each penalty element. These are determined depending on whether AIC or BIC is used as the information criterion, and the magnitude of the entire penalty term is adjusted. For example, if BIC is used as the information criterion, n, which is the sample size of the kth dataset, is used. k the logarithm of, i.e., log n k λ d2 is set to

[0046]

number

[0047] Another form of the penalty term is R B It can also be configured as a weighted sum of three terms: the L0 norm of the first precision matrix, the L0 norm of the second precision matrix, and the L0 norm of the difference matrix, as shown below. This form of penalty term is an example of a penalty term that includes a first penalty term based on the number of non-zero elements in the first precision matrix, a second penalty term based on the number of non-zero elements in the second precision matrix, and a third penalty term based on the number of non-zero elements in the difference between the first precision matrix and the second precision matrix.

[0048]

number

[0049] Equation (6) shows the log-likelihood function for calculating the likelihood term mentioned above. This log-likelihood function is the log-likelihood function of the multivariate normal distribution. The log-likelihood function of the k-th dataset is given by its precision matrix Λ (k) From the logarithmic determinant of S (k) Λ (k) is proportional to the value of the trace of S (k) is the sample covariance matrix of the kth dataset.

[0050]

number

[0051] Equation (7) shows an approximation of the number of non-zero elements. The penalty term mentioned above evaluates the sparsity of the precision matrix based on the number of non-zero elements. Therefore, the information amount including this penalty term is Rules The problem of minimizing the criterion is a combinatorial optimization problem, which is difficult in terms of calculation time and numerical handling. Therefore, in order to ease this combinatorial optimization problem into a continuous optimization problem, the information processing device 1 introduces a proxy function that substitutes for the penalty term into the estimation processing algorithm.

[0052]

number

[0053] ||z||0 in equation (7) is called the quasi-norm or L0 norm and indicates the number of nonzero elements in z. If z is a matrix or vector, ||z||0 is the total number of nonzero elements in z. Furthermore, if z is a scalar, ||z||0 is 0 when z = 0 and 1 when z ≠ 0. For simplicity, equation (7) is explained assuming z is a scalar. In this case, the L0 norm of z, which is the left-hand side, is approximated by the right-hand side. The right-hand side consists of the absolute value of z and a small positive constant η (η > 0). This approximation is justified by the fact that the right-hand side is 0 when z = 0, rapidly approaches 1 as the absolute value of z increases, and is upwardly convex with respect to the absolute value of z. The fact that the right-hand side is upwardly convex can be shown by the fact that the second derivative of the function g(|z|) representing the right-hand side is negative throughout the entire domain.

[0054] Equation (8) shows an inequality that gives an upper bound to the approximate value of the number of non-zero elements. The fact that the above-mentioned g(|z|) is upward convex means that the tangent at any point on it is greater than or equal to this function over the entire domain. In this equation, the left-hand side represents the above function, and the right-hand side represents the tangent to that function at any point |z0|, and this indicates that the right-hand side is always greater than or equal to the left-hand side.

[0055]

number

[0056] Equation (9) is an inequality obtained by rearranging equation (8). Here, the right-hand side of equation (8), which indicates the tangent line, is equal to the proxy function q(z|z0) of equation (9). Therefore, ||z||0 can be constrained from above by the proxy function q(z|z0), which is determined by the variable z when z0 is taken as an estimated value.

[0057]

number

[0058] Equation (10) is an extension of the inequality in equation (9) to the precision matrix Λ. In equation (10), |Λ uv| is the absolute value of the element in the u-th row and v-th column of the precision matrix Λ, η is a small positive definite number, and Λ (t) uv is the estimated value of Λ in each iteration. That is, when the right side shown in Equation (10) is used for the above-mentioned penalty term, the information processing device 1 can approximate the precision matrix Λ to an optimal value in the iterative process. Here, the right side shown in Equation (10) is an example of a surrogate function that is constructed based on the estimated value of the precision matrix in the iteration and takes a value greater than or equal to the penalty term.

[0059] By replacing the penalty term of the information amount Rules standard adopted in the objective function with a surrogate function, the information processing device 1 will solve a continuous optimization problem instead of a combinatorial optimization problem. That is, this process of estimating the precision matrix performs the process of minimizing a surrogate objective function in which the penalty term is replaced with a surrogate function that takes a value greater than or equal to it, so it becomes easier to execute compared to the case where no replacement is made.

[0060]

Number

[0061] Note that Λ is a symmetric matrix and the diagonal elements are positive. Therefore, to evaluate the sparsity of this precision matrix Λ, it is sufficient to sum only the number of non-zero elements of the strictly upper triangular components excluding the diagonal components from the upper triangular components. Therefore, Equation (10) limits the components to be counted to the strictly upper triangular components (1 ≤ u < v ≤ d). Of course, since Λ is a symmetric matrix, the components to be counted may be limited to the strictly lower triangular components (1 ≤ v < u ≤ d) excluding the diagonal components from the lower triangular components.

[0062] The precision matrix estimated in this way indicates that when its component is 0, the corresponding two variables are statistically independent. For example, Λ of the precision matrix estimated for the dataset X uv ​​​​​​​When u≠v is 0, two variables x u and x v are statistically independent.

[0063] <Operation of information processing device> <Journal data retrieval behavior> 5 is a flow diagram showing an example of the operation flow of acquiring journal data. The processor 11 of the information processing device 1 determines whether or not an instruction to acquire journal data or to execute preprocessing has been received from the user (step S001). While it is determined that neither of these instructions has been received (step S001; NO), the processor 11 continues this determination process.

[0064] When it is determined that an instruction to obtain journal data has been received (step S001; YES), the processor 11 obtains the journal data in accordance with the instruction from a user's operation on the operation unit 14 or from an external device via the communication unit 13 (step S002).

[0065] Furthermore, when the processor 11 determines in step S001 that an instruction to execute preprocessing has been received, the processor 11 reads out journal data from the journal DB 121 in accordance with the instruction and generates matrices that are accounting data sets.

[0066] If an instruction to execute preprocessing has been received together with an instruction to acquire journal data, processor 11 acquires the journal data and executes preprocessing based on the journal data to generate matrices that are accounting data sets (step S003). Processor 11 then stores the generated matrices in memory 12 (step S004).

[0067] <Difference information output behavior> 6 is a flow diagram showing an example of the operation flow for outputting difference information. Processor 11 determines whether or not an instruction to output difference information has been received from the user (step S101). While it is determined that an instruction to output difference information has not been received (step S101; NO), processor 11 continues this determination process.

[0068] When it is determined that an instruction to output difference information has been received (step S101; YES), the processor 11 acquires two accounting data sets (matrices) stored in the memory 12 in accordance with the instruction (step S102). These two accounting data sets are a first data set corresponding to a first period and a second data set corresponding to a second period different from the first period. Therefore, this process is an example of an acquisition step for acquiring a first data set and a second data set different from the first data set. Here, examples of the first and second periods include last month and this month, or previous and current periods. Examples of periods include a week, month, quarter, or year. These two periods may be consecutive or non-consecutive. For example, the two periods may be the current quarter and the same quarter last year.

[0069] Then, the processor 11 estimates a first precision matrix from a first data set corresponding to the first period, and estimates a second precision matrix from a second data set corresponding to a second period different from the first period (step S200). In the example shown in Fig. 6, these two estimation processes are performed in parallel. The details of the estimation processes will be described later.

[0070] When both of the two estimation processes are completed, the processor 11 compares the patterns related to the sparsity of the precision matrices estimated in each process and detects points where the relationship between the variable groups between the first data set and the second data set has changed, or variable pairs that have changed (step S103). Note that, if the comparison shows that the patterns related to the sparsity of the precision matrices corresponding to the two periods are substantially the same, the processor 11 determines that the accounting datasets for these two periods are substantially the same.

[0071] Then, the processor 11 outputs information indicating the change (difference) in the relationships between the variable sets between the two accounting data sets to the display unit 15 or the like (step S104). Therefore, this process is an example of an output step of outputting information indicating the difference in the relationships between the variable sets between the first data set and the second data set based on the estimated first precision matrix and second precision matrix.

[0072] Processor 11 may output a list of variable pairs with differences as information indicating differences in the relationships between the variable sets between the two accounting data sets. In this case, the above process of outputting the relationship differences is an example of an output step of outputting a list of variable pairs with differences in relationship.

[0073] Processor 11 may output the difference in the relationships between the variable sets between the two accounting data sets as a graph structure as information indicating the difference in the relationships. In this case, the above process of outputting the relationship difference is an example of an output step of outputting the relationships between the variable sets or the difference in the relationships as a graph structure.

[0074] <Operation of estimation process> 7 is a flow diagram showing an example of the operation flow of the estimation process. The processor 11 initializes variables to be subjected to the estimation process, i.e., a precision matrix (step S201). The precision matrix is ​​initialized, for example, by substituting a unit matrix of a d-th order square matrix.

[0075] Next, processor 11 searches for the optimum value of the precision matrix using the coordinate descent method. That is, processor 11 selects one of the variables that are elements of these precision matrices (step S202), and while keeping the other variables fixed, varies the selected variable, evaluating a proxy objective function that substitutes for the above-mentioned objective function each time. Then, processor 11 updates the selected variable so that the proxy objective function is optimized (step S203).

[0076] When there is no change in the proxy objective function, processor 11 stops updating the one variable described above and determines whether all variables have been updated (step S204). If it is determined that all variables have not been updated (step S204; NO), processor 11 returns the process to step S202 and selects an unupdated variable.

[0077] On the other hand, if it is determined that all variables have been updated (step S204; YES), processor 11 determines whether the change in the proxy objective function has fallen within a certain range compared to before the completion of one cycle of updating all variables, that is, whether the proxy objective function has converged (step S205). If it is determined that the proxy objective function has not converged (step S205; NO), processor 11 resets, for example, the variable selection history and returns the process to step 202. This causes processor 11 to start the next cycle of updating all variables.

[0078] On the other hand, if it is determined that convergence has occurred (step S205; YES), the processor 11 stores the estimation result at that time, that is, the precision matrix, in the memory 12 (step S206), and ends the process.

[0079] Therefore, the operation of this estimation process is an example of an estimation step in which the first precision matrix and the second precision matrix are estimated so as to minimize an information criterion defined based on a likelihood term and a penalty term.

[0080] As described above, the operation of this estimation process involves iteratively minimizing a surrogate objective function in which a part of the objective function is replaced with a surrogate function. That is, this process is an example of an estimation step in which estimation is performed by iteratively minimizing a surrogate objective function in which a penalty term included in the information criterion is replaced with a surrogate function that is configured based on estimated values ​​of the first precision matrix and the second precision matrix in each iteration and takes a value equal to or greater than the penalty term.

[0081] Furthermore, the operation of the estimation process described in this embodiment employs the coordinate descent method as an optimization algorithm, and therefore this process is an example of a process for minimizing a surrogate objective function that is performed using the coordinate descent method.

[0082] <Graph structure output example> Figure 8 is an example of output that expresses differences in the relationships between a group of variables using a graph structure. Points P0 to P9 shown in Figure 8 are 10 variables in accounting information, and correspond to account items such as "accounts receivable," "sales," "purchases," "accounts payable," "uncollected income," and "accounts payable." Note that the number of account items is not limited to the example shown in Figure 8 and is generally greater than this, but for the sake of explanation, the number shown in Figure 8 is 10. The lines connecting these points are then drawn based on the components in the estimated precision matrix.

[0083] The graph structure shown in Figure 8(a) indicates, for example, the independence between variables in a first data set observed in a first period. In this graph structure, the number of connections between each point and other points (hereinafter also referred to as the number of connections) is 6 for point P0, 3 for point P4, 5 for point P5, 4 for point P6, 2 for point P7, 4 for point P8, and 5 for point P9, and all other points (i.e., points P1, P2, and P3) are 1. Two points connected to each other by a line indicate that the two variables they represent are related. Therefore, points not connected by a line are conditionally independent.

[0084] On the other hand, the graph structure shown in FIG. 8(b) indicates, for example, the independence between variables in a second data set observed in a second period different from the first period. In this graph structure, the number of connections at point P0 decreases by one because it changes from six to five. Furthermore, the number of connections at point P4 increases by two because it changes from three to five. As a result, when moving from the first period to the second period, the lines connecting points P0 and P7 and points P5 and P8 disappear, while lines connecting points P4 and P6 and points P4 and P9 are generated. In this way, the information processing device 1 represents the differences in the relationships between variable sets in two different periods using points and lines. Therefore, a user viewing this can understand the creation and disappearance of variable pairs. The information processing device 1 may change the thickness or shape of the lines connecting points depending on the strength of the relationship, for example, the magnitude of the absolute values ​​of corresponding elements in the precision matrix.

[0085] Through the above-described operations, the information processing device 1 can make theoretically and practically valid estimates of the differences in the relationships between groups of variables between accounting data sets corresponding to two different periods. In particular, the information processing device 1 can estimate the differences in the relationships between groups of variables between accounting data sets corresponding to two different periods. Rules Since it uses a standard, when the number of samples is large, estimation results close to the true model can be obtained.

[0086] In particular, the information processing device 1 described above analyzes account items as variables. For example, in an audit procedure that anticipates the risk of overstating sales or profits, the information processing device 1 evaluates the homogeneity of an accounting data set obtained from journal entry data such as journal vouchers based on the relationship structure between account items, thereby identifying changes that should be considered. For example, a user of the information processing device 1 can identify pairs of account items extracted as a group of changed variables as the cause of changes in the journal entry vouchers and use this information as information for qualitative reasoning in the audit.

[0087] <Modification> The above is a description of the embodiment, but the contents of this embodiment can be modified as follows. In addition, the following modifications can be combined with each other.

[0088] <1> In the above-described embodiment, the information processing device 1 has the processor 11 configured as a CPU, but the control means for controlling the information processing device 1 may have other configurations.

[0089] That is, the information processing device 1 may have, in addition to a CPU, various types of processors as the processor 11, such as a GPU (Graphics Processing Unit), ASIC (Application Specific Integrated Circuit), FPGA (Field Programmable Gate Array), programmable logic device, etc.

[0090] <2> The operations of the processors in the above-described embodiments may be performed not only by a single processor but also by multiple processors located at physically separate locations working together. In this case, the information processing device 1 may be configured as a server-client system or may be realized in a cloud computing environment.

[0091] Furthermore, the order of the operations of the processor is not limited to the order described in the above embodiment, and may be changed as appropriate.

[0092] <3> In the above-described embodiment, each data set is generated based on journal entry data, which is one type of accounting data subject to audit. However, the data sets may be generated based on other data. In other words, the information processing device 1 is applicable to analyses other than audits. For example, the data sets may be generated based on biosensor data for monitoring health status, sensor data for monitoring abnormalities in the production lines of various products, purchase history data in e-commerce, website access log data, etc. In this case, the information processing device 1 outputs information indicating changes (differences) in health status between different periods, product manufacturing environments, etc.

[0093] Although the two data sets corresponding to different time periods are selected, the difference between the data sets is not limited to the time period, but may be the environment, conditions, location, etc. For example, the information processing device 1 may analyze two data sets generated from biosensor data of different people. Also, for example, the information processing device 1 may analyze two data sets generated from monitoring data of different production lines.

[0094] <4> In the above-described embodiment, the information processing device 1 uses the coordinate descent method as the optimization algorithm for the estimation process, but other algorithms such as the gradient proximity method may also be used.

[0095] <5> Information processing using the above-described information processing device 1 can be conceived as a method for analyzing differences in relationships between sets of variables in two data sets. That is, this method is an example of a data analysis method that acquires a first data set and a second data set different from the first data set, estimates a first precision matrix and a second precision matrix based on the acquired first and second data sets so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first data set and a second likelihood for the second data set, and a penalty term that evaluates sparsity indicated by the number of non-zero elements in at least one of the first precision matrix in the first data set, the second precision matrix in the second data set, and the difference between the first precision matrix and the second precision matrix, and outputs information indicating differences in relationships between sets of variables between the first data set and the second data set based on the estimated first precision matrix and second precision matrix.

[0096] <6> In the above-described embodiment, the program loaded by the processor 11 of the information processing device 1 is an example of a program that causes a computer to execute: an acquisition step of acquiring a first dataset and a second dataset different from the first dataset; an estimation step of estimating the first precision matrix and the second precision matrix based on the first dataset and the second dataset acquired in the acquisition step, so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first dataset and a second likelihood for the second dataset, and a penalty term that evaluates sparsity indicated by the number of non-zero elements in at least one of the first precision matrix in the first dataset, the second precision matrix in the second dataset, and the difference between the first precision matrix and the second precision matrix; and an output step of outputting information indicating a difference in the relationship between the sets of variables between the first dataset and the second dataset, based on the first precision matrix and the second precision matrix estimated in the estimation step.

[0097] This program may be provided in a state where it is stored on a computer-readable recording medium, such as a magnetic recording medium such as a magnetic tape or a magnetic disk, an optical recording medium such as an optical disk, a magneto-optical recording medium, a semiconductor memory, etc. This program may also be downloaded via a communication line such as the Internet. [Explanation of symbols]

[0098] 1...information processing device, 11...processor, 111...receiving means, 112...acquisition means, 113...preprocessing means, 114...estimation means, 115...output means, 12...memory, 121...journalization DB, 1211...journalization ID list, 1212...journalization table, 122...matrix DB, 1221...matrix ID list, 1222...matrix element value group, 13...communication unit, 14...operation unit, 15...display unit.

Claims

1. On the computer, an acquisition step of acquiring a first data set and a second data set different from the first data set as targets for audit; an estimation step of estimating the first precision matrix and the second precision matrix based on the first data set and the second data set acquired in the acquisition step so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first data set and a second likelihood for the second data set, and a penalty term evaluating sparsity indicated by the number of non-zero elements in at least one of a first precision matrix in the first data set, a second precision matrix in the second data set, and a difference between the first precision matrix and the second precision matrix; an output step of outputting information indicating a difference in a relationship between a set of variables between the first data set and the second data set based on the first precision matrix and the second precision matrix estimated in the estimation step; A program for executing The estimation step performs the estimation by iteratively minimizing a surrogate objective function in which the penalty term included in the information criterion is replaced with a surrogate function that is configured based on estimated values ​​of the first precision matrix and the second precision matrix in each iteration and takes a value equal to or greater than the penalty term. A program characterized by:

2. The information criterion is defined based on the Akaike information criterion or the Bayes information criterion.

2. The program according to claim 1 .

3. The penalty terms include a first penalty term based on the number of non-zero elements of the first precision matrix, a second penalty term based on the number of non-zero elements of the second precision matrix, and a third penalty term based on the number of non-zero elements of a difference between the first precision matrix and the second precision matrix.

2. The program according to claim 1 .

4. the penalty terms include a first penalty term based on the number of non-zero elements of the first precision matrix, and a second penalty term based on the number of non-zero elements of a Hadamard product of the second precision matrix and a difference between the first precision matrix and the second precision matrix.

2. The program according to claim 1 .

5. The process of minimizing the surrogate objective function is performed using a coordinate descent method.

2. The program according to claim 1 .

6. The proxy function is |Λ ｕｖ | is the absolute value of the element in the u-th row and v-th column of the precision matrix, η is a small positive constant, and Λ （ｔ） ｕｖ is the estimated value of the precision matrix at each iteration, and the terms corresponding to each element of the penalty term are is given in the form 2. The program according to claim 1 .

7. The output step outputs a list of variable pairs having differences in the relationship.

2. The program according to claim 1 .

8. The output step outputs the relationships or differences between the variable groups as a graph structure.

2. The program according to claim 1 .

9. The first data set and the second data set are generated based on journal data.

2. The program according to claim 1 .

10. acquiring means for acquiring a first data set and a second data set different from the first data set; an estimation means for estimating the first precision matrix and the second precision matrix based on the first data set and the second data set acquired by the acquisition means so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first data set and a second likelihood for the second data set, and a penalty term evaluating sparsity indicated by the number of non-zero elements in at least one of a first precision matrix in the first data set, a second precision matrix in the second data set, and a difference between the first precision matrix and the second precision matrix; an output means for outputting information indicating a difference in a relationship between a set of variables between the first data set and the second data set based on the first precision matrix and the second precision matrix estimated by the estimation means; and The estimation means performs the estimation by iteratively executing a process of minimizing a proxy objective function in which the penalty term included in the information criterion is replaced with a proxy function that is configured based on estimated values ​​of the first precision matrix and the second precision matrix in each iteration and takes a value equal to or greater than the penalty term.

1. An information processing device comprising:

11. A computer-implemented method for data analysis, comprising: an acquisition step of acquiring a first data set and a second data set different from the first data set as targets for audit; an estimation step of estimating the first precision matrix and the second precision matrix based on the first data set and the second data set acquired in the acquisition step so as to minimize an information criterion defined based on a likelihood term based on a first likelihood for the first data set and a second likelihood for the second data set, and a penalty term evaluating sparsity indicated by the number of non-zero elements in at least one of a first precision matrix in the first data set, a second precision matrix in the second data set, and a difference between the first precision matrix and the second precision matrix; an output step of outputting information indicating a difference in a relationship between a set of variables between the first data set and the second data set based on the first precision matrix and the second precision matrix estimated in the estimation step, The estimation step performs the estimation by iteratively minimizing a surrogate objective function in which the penalty term included in the information criterion is replaced with a surrogate function that is configured based on estimated values ​​of the first precision matrix and the second precision matrix in each iteration and takes a value equal to or greater than the penalty term. Data analysis methods.

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