Information processing device, information processing method, and recording medium

Abstract

This information processing device comprises: an acquisition unit that sequentially acquires a finite number of elements included in sequence data; an index calculation unit that, each time one of the elements is acquired, calculates an index indicating which of a plurality of classes the sequence data belongs to; a classification unit that classifies the sequence data into one of the plurality of classes by comparing the index with a threshold; a risk calculation unit that back-calculates a recurrence formula from the final acquisition time at which all the elements have been acquired to calculate risks of classifying and not classifying the sequence data at each acquisition time of one of the elements; an expected value calculation unit that calculates expected values of the risks; and a threshold calculation unit that calculates the threshold on the basis of the risks. The expected value calculation unit calculates, on the basis of a pair of the index calculated at a certain acquisition time of one of the elements and the risks at the subsequent acquisition time, the expected values of the risks at the subsequent acquisition time on the assumption that the index is calculated at the certain acquisition time. The risk calculation unit calculates the risk of not classifying the sequence data at the certain acquisition time on the basis of the expected values.

Description

Information processing device, information processing method, and recording medium

[0001] The present disclosure relates to the technical fields of an information processing device, an information processing method, and a recording medium.

[0002] As an apparatus for classifying data, an apparatus that classifies data using a likelihood ratio that the data belongs to a class is known. For example, Patent Document 1 discloses an information processing apparatus including: an acquisition unit that sequentially acquires multiple elements included in sequence data; a first calculation unit that calculates an index indicating to which of multiple classes each of the multiple elements likely belongs, taking into account two or more of the multiple elements; a second calculation unit that integrates the indexes of the multiple elements to calculate an integrated index indicating to which of the multiple classes each of the multiple elements likely belongs; and a classification unit that classifies the sequence data into one of the classes based on the integrated index.

[0003] International Publication No. 2020 / 194497

[0004] This disclosure aims to improve upon the related art discussed above.

[0005] One aspect of the information processing device disclosed herein includes an acquisition means for sequentially acquiring a finite number of elements included in sequence data; an index calculation means for calculating, for each acquired element, an index indicating to which of multiple classes the sequence data belongs; a classification means for classifying the sequence data into one of the multiple classes by comparing the index with a threshold; a risk calculation means for calculating risks in the case of classifying and not classifying the sequence data in each acquisition of the elements by working backwards from the final acquisition of all the elements using a recurrence formula; an expected value calculation means for calculating an expected value of the risk; and a threshold calculation means for calculating the threshold based on the risk, wherein the expected value calculation means calculates an expected value of the risk in the acquisition one time after the certain acquisition when the index was calculated in the certain acquisition, based on a pair of the index calculated in the certain acquisition of the element and the risk in the acquisition one time after the certain acquisition, and the risk calculation means calculates the risk in the case of not classifying the sequence data in the certain acquisition based on the expected value.

[0006] One aspect of the information processing method disclosed herein is an information processing method for calculating the threshold used by an information processing device that includes: acquisition means for sequentially acquiring a finite number of elements included in sequence data; index calculation means for calculating, for each acquired element, an index indicating to which of multiple classes the sequence data belongs; classification means for classifying the sequence data into one of the multiple classes by comparing the index with a threshold; and risk calculation means for calculating the risk of classifying and not classifying the sequence data for each acquisition of the elements. The information processing method calculates the threshold based on a pair of the index calculated in a certain acquisition of the element and the risk in the acquisition one acquisition after the certain acquisition, and calculates an expected value of the risk in the acquisition one acquisition after the certain acquisition when the index was calculated in the certain acquisition. The risk is calculated by back-calculating a recurrence formula from the final acquisition when all of the elements are acquired. The risk of not classifying the sequence data into the certain acquisition is calculated based on the expected value, and the threshold is calculated based on the risk.

[0007] One aspect of the recording medium disclosed herein is an information processing method for calculating the threshold used by an information processing device that includes: acquisition means for sequentially acquiring a finite number of elements included in sequence data; index calculation means for calculating, for each acquired element, an index indicating to which of multiple classes the sequence data belongs; classification means for classifying the sequence data into one of the multiple classes by comparing the index with a threshold; and risk calculation means for calculating the risk of classifying and not classifying the sequence data for each acquisition of the elements. The recording medium stores a computer program that causes a computer to execute the information processing method, which calculates an expected value of the risk in the acquisition one time after the certain acquisition when the index was calculated in the certain acquisition based on a pair of the index calculated in the certain acquisition of the element and the risk in the acquisition one time after the certain acquisition, and calculates the risk by back-calculating a recurrence formula from the final acquisition time when all of the elements are acquired, and calculates the risk of not classifying the sequence data into the certain acquisition based on the expected value, and calculates the threshold based on the risk.

[0008] FIG. 1 is a block diagram showing the configuration of an information processing device according to the present disclosure. FIG. 2 is a flowchart showing the flow of operation of an information processing device according to the present disclosure. FIG. 3 is a block diagram showing the configuration of an information processing device according to the present disclosure. FIG. 4 is a flowchart showing the flow of classification operation in an information processing device according to the present disclosure. FIG. 5 is a flowchart showing the flow of threshold calculation operation in an information processing device according to the present disclosure. FIG. 6 is a graph showing a method of calculating a conditional risk expectation in an information processing device according to the present disclosure. FIG. 7 is a graph showing a method of calculating a conditional risk expectation in an information processing device according to the present disclosure. FIG. 8 is a graph showing a method of calculating a conditional risk expectation in an information processing device according to the present disclosure. FIG. 9 is a graph showing an example of a threshold calculated in an information processing device according to the present disclosure. FIG. 10 is a block diagram showing the configuration of an information processing device according to the present disclosure.

[0009] Hereinafter, an information processing device, an information processing method, and a recording medium according to an embodiment will be described with reference to the drawings. [1: First Embodiment]

[0010] A first embodiment of an information processing device, an information processing method, and a recording medium will be described below. Hereinafter, the first embodiment of the information processing device, the information processing method, and the recording medium will be described using an information processing device 1 according to this disclosure. [1-1: Configuration of Information Processing Device 1]

[0011] The configuration of an information processing device 1 according to this disclosure will be described with reference to Fig. 1. Fig. 1 is a block diagram showing the configuration of an information processing device 1 according to this disclosure.

[0012] 1, the information processing device 1 includes a calculation device 11, a storage device 12, and a communication device 13. The calculation device 11, the storage device 12, and the communication device 13 may be connected via a data bus 16.

[0013] The arithmetic device 11 includes at least one processor (i.e., one processor or multiple processors) as hardware. The processor may include, for example, a processor conforming to a von Neumann computer architecture. The processor conforming to the von Neumann computer architecture may include at least one of a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit). The processor may include, for example, a processor conforming to a non-von Neumann computer architecture. The processor conforming to the non-von Neumann computer architecture may include at least one of an FPGA (Field Programmable Gate Array) and an ASIC (Application Specific Circuit).

[0014] The arithmetic device 11 reads a computer program 121 including at least one of computer program code and computer program instructions. For example, the arithmetic device 11 may read the computer program 121 stored in the storage device 12. For example, the arithmetic device 11 may read the computer program 121 stored in a computer-readable, non-transitory recording medium using a recording medium reading device (not shown) included in the information processing device 1. The computer program 121 read from the recording medium may be stored in the storage device 12. The arithmetic device 11 may acquire (i.e., download or read) the computer program 121 from a device (not shown) located outside the information processing device 1 via the communication device 13 (or another communication device). The downloaded computer program 121 may be stored in the storage device 12.

[0015] The arithmetic device 11 executes the loaded computer program 121. As a result, a logical functional block for executing processing to be performed by the information processing device 1 (e.g., authentication processing described below) is realized within the arithmetic device 11. In other words, the arithmetic device 11, together with the storage device 12 in which the computer program 121 is recorded (in other words, together with the storage device 12 and the computer program 121 recorded in the storage device 12, etc.), can function as a controller or computer for realizing the logical functional block for executing processing to be performed by the information processing device 1. In other words, the at least one processor included in the arithmetic device 11, the memory (recording medium) included in the storage device 12, etc., and the computer program 121 are configured to cause the information processing device 1 to perform processing to be performed by the information processing device 1 (e.g., authentication processing described below). The arithmetic device 11 may output information to another computer, cloud server, or other device (not shown) provided outside the information processing device 1 via the communication device 13 (or other communication device).

[0016] The recording medium for recording the computer program 121 executed by the arithmetic device 11 may be at least one of a CD-ROM, CD-R, CD-RW, flexible disk, MO, DVD-ROM, DVD-RAM, DVD-R, DVD+R, DVD-RW, DVD+RW, and Blu-ray (registered trademark) optical disk, magnetic medium such as magnetic tape, magneto-optical disk, semiconductor memory such as USB memory, and any other medium capable of storing a program. The recording medium may include a device capable of recording the computer program 121 (for example, a general-purpose device or a dedicated device in which the computer program 121 is implemented in a state in which it can be executed in at least one of the forms of software and firmware). Furthermore, each process or function included in the computer program 121 may be realized by a logical processing block realized within the arithmetic device 11 when the arithmetic device 11 (i.e., processor) executes the computer program 121, or may be realized by hardware such as a predetermined gate array (FPGA (Field Programmable Gate Array), ASIC (Application Specific Integrated Circuit)) included in the arithmetic device 11, or may be realized in a form that mixes logical processing blocks and partial hardware modules that realize some elements of the hardware.

[0017] 1 shows an example of logical functional blocks implemented within the computing device 11 for executing authentication processing. As shown in FIG. 1, an acquisition unit 111, an index calculation unit 112, a classification unit 113, a risk calculation unit 114, and a threshold calculation unit 115 are implemented within the computing device 11. The risk calculation unit 114 has an expected value calculation unit 1141. Note that the processes performed by the acquisition unit 111, the index calculation unit 112, the classification unit 113, the risk calculation unit 114, and the threshold calculation unit 115 will be described later with reference to FIG. 2.

[0018] The storage device 12 includes at least one memory capable of storing desired data. In other words, the storage device 12 includes at least one memory containing desired data. For example, the storage device 12 may store a computer program 121 executed by the arithmetic device 11. In this case, the storage device 12 (memory) may be used as the above-mentioned recording medium for recording the computer program 121 executed by the arithmetic device 11. The storage device 12 may temporarily store data used by the arithmetic device 11 when the arithmetic device 11 is executing the computer program 121. The storage device 12 may also store data to be stored long-term by the information processing device 1. The storage device 12 may include at least one of a RAM (Random Access Memory), a ROM (Read Only Memory), a hard disk device, a magneto-optical disk device, an SSD (Solid State Drive), and a disk array device. In other words, the storage device 12 may include a non-temporary recording medium.

[0019] The communication device 13 can communicate with devices external to the information processing device 1 or 2 via a communication network (not shown). The communication device 13 may be a communication interface based on standards such as Ethernet (registered trademark), Wi-Fi (registered trademark), Bluetooth (registered trademark), or USB (Universal Serial Bus). [1-2: Information Processing Method Executed by the Information Processing Device 1]

[0020] An information processing method executed by the information processing device 1 will be described with reference to Fig. 2. Fig. 2 is a flowchart showing an example of the flow of the information processing method executed by the information processing device 1. [a: Classification Operation]

[0021] 2A, the acquiring unit 111 sequentially acquires a finite number of elements included in the sequence data (step S11). In this embodiment, the sequence data is data including multiple elements arranged in a predetermined order, such as time-series data.

[0022] The index calculation unit 112 calculates an index indicating which of multiple classes the sequence data belongs to each time an element is acquired (Step S12). In other words, the index calculation unit 112 calculates an index each time an element is acquired. The classification unit 113 compares the index with a threshold (Step S13).

[0023] The classification unit 113 classifies the sequence data into one of a plurality of classes according to the comparison result between the index and the threshold (step S14). The operations of steps S11, S12, and S13 are repeated until the classification unit 113 classifies the sequence data into one of a plurality of classes in step S14. If the sequence data is classified in a certain acquisition among the number of times elements are acquired, the elements are not acquired sequentially after that acquisition. On the other hand, if the sequence data is not classified in a certain acquisition, the elements are acquired sequentially after that acquisition. [b: Threshold calculation operation]

[0024] 2(b), the risk calculation unit 114 calculates the risk for each acquisition of the elements by back-calculating the recurrence formula using the index from the final acquisition of all elements (step S15). The risk in this case includes the risk of classifying and not classifying the sequence data in a certain acquisition. The operation of step S15 includes the operations of steps S15-1 and S15-2 below.

[0025] The expected value calculation unit 1141 calculates the expected value of risk (referred to as the "risk expected value") in the acquisition cycle immediately following a given acquisition cycle when an index is calculated in a given acquisition cycle (step S15-1). The risk expected value may be rephrased as the expected value of risk in the acquisition cycle immediately following a given acquisition cycle, with the condition "when an index is calculated in a given acquisition cycle." The risk expected value may also be rephrased as being conditioned by the index calculated in a given acquisition cycle. The expected value calculation unit 1141 calculates the risk expected value based on a pair of the index calculated in a given acquisition cycle and the risk (the risk calculated by the risk calculation unit 114) in the acquisition cycle immediately following the given acquisition cycle. The risk calculation unit 114 calculates the risk in the case where sequence data is not classified into a given acquisition cycle based on the risk expected value (step S15-2).

[0026] The number of times an element is acquired may be expressed as the time at which the element is acquired. In other words, the risk calculation unit 114 calculates the risk at each time by back-calculating the recurrence formula for risk from the final time (e.g., t = T) at which all of the finite number (T) of elements included in the sequence data are acquired. The risk calculation unit 114 back-calculates the recurrence formula to calculate the risk at the previous time (e.g., t = T-1). The risk calculation unit 114 calculates the risk at each time before the final time (e.g., t = 1 to T-1) by repeating the back-calculation of the recurrence formula.

[0027] The threshold calculation unit 115 calculates a threshold based on the risk (step S16). [1-3: Technical Effects of the Information Processing Device 1]

[0028] The information processing device 1 disclosed herein calculates the risk associated with classification for each acquisition of an element and performs classification using a threshold calculated based on the risk, thereby enabling classification with a low potential risk. The information processing device 1 reverse-calculates a recurrence formula using an index from the final acquisition in which all elements are acquired, enabling appropriate calculation of the risk associated with classification for each acquisition of an element. The information processing device 1 also calculates a risk expectation value based on a sample of a pair of an index calculated in a certain acquisition and a risk in the acquisition one acquisition after the certain acquisition, and calculates the risk of not classifying sequence data into a certain acquisition based on this risk expectation value. The information processing device 1 calculates the risk expectation value with a relatively small processing load based on the sample, enabling appropriate risk calculation with a relatively small processing load and classification using an appropriate threshold. [2: Second Embodiment]

[0029] A second embodiment of an information processing device, an information processing method, and a recording medium will be described below. Hereinafter, the second embodiment of an information processing device, an information processing method, and a recording medium will be described using an information processing device 2 according to this disclosure. [2-1: Configuration of Information Processing Device 2]

[0030] The configuration of the information processing device 2 according to this disclosure will be described with reference to Fig. 3. Fig. 3 is a block diagram showing the configuration of the information processing device 2 according to this disclosure.

[0031] 3 , the information processing device 2 may further include an input device 14 and an output device 15 in addition to the calculation device 11, the storage device 12, and the communication device 13. However, the information processing device 2 does not necessarily have to include at least one of the input device 14 and the output device 15. The calculation device 11, the storage device 12, the communication device 13, the input device 14, and the output device 15 may be connected via a data bus 16.

[0032] 3 , the index calculation unit 212 may include a likelihood ratio calculation unit 2121, a posterior probability conversion unit 2122, and an index holding unit 2123. Furthermore, the risk calculation unit 214 may include a termination risk calculation unit 2142, a continuation risk calculation unit 2143, and a minimum risk holding unit 2144 in addition to an expected value calculation unit 2141.

[0033] The input device 14 is a device that accepts information input to the information processing device 2 from outside the information processing device 2. For example, the input device 14 may include an operation device (e.g., at least one of a keyboard, a mouse, and a touch panel) that can be operated by an operator of the information processing device 2. For example, the input device 14 may include a reading device that can read information recorded as data on a recording medium that can be externally attached to the information processing device 2.

[0034] The output device 15 is a device that outputs information to the outside of the information processing device 2. For example, the output device 15 may output information as an image. That is, the output device 15 may include a display device (a so-called display) that can display an image showing the information to be output. For example, the output device 15 may output information as sound. That is, the output device 15 may include an audio device (a so-called speaker) that can output sound. For example, the output device 15 may output information on paper. That is, the output device 15 may include a printing device (a so-called printer) that can print desired information on paper. [2-2: Information Processing Method Executed by Information Processing Device 2] [a: Classification Operation]

[0035] The information processing device 2 is configured as a device for classifying time-series data. For example, the information processing device 2 may be configured as a device that acquires images of time-series data and classifies the types of objects included in the images.

[0036] The operation of classifying sequence data into one of a plurality of classes (classification operation) in the information processing device 2 will be described with reference to Fig. 4. Fig. 4 is a flowchart showing the flow of the classification operation in the information processing device 2.

[0037] As shown in FIG. 4 , when the classification operation in the information processing device 2 starts, the acquisition unit 211 sequentially acquires a finite number of elements included in the sequence data (step S201). For example, the acquisition unit 211 acquires the elements included in the sequence data one by one in order. An "element" may be considered a "unit" acquired by the acquisition unit 211 in a single acquisition. For example, if the sequence data is video data, an element may be one frame or multiple frames. What is considered an element may be determined arbitrarily depending on the requirements for applying the classification operation.

[0038] The acquisition unit 211 may acquire data directly from any data acquisition device (for example, a camera, a microphone, etc.). Alternatively, the acquisition unit 211 may read data that has been acquired in advance by a data acquisition device and stored in storage, etc. When acquiring data from a camera, the acquisition unit 211 may be configured to acquire data from each of a plurality of cameras.

[0039] The index calculation unit 212 calculates an index based on the elements acquired by the acquisition unit 211 (step S202). The "index" here is a value indicating to which of multiple classes, which are classification candidates, the sequential data belongs. In this embodiment, at least one of a likelihood ratio and a posterior probability is used as the "index." The likelihood ratio and the posterior probability will be described later.

[0040] The index calculation unit 212 calculates an index each time an element is acquired. The index calculation unit 212 may calculate an index corresponding to each of a plurality of classes. The index calculation unit 212 calculates an index when the acquisition unit 211 acquires one element, and calculates a new index when the acquisition unit 211 acquires another element. The index calculation unit 212 may calculate an index using the element acquired this time and an element acquired previously. In this case, the index calculation unit 212 may calculate a new index using the index calculated from the element acquired this time and an index calculated previously (specifically, an index calculated from the element acquired previously).

[0041] The classification unit 213 compares the index calculated by the index calculation unit 212 with a preset threshold. The classification unit 213 may compare the index with the threshold for multiple classes. The threshold is set so as to perform appropriate classification. The classification unit 213 determines whether the index exceeds the threshold (step S203). The classification unit 213 may determine whether the index exceeds the threshold for any class.

[0042] If there is a class whose index exceeds the threshold (step S203: Yes), the classifying unit 213 classifies the sequence data into the class whose index exceeds the threshold (step S204). For example, if the sequence data is to be classified into two classes, class 0 and class 1, and the index corresponding to class 0 exceeds the threshold, the classifying unit 213 classifies the sequence data into class 0. Similarly, if the index corresponding to class 1 exceeds the threshold, the classifying unit 213 classifies the sequence data into class 1. Note that the number of classes may be three or more.

[0043] On the other hand, if the index does not exceed the threshold (step S203: No), the process is executed again from step S201. That is, the steps from step S201 to step S203 are repeated until the index exceeds the threshold. In this way, the information processing device 2 performs sequential operations to classify the sequence data into appropriate classes.

[0044] The index calculation unit 212 is configured to calculate a larger index for the class to be classified as the number of acquired elements increases. The threshold is set as a criterion for determining how large the index must be to classify the sequence data. Next, the setting of the threshold will be described. [b: Threshold Calculation Operation]

[0045] The information processing device 2 is configured as a device that sets thresholds for classifying sequence data. The information processing device 2 may be configured as a device that calculates thresholds that reduce risks associated with classification.

[0046] Risks related to classification may include the risk of incorrectly classifying sequential data and the risk of spending time classifying sequential data. The risk of incorrectly classifying sequential data is the risk of not classifying the sequential data into the class it should be classified into. This can also be rephrased as the risk of classifying sequential data into a class it should not be classified into. For example, it is the risk of classifying sequential data that should be classified into class 0 into class 1.

[0047] The formula representing the classification risk can be set to include a term corresponding to the penalty for misclassifying sequential data and a penalty related to the time spent classifying sequential data. Specifically, the classification risk may be expressed, for example, by the following formula 1:

[0048] [Formula 1] In the above formula 1, i and j each represent a class, and X （１,t） indicates the elements of the sequence data acquired up to time t. ｔ =j indicates that the predicted class is j. Therefore, the above formula 1 represents the risk when the sequence data is classified into class j at time t.

[0049] The first term on the right side of the above equation 1 represents the risk of misclassifying sequence data. y is the class label. L ｉｊ is the penalty when a class other than class j is the class to be classified, and when i=j, L ｉｊ = 0. π(y = i | X （１,t） ) is the index of class i calculated from the elements acquired up to time t. In other words, the index represents the risk of misclassifying sequential data. The risk of misclassifying sequential data increases when the index value of a class other than class j is large, and decreases when the index value of a class other than class j is small. This index may be calculated by the index calculation unit 212. Alternatively, the index may be a true index (in other words, a correct label) that is assigned to sequential data in advance.

[0050] The second term on the right side of the above equation 1 represents the risk associated with the time spent classifying sequential data. The risk associated with the time spent classifying sequential data can be expressed as a function f(t) of time t. As shown in the second term on the right side of the above equation 1, the risk associated with the time spent classifying sequential data may be expressed by the cost c for acquiring the next element and time t (the number of times the element is acquired).

[0051] As expressed in the above formula 1, the risk related to classification for each time and each class can be calculated. The class with the smallest risk at a certain time is the class that should most be classified at that time when classification is performed at that time. Classification at a certain time can also be rephrased as ending element acquisition at that time. The smallest risk at a certain time (in other words, the risk of classifying into the class that should most be classified at that time) is called the termination risk. The termination risk is the smallest risk that can be taken when element acquisition is ended at that time.

[0052] The termination risk may be rephrased as the risk when classifying sequence data at a certain time. The termination risk may be rephrased as the risk when classifying by an index that can be obtained at a certain time. Specifically, the termination risk G ｓｔ may be expressed by, for example, the following equation 2. The termination risk is the smallest possible risk when element acquisition is terminated at a certain time, and is therefore expressed only as the risk of incorrectly classifying sequential data.

[0053] [Formula 2] The right side of the above formula 2 means that the risk of class j, which has the smallest risk of misclassifying sequential data, is set as the termination risk. Also, as shown in the above formula 2, the termination risk G ｓｔ can be expressed as an index at time t (an index that can be calculated based on elements acquired from time 1 to time t). Therefore, the termination risk G ｓｔ can be calculated when the index at time t can be obtained. Note that π without a subscript, such as π appearing on the left side of the above equation 2, is a vector that collects the indexes of all classes.

[0054] Next, consider the case where no classification is performed at a certain time, and acquisition of an element is continued at the next time. The risk in this case is called the continuation risk. Whether or not to perform classification at a certain time can be determined by comparing the termination risk and the continuation risk. In other words, if the termination risk is smaller than the continuation risk at a certain time, this indicates that ending acquisition of the element will result in a lower risk of classification than continuing acquisition of the element, so it can be determined that classification will be performed at a certain time. Conversely, if the continuation risk is smaller than the termination risk at a certain time, this indicates that continuing acquisition of the element will result in a lower risk of classification than ending acquisition of the element, so it can be determined that classification will not be performed at a certain time. The smaller of the continuation risk and the termination risk at a certain time is called the minimum risk at a certain time.

[0055] When elements are continued to be acquired at the next time, there is a possibility that the risk of misclassification can be reduced by acquiring more elements, but there is also a risk of acquiring more elements. The continuation risk can be expressed as the expected value of the risk that can be calculated when an index is calculated from elements acquired up to time t and the next element is acquired (the risk of misclassifying sequential data), and the cost of acquiring the next element. This expected value of risk is called a conditional risk expectation because it is conditional on the index being calculated from elements acquired up to time t. The continuation risk G(tilde)t may be expressed, for example, as in Equation 3 below.

[0056] [Formula 3] The first term on the right side of the above equation 3 represents the conditional risk expectation. G on the right side of the above equation 3 is the minimum risk at time t+1, which is one time after time t. In other words, the continuing risk can be expressed using information from time t+1, which is one time after time t.

[0057] The above formula 3 indicates that the continuing risk at time t can be calculated using the minimum risk at time t+1. The continuing risk can be calculated by inversely calculating the recurrence formula including the minimum risk.

[0058] In this way, it can be seen that classification can be performed accurately in the minimum amount of time by performing classification when the termination risk and the continuation risk are the same. For this reason, the above-mentioned threshold may be calculated based on the termination risk and the continuation risk. The threshold may be calculated so as to minimize the difference between the continuation risk and the termination risk. For example, it may be calculated based on the intersection of the continuation risk and the termination risk. Furthermore, since the threshold is compared with an index, the threshold may be calculated based on an index that minimizes the difference between the continuation risk and the termination risk.

[0059] In this embodiment, "time" advances each time an element is acquired. Therefore, the time corresponds to the number of times an element has been acquired up to that point. Furthermore, the progression from time t to time t+1 is sometimes referred to as progressing forward, and the progression from time t to time t-1 is sometimes referred to as progressing backward.

[0060] 5 to 9, the operation of calculating a threshold value used for classifying sequence data in the information processing device 2 (threshold calculation operation) will be described. FIG. 5 is a flowchart showing the flow of the threshold calculation operation in the information processing device 2. FIGS. 6 to 9 are graphs showing sample pairs of an index calculated at a certain time and the minimum risk at the time immediately following that time. [b-1: Forward processing (calculation of posterior probability and termination risk)]

[0061] 5A, when the threshold calculation operation is started in the information processing device 2, the time t becomes 0. The acquisition unit 211 acquires an element included in the sequence data, and the time t is incremented (step S251).

[0062] The index calculation unit 212 calculates an index at time t based on the elements acquired by the acquisition unit 211. The index calculation unit 212 calculates an index for each class at time t. The index calculation unit 212 calculates a likelihood ratio and a posterior probability as the index.

[0063] The likelihood ratio calculation unit 2121 calculates a likelihood ratio at time t based on the elements acquired by the acquisition unit 211 (step S252). The "likelihood ratio" is an index indicating the likelihood of the class to which the sequence data belongs. The likelihood ratio calculation unit 2121 may calculate a likelihood ratio using elements acquired at time t and elements acquired before time t. The likelihood ratio calculation unit 2121 may calculate a new likelihood ratio using the likelihood ratio calculated at time t and the likelihood ratio calculated before time t. The likelihood ratio may be a value that can be obtained as a result of likelihood ratio learning using a SPRT-based algorithm that treats sequence data as an Nth-order Markov series (SPRT-TANDEM) process. The likelihood ratio calculation unit 2121 may be configured by, for example, a trained neural network.

[0064] The posterior probability conversion unit 2122 converts the likelihood ratio calculated by the likelihood ratio calculation unit 2121 to calculate the posterior probability at time t (step S253). The posterior probability conversion unit 2122 is configured to be able to convert the likelihood ratio calculated by the likelihood ratio calculation unit 2121 into a posterior probability. The posterior probability for each class indicates the probability that an input element will be classified into the corresponding class, and is a value that corresponds one-to-one to the likelihood ratio calculated by the likelihood ratio calculation unit 2121. The posterior probability is an index calculated by the index calculation unit 212, and is used for classification by the classification unit 213 and risk calculation by the threshold calculation unit 215.

[0065] However, the classification unit 213 and the threshold calculation unit 215 may use the likelihood ratio calculated by the likelihood ratio calculation unit 2121 as an index. In this case, the information processing device 2 may be configured without including the posterior probability conversion unit 2122. When the likelihood ratio is used as an index, the processing of step S253 may be omitted. Whether the posterior probability or the likelihood ratio is used as an index, it is possible to appropriately calculate the risk.

[0066] The index storage unit 2123 stores at least one of the likelihood ratio at time t and the posterior probability at time t (step S254). Below, a case where the "posterior probability" at each time is used as the "index" for each time will be described. When the likelihood ratio is used as the index, the "posterior probability" can be replaced with the "likelihood ratio."

[0067] The termination risk calculation unit 2142 calculates the termination risk at time t (step S255). The termination risk calculation unit 2142 causes the minimum risk holding unit 2144 to hold the termination risk at time t (step S256). At this point, the minimum risk holding unit 2144 holds the termination risk as a provisional minimum risk. As will be described later, if the continuing risk calculated by the reverse processing is smaller than the minimum risk, the minimum risk holding unit 2144 replaces the termination risk with the continuing risk.

[0068] The information processing device 2 determines whether the time t is the final time (T) (step S257). If the time is not the final time (T), the process returns to step S251. If the time is the final time (T), the index holding unit 2123 holds the posterior probability at each time from 1 to T, and the minimum risk holding unit 2144 holds the termination risk at each time from 1 to T.

[0069] The information processing device 2 may perform the above-described forward processing on each of the m pieces of sequence data. Each of the m pieces of sequence data may include a finite number (T) of elements, and the likelihood ratio and posterior probability may be calculated for each of the times 1 to T. [b-2: Backward processing (calculation of continuing risk and threshold)]

[0070] As shown in FIG. 5B, time t becomes T (step S260). The risk calculation unit 214 decrements time t, obtains the termination risk at time t from the minimum risk holding unit 2144, and obtains the posterior probability at time t from the index holding unit 2123 (step S261). The risk calculation unit 214 obtains the minimum risk at time t+1 from the minimum risk holding unit 2144 (step S262). For example, if time t is T-1, the operations of steps S261 and S262 obtain the termination risk as the minimum risk at the final time T, the termination risk at time T-1, and the posterior probability at time T-1. Note that the termination risk may be calculated in step S261 instead of step S255.

[0071] The expected value calculation unit 2141 calculates a conditional risk expectation at time t (step S263). When the posterior probability at time t is calculated (when elements are acquired from times 1 to t and the posterior probabilities are calculated) (risk expectation condition), the expected value calculation unit 2141 calculates the minimum risk expected when an element is also acquired at time t+1. In other words, the expected value calculation unit 2141 estimates the minimum possible risk at time t+1 given the posterior probability at time t. The expected value calculation unit 2141 calculates the conditional risk expectation based on a pair of the posterior probability at time t and the minimum risk at time t+1. For example, if the information processing device 2 can use m pieces of sequence data, the expected value calculation unit 2141 can calculate the conditional risk expectation based on m paired samples.

[0072] As shown in the above formula 3, in order to calculate the conditional risk expectation, it is necessary to handle the joint distribution of the posterior probability and the minimum risk. In this embodiment, instead of calculating the conditional risk expectation by numerical calculation or the like, the expectation calculation unit 2141 estimates the conditional risk expectation based on the posterior probability calculated from the acquired elements and the termination risk calculated from the posterior probability.

[0073] The expected value calculation unit 2141 may estimate the conditional risk expectation based on the positions of m samples, as illustrated in FIG. 6. The horizontal axis of the graph illustrated in FIG. 6 represents the posterior probability, and the vertical axis represents the minimum risk. The expected value calculation unit 2141 sets the conditional risk expectation to zero when the posterior probability is at the minimum and maximum possible values ​​(in the example illustrated in FIG. 6, the horizontal axis is 0 and 1). Calculating the risk to zero when the posterior probability is at the minimum and maximum possible values ​​is one of the conditions for calculating the conditional risk expectation. This condition may be referred to as a "boundary condition."

[0074] For example, the expected value calculation unit 2141 may interpolate a straight line through at least one of the multiple samples and calculate the conditional risk expectation based on the straight line. As illustrated in Fig. 7 , the expected value calculation unit 2141 may connect the positions of each of the multiple samples in order with a straight line and calculate the conditional risk expectation based on the line. Alternatively, as illustrated in Fig. 8 , the expected value calculation unit 2141 may connect the position of 0 on the horizontal axis and 0 on the vertical axis (the position where the minimum possible value of the posterior probability and the minimum risk are zero) with the position of the sample with the largest minimum risk (the value on the vertical axis) with a straight line, and may connect the position of 1 on the horizontal axis and 0 on the vertical axis (the position where the maximum possible value of the posterior probability and the minimum risk are zero) with the position of the sample with the largest minimum risk with a straight line and calculate the conditional risk expectation based on the straight line.

[0075] 9 , the expected value calculation unit 2141 may form a convex envelope of samples based on at least one of a plurality of samples, and calculate the conditional risk expectation based on the convex envelope. For example, the expected value calculation unit 2141 may calculate the conditional risk expectation based on an outer envelope O. The expected value calculation unit 2141 may also calculate the conditional risk expectation based on an inner envelope I. The expected value calculation unit 2141 may also calculate the conditional risk expectation based on any line in the area surrounded by the outer envelope O and the inner envelope I. The expected value calculation unit 2141 may also calculate the conditional risk expectation based on a line connecting the midpoints of the outer envelope O and the inner envelope I. The expected value calculation unit 2141 may form the convex envelope using any method. For example, the expected value calculation unit 2141 may form the convex envelope using a gift wrapping method.

[0076] The continuing risk calculation unit 2143 calculates the continuing list at time t based on the calculated conditional risk expectation (step S2565). The continuing risk calculation unit 2143 adds c (sampling cost) to the conditional risk expectation to calculate the continuing risk.

[0077] If the continuation risk at time t is smaller than the termination risk at time t, the expected value calculation unit 2141 replaces the held termination risk at time t with the continuation risk at time t. As a result, the minimum risk holding unit 2144 holds the minimum risk at time t.

[0078] The threshold calculation unit 215 calculates the threshold for time t based on the termination risk at time t and the continuation risk at time t. The threshold calculation unit 215 may calculate the threshold for time t based on the posterior probability that the difference between the continuation risk at time t and the termination risk at time t is minimized. The threshold calculation unit 215 sets the intersection of the termination risk at time t and the continuation risk at time t as the threshold for time t. The threshold calculation unit 215 holds the threshold for time t (step S267).

[0079] The threshold calculation unit 215 determines whether to end the calculation of the threshold (step S268). For example, the threshold calculation unit 215 may determine to end the calculation of the threshold when it has calculated the threshold for all time points (specifically, when it has completed the backward calculation from the final time T to the first time 1). If it has determined to end the calculation (step S268: Yes), the threshold calculation operation ends. On the other hand, if it has determined not to end the calculation (step S268: No), it starts the processing again from step S262. That is, it returns to the previous time point and repeats the same processing as described above. By repeating the processing in this manner, the backward calculation from the final time progresses, and it is possible to ultimately calculate the risks and thresholds for all time points.

[0080] The threshold calculation unit 215 calculates thresholds for all times and then combines them in the time direction to obtain a final threshold. In this way, the information processing device 2 can appropriately calculate a threshold that minimizes risk. [2-3: Technical Effects of the Information Processing Device 2]

[0081] As shown in FIG. 10 , the information processing device 2 calculates a threshold that changes over time. The information processing device 2 calculates a threshold that enables early classification while reducing the risk of classification. For example, the sequence data A, B, and C illustrated in FIG. 10 each have different trends in likelihood ratio fluctuations. While sequence data A is relatively easy to classify, sequence data C is relatively difficult to classify. When classifying such sequence data A, B, and C, if the threshold is fixed at the initial value, classification of sequence data with a small likelihood ratio gradient will be slow. Furthermore, for sequence data such as sequence data C, where the likelihood ratio changes only slightly, even if all elements are acquired, the likelihood ratio may not exceed the threshold, and the processing may ultimately terminate without classification. However, since the information processing device 2 changes the threshold over time, it is possible to quickly and accurately classify all sequence data. Furthermore, since the information processing device 2 changes the threshold to minimize risk, it is possible to achieve early classification while minimizing the possibility of incorrect classification.

[0082] Furthermore, the information processing device 2 according to this disclosure calculates the minimum risk expected value in the acquisition cycle immediately following the given acquisition cycle when an index is calculated in the given acquisition cycle based on a plurality of samples as exemplified in Figures 6 to 9, so that the minimum risk expected value can be calculated with a relatively small amount of calculation. Also, the information processing device 2 can calculate the conditional risk expected value while satisfying boundary conditions. [3: Third Embodiment]

[0083] A third embodiment of an information processing device, an information processing method, and a recording medium will be described. Hereinafter, a third embodiment of an information processing device, an information processing method, and a recording medium will be described using an information processing device 3 according to this disclosure.

[0084] The third embodiment is an operation form in step S264 of Fig. 5(b). The third embodiment may be similar to the second embodiment except for the operation of calculating the conditional risk expectation value. Therefore, hereinafter, only the parts that differ from the second embodiment will be described in detail, and descriptions of other overlapping parts will be omitted as appropriate.

[0085] A specific calculation operation of the conditional risk expectation value will be described below. As shown in FIG.

[0086] The generation unit 3145 generates an expectation output mechanism that outputs a conditional risk expectation value when an index (posterior probability or likelihood ratio) calculated in a certain acquisition is input. The expectation output mechanism is a mechanism that outputs the minimum risk at time t+1 in response to an input of an arbitrary index (posterior probability or likelihood ratio) at time t. The generation unit 3145 generates an expectation output mechanism based on a plurality of samples (paired samples of an index calculated in a certain acquisition and the minimum risk in the acquisition one acquisition after the certain acquisition). The generation unit 3145 generates an expectation output mechanism that outputs zero when the minimum and maximum possible values ​​of the index are input. The generation unit 3145 may generate an upward convex function as the expectation output mechanism.

[0087] The expected value calculation unit 3141 calculates the conditional risk expected value at the next time t+1 from the index at time t using the expected value output mechanism. The continuing risk calculation unit 3143 calculates the continuing risk by adding c (sampling cost) to the calculated conditional risk expected value. [3-1: First expected value output mechanism]

[0088] The generating unit 3145 may generate an expected value output mechanism by interpolating a straight line through at least one of the multiple samples. The generating unit 3145 may generate the expected value output mechanism by sequentially connecting the positions of the multiple samples with a straight line, as illustrated in FIG. 7. The generating unit 3145 may also generate the expected value output mechanism by connecting the position where the minimum possible value of the posterior probability is zero and the minimum risk is zero with the position of the sample with the maximum minimum risk with a straight line, as illustrated in FIG. 8. [3-2: Second expected value output mechanism]

[0089] The generation unit 3145 may form a convex envelope of the samples based on at least one of the multiple samples, and may generate an expected value output mechanism based on the convex envelope. The generation unit 3145 may generate an expected value output mechanism by forming a convex envelope of the samples based on at least one of the multiple samples, as illustrated in FIG. 9. [3-3: Technical Effects of the Information Processing Device 3]

[0090] The information processing device 3 disclosed herein generates an expected value output mechanism, and is therefore capable of calculating a conditional risk expectation for any index t. The expected value output mechanism outputs zero when the minimum and maximum possible values ​​of the index are input, and therefore the information processing device 3 can calculate a conditional risk expectation that satisfies the boundary conditions described above. Furthermore, when the information processing device 3 generates an upward convex function as the expected value output mechanism, this is advantageous for calculating thresholds based on termination risk and continuation risk.

[0091] [4: Supplementary Notes] The above-described embodiment may be further described as in the following supplementary notes, but is not limited to the following. an information processing device comprising: an acquisition means for sequentially acquiring a finite number of elements included in sequence data; an index calculation means for calculating, for each acquisition of an element, an index indicating to which of a plurality of classes the sequence data belongs; a classification means for classifying the sequence data into one of the plurality of classes by comparing the index with a threshold; a risk calculation means for calculating risks in the case of classifying and not classifying the sequence data at each acquisition of the elements by back-calculating a recurrence formula using the index from the final acquisition when all of the elements are acquired; an expected value calculation means for calculating an expected value of the risk; and a threshold calculation means for calculating the threshold based on the risk, wherein the expected value calculation means calculates an expected value of the risk at an acquisition time one time after the certain acquisition time when the index was calculated at the certain acquisition time based on a pair of the index calculated at the certain acquisition time of the element and the risk at the acquisition time one time after the certain acquisition time, and the risk calculation means calculates the risk in the case of not classifying the sequence data at the certain acquisition time based on the expected value. [Supplementary Note 2] The information processing device according to Supplementary Note 1, wherein the expected value calculation means interpolates a straight line into at least one of the plurality of pairs and calculates the expected value based on the straight line. [Supplementary Note 3] The information processing device according to Supplementary Note 1, wherein the expected value calculation means forms a convex envelope of the pair based on at least one of the plurality of pairs and calculates the expected value based on the convex envelope. [Supplementary Note 4] The information processing device according to Supplementary Note 1, further comprising: generation means for generating an expected value output mechanism that outputs the expected value when the index calculated for the certain acquisition time is input based on the plurality of pairs, and the expected value calculation means calculates the expected value using the expected value output mechanism. [Supplementary Note 5] The information processing device according to Supplementary Note 4, wherein the generation means interpolates a straight line into at least one of the plurality of pairs and generates the expected value output mechanism based on the straight line.[Supplementary Note 6] The information processing device of Supplementary Note 4, wherein the generation means forms a convex envelope of the pair based on at least one of the plurality of pairs, and generates the expected value output mechanism based on the convex envelope. [Supplementary Note 7] The information processing device of Supplementary Note 4, wherein the generation means generates the expected value output mechanism that outputs zero when the minimum and maximum possible values ​​of the index are input. [Supplementary Note 8] The information processing device of Supplementary Note 4, wherein the generation means generates an upward convex function as the expected value output mechanism. [Supplementary Note 9] The risk calculation means calculates a termination risk, which is the risk when classifying the sequence data into the certain acquisition time, and a continuation risk, which is the risk when continuing to acquire the next element without classifying the sequence data into the certain acquisition time, based on the index, and the threshold calculation means calculates the threshold based on the index that minimizes the difference between the continuation risk and the termination risk. [Supplementary Note 10] The information processing device of Supplementary Note 9, wherein the threshold calculation means calculates the threshold based on the index that minimizes the difference between the continuation risk and the termination risk. [Supplementary Note 11] The information processing device according to Supplementary Note 9, wherein the expected value calculation means calculates the expected value based on a pair of the index calculated in the certain acquisition cycle and the minimum risk, which is the smaller of the continuation risk and the termination risk in the subsequent acquisition cycle. [Supplementary Note 12] The information processing device according to Supplementary Note 11, wherein the risk calculation means sets the value of the termination risk in the final acquisition cycle to the value of the minimum risk in the final acquisition cycle, and then calculates the continuation risk corresponding to each acquisition cycle by back-calculating the recurrence formula from the final acquisition cycle. [Supplementary Note 13] The information processing device according to Supplementary Note 1, wherein the index is at least one of a likelihood ratio indicating the likelihood that the sequence data belongs to a certain class of the plurality of classes, and a posterior probability corresponding to the likelihood ratio.[Supplementary Note 14] An information processing method for calculating the threshold used by an information processing device comprising: acquisition means for sequentially acquiring a finite number of elements included in sequence data; index calculation means for calculating, for each acquisition of the element, an index indicating to which of a plurality of classes the sequence data belongs; classification means for classifying the sequence data into one of the plurality of classes by comparing the index with a threshold; and risk calculation means for calculating a risk of classifying and not classifying the sequence data at each acquisition of the element, the information processing method comprising: calculating an expected value of the risk at an acquisition time one time after the certain acquisition when the index was calculated at the certain acquisition time based on a pair of the index calculated at the certain acquisition time and the risk at an acquisition time one time after the certain acquisition time; calculating the risk by back-calculating a recurrence formula using the index from a final acquisition time when all of the elements are acquired, and calculating the risk of not classifying the sequence data into the certain acquisition time based on the expected value; and calculating the threshold based on the risk. [Supplementary Note 15] An information processing method for calculating the threshold used by an information processing device comprising: acquisition means for sequentially acquiring a finite number of elements included in sequence data; index calculation means for calculating, for each acquisition of the element, an index indicating to which of a plurality of classes the sequence data belongs; classification means for classifying the sequence data into one of the plurality of classes by comparing the index with a threshold; and risk calculation means for calculating risks in the case of classifying and not classifying the sequence data at each acquisition of the element, wherein the information processing method includes: calculating an expected value of the risk at an acquisition time one time after the certain acquisition when the index was calculated at the certain acquisition time based on a pair of the index calculated at the certain acquisition time and the risk at an acquisition time one time after the certain acquisition time; calculating the risk by back-calculating a recurrence formula using the index from a final acquisition time when all of the elements are acquired, based on the expected value; and calculating the threshold based on the risk.

[0092] This disclosure may be modified as appropriate within the scope that does not contradict the gist or idea of ​​the invention that can be read from the claims and the entire specification, and information processing devices, information processing methods, and recording media that involve such modifications are also included in the technical idea of ​​this disclosure.

[0093] Information processing devices 1, 2, 3 Acquisition units 111, 211 Index calculation units 112, 212 Classification units 113, 213 Risk calculation units 114, 214, 314 Expected value calculation units 1141, 2141, 3141 Threshold calculation units 115, 215 Likelihood ratio calculation unit 2121 Posterior probability conversion unit 2122 Index storage unit 2123 Termination risk calculation unit 2142 Continuation risk calculation unit 2143 Minimum risk storage unit 2144 Generation unit 3145

Claims

1. An acquisition means for sequentially acquiring a finite number of elements included in series data; an index calculation means for calculating an index indicating to which of a plurality of classes the series data belongs each time the element is acquired; a classification means for classifying the series data into one of the plurality of classes by comparing the index with a threshold value; a risk calculation means for calculating the risk of classifying and not classifying the series data at each acquisition of the element by calculating a recurrence formula using the index in reverse from the final acquisition for acquiring all of the elements; an expected value calculation means for calculating an expected value of the risk; and a threshold value calculation means for calculating the threshold value based on the risk, wherein the expected value calculation means calculates an expected value of the risk at the next acquisition after a certain acquisition when the index calculated at the certain acquisition is calculated, based on a pair of the index calculated at a certain acquisition of the element and the risk at the next acquisition after the certain acquisition, and the risk calculation means calculates the risk of not classifying the series data at the certain acquisition based on the expected value. An information processing apparatus.

2. The information processing apparatus according to claim 1, wherein the expected value calculation means inserts a straight line into at least one of the plurality of pairs and calculates the expected value based on the straight line.

3. The information processing apparatus according to claim 1, wherein the expected value calculation means forms a convex hull of the pair based on at least one of the plurality of pairs and calculates the expected value based on the convex hull.

4. The information processing apparatus according to claim 1, further comprising a generation means for generating an expected value output mechanism that outputs the expected value when the index calculated at a certain acquisition is input based on the plurality of pairs, and the expected value calculation means calculates the expected value using the expected value output mechanism.

5. The information processing apparatus according to claim 4, wherein the generation means inserts a straight line into at least one of the plurality of pairs and generates the expected value output mechanism based on the straight line.

6. The information processing apparatus according to claim 4, wherein the generation means forms a convex hull of the pair based on at least one of the plurality of pairs and generates the expected value output mechanism based on the convex hull.

7. The information processing apparatus according to claim 4, wherein the generation means generates the expected value output mechanism that outputs zero when the minimum value and the maximum value that the index can take are input.

8. The information processing apparatus according to claim 4, wherein the generation means generates a convex upward function as the expected value output mechanism.

9. The risk calculation means calculates an end risk, which is a risk when classifying the series data in a certain acquisition round based on the index, and a continuation risk, which is a risk when continuing to acquire the next element without classifying the series data in a certain acquisition round. The threshold calculation means calculates the threshold based on the index at which the difference between the continuation risk and the end risk is minimized. The information processing apparatus according to claim 1.

10. The information processing apparatus according to claim 9, wherein the threshold calculation means calculates the threshold based on the intersection point of the continuation risk and the end risk.

11. The information processing apparatus according to claim 9, wherein the expected value calculation means calculates the expected value based on a pair of the index calculated in a certain acquisition round and the minimum risk, which is the smaller one of the continuation risk and the end risk in the next acquisition round.

12. The information processing apparatus according to claim 11, wherein the risk calculation means calculates the continuation risk corresponding to each acquisition round by performing a backward calculation of the recurrence formula from the final acquisition round after setting the value of the end risk in the final acquisition round as the value of the minimum risk in the final acquisition round.

13. The information processing apparatus according to claim 1, wherein the index is at least one of a likelihood ratio indicating the likelihood that the series data belongs to a certain class among the plurality of classes, and a posterior probability corresponding to the likelihood ratio.

14. An information processing method for calculating a threshold value used by an information processing apparatus including: an acquisition unit that sequentially acquires a finite number of elements included in series data; an index calculation unit that calculates an index indicating to which of a plurality of classes the series data belongs each time the element is acquired; a classification unit that classifies the series data into one of the plurality of classes by comparing the index with a threshold value; and a risk calculation unit that calculates a risk when classifying the series data and when not classifying it at each acquisition of the element, the method including: calculating an expected value of the risk at the next acquisition after a certain acquisition when the index is calculated at the certain acquisition, based on a pair of the index calculated at the certain acquisition of the element and the risk at the next acquisition after the certain acquisition; calculating, in the calculation of the risk by back-calculating a recurrence formula using the index from a final acquisition for acquiring all of the elements, the risk when not classifying the series data at the certain acquisition based on the expected value; and calculating the threshold value based on the risk.

15. A recording medium having recorded thereon a computer program for causing a computer to execute an information processing method for calculating a threshold value used by an information processing apparatus including: an acquisition unit that sequentially acquires a finite number of elements included in series data; an index calculation unit that calculates an index indicating to which of a plurality of classes the series data belongs each time the element is acquired; a classification unit that classifies the series data into one of the plurality of classes by comparing the index with a threshold value; and a risk calculation unit that calculates a risk when classifying the series data and when not classifying it at each acquisition of the element, the method including: calculating an expected value of the risk at the next acquisition after a certain acquisition when the index is calculated at the certain acquisition, based on a pair of the index calculated at the certain acquisition of the element and the risk at the next acquisition after the certain acquisition; calculating, in the calculation of the risk by back-calculating a recurrence formula using the index from a final acquisition for acquiring all of the elements, the risk when not classifying the series data at the certain acquisition based on the expected value; and calculating the threshold value based on the risk.

Images