Information processing device and information processing method

Abstract

An information processing device 10 comprises: a normal approximation unit that performs approximation processing for approximating an estimate distribution with a normal distribution; a deviation evaluation unit that evaluates a deviation which occurs in the approximation processing; and a data evaluation unit that evaluates data pertaining to calculation of an estimate from the result of the approximation processing and the deviation.

Description

[Technical Field]

[0001] The present invention relates to an information processing device and an information processing method. [Background technology]

[0002] An example of a sample size determination method is described in Non-Patent Document 1. In this method, the specified errors ε1, ε2 (>0), the confidence rate (confidence level) 1-δ, and the variance σ 2 With respect to the finite samples x1, ,x n is the mean μ and variance σ 2 The method determines the sample size n required for the sample mean (1) to satisfy the inequality (2) with a probability of 1-δ or greater, as the smallest natural number greater than or equal to the value (3). δ / 2 is the upper δ / 2 point of the standard normal distribution. min{ε1,ε2} is the minimum value of ε1,ε2.

[0003]

number

[0004] [Non-Patent Document 1] Yasushi Nagata, "How to Determine Sample Size," Asakura Publishing, September 20, 2003, pp. 182-183 Summary of the Invention [Problem to be solved by the invention]

[0005] The scope of application of the sample size determination method described in Non-Patent Document 1 is limited to normal distributions. The reason is that if properties inherent to normal distributions, such as reproducibility, cannot be assumed, the distribution of the estimator cannot be reduced to a known distribution having the sample size n as a parameter.

[0006] An object of the present invention is to provide an information processing device and an information processing method that can determine sample size and the like even when normality cannot be assumed. [Means for solving the problem]

[0007] The information processing device according to one aspect of the present invention is Probability of following normal approximation means for performing approximation processing to approximate the distribution with a normal distribution; The deviation is the difference between the probability that the value obtained by subtracting the estimated value from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated value from the true value is equal to or less than the right-side error value, and the value obtained by approximating this probability using the asymptotic normality of the probability distribution. a deviation evaluation unit for performing a deviation evaluation process for evaluating a deviation occurring in the approximation process; and a deviation evaluation unit for performing a deviation evaluation process for evaluating a deviation occurring in the approximation process based on the result of the approximation process and the deviation. , a sample size determination means for determining the sample size for calculating the estimator; and The sample size determination means determines the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined reliability rate as the sample size. .

[0008] In one aspect of the present invention, an information processing method includes: Probability of following An approximation process is performed to approximate the distribution with a normal distribution. The deviation is the difference between the probability that the value obtained by subtracting the estimated value from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated value from the true value is equal to or less than the right-side error value, and the value obtained by approximating this probability using the asymptotic normality of the probability distribution. The deviation caused by the approximation process is evaluated, and the result of the approximation process and the deviation are compared. A sample size for calculating the estimator is determined, and the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined confidence rate is determined as the sample size. .

[0009] An information processing program according to one aspect of the present invention includes: Probability of following An approximation process is performed to approximate the distribution with a normal distribution. The deviation is the difference between the probability that the value obtained by subtracting the estimated value from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated value from the true value is equal to or less than the right-side error value, and the value obtained by approximating this probability using the asymptotic normality of the probability distribution. The deviation caused by the approximation process is evaluated, and the result of the approximation process and the deviation are compared. A sample size for calculating the estimator is determined, and the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined confidence rate is determined as the sample size. . [Effects of the Invention]

[0010] According to the present invention, it is possible to determine the sample size required for calculating an estimator for general distributions, not limited to normal distributions, because normal approximation and deviation evaluation enable the evaluation of the distribution of the estimator without using properties specific to normal distributions. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a block diagram illustrating an example of the configuration of a sample size determination device. [Figure 2] 1 is a flowchart illustrating the operation of the sample size determination device. [Figure 3]FIG. 1 is a block diagram illustrating an example of the configuration of a reliability rate determination device. [Figure 4] 10 is a flowchart showing the operation of the reliability rate determination device. [Figure 5] FIG. 1 is a block diagram showing an example of the configuration of an error determination device. [Figure 6] 4 is a flowchart illustrating the operation of the error determination device. [Figure 7] FIG. 1 is a block diagram showing a first embodiment. [Figure 8] FIG. 10 is a block diagram showing a second embodiment. [Figure 9] FIG. 10 is a block diagram showing a third embodiment. [Figure 10] FIG. 10 is a block diagram showing a fourth embodiment. [Figure 11] FIG. 10 is a block diagram showing a fifth embodiment. [Figure 12] FIG. 1 is a block diagram illustrating an example of a computer having a CPU. [Figure 13] FIG. 1 is a block diagram showing a main part of an information processing device. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0013] [First embodiment] [Configuration Description] Fig. 1 is a block diagram showing an example of the configuration of a sample size determination device as a first embodiment of an information processing device. As shown in Fig. 1, the sample size determination device includes an estimator type determination unit 100, a left-side error input unit 110, a right-side error input unit 111, a reliability factor input unit 120, a standard deviation lower-bound input unit 130, a standard deviation upper-bound input unit 131, a third-order moment upper-bound input unit 132, a fourth-order moment lower-bound input unit 133, a fourth-order moment upper-bound input unit 134, a sixth-order moment upper-bound input unit 135, a left-side distribution function lower-bound input unit 136, a left-side distribution function upper-bound input unit 137, a right-side distribution function lower-bound input unit 138, a right-side distribution function upper-bound input unit 139, and a sample size evaluation unit 140.

[0014] The left-side error input unit 110, the right-side error input unit 111, the reliability factor input unit 120, the standard deviation lower bound input unit 130, the standard deviation upper bound input unit 131, the third-order moment upper bound input unit 132, the fourth-order moment lower bound input unit 133, the fourth-order moment upper bound input unit 134, the sixth-order moment upper bound input unit 135, the left-side distribution function lower bound input unit 136, the left-side distribution function upper bound input unit 137, the right-side distribution function lower bound input unit 138, and the right-side distribution function upper bound input unit 139 input the left-side error, the right-side error, the reliability factor, the standard deviation lower bound, the standard deviation upper bound, the third-order moment upper bound, the fourth-order moment lower bound, the fourth-order moment upper bound, the sixth-order moment upper bound, the left-side distribution function lower bound, the left-side distribution function upper bound, the right-side distribution function lower bound, and the right-side distribution function upper bound, respectively.

[0015] The estimator type determination unit 100 determines the type of the input estimator. That is, the estimator type determination unit 100 determines the type of estimator to be calculated. The type of estimator is a sample mean, an unbiased variance, or a sample quantile. Therefore, the estimator type determination unit 100 receives data that can identify the sample mean, the unbiased variance, or the sample quantile.

[0016] The sample size evaluation unit 140 includes a normal approximation unit 141 , a deviation evaluation unit 142 , and a size determination unit 143 .

[0017] Assuming that an input type of estimator is calculated from a sample having a fixed sample size, the normal approximation unit 141 calculates a value (hereinafter also referred to as "asymptotic approximation probability") that approximates the probability that the value obtained by subtracting the estimator from the true value, which is the value to be estimated, for the fixed sample size is equal to or less than the left-side error value and the value obtained by subtracting the estimator from the true value is equal to or less than the right-side error value, using the asymptotic normality of the estimator distribution. That is, the normal approximation unit 141 performs an approximation process that approximates the estimator distribution with a normal distribution. The estimator distribution is a probability distribution that the estimator follows.

[0018] The deviation evaluation unit 142 evaluates the deviation that occurs in the approximation process by the normal approximation unit 141. Specifically, assuming a case where an input type of estimator is calculated from a sample having a fixed sample size, the deviation evaluation unit 142 calculates the upper bound of the absolute value of the difference (hereinafter also referred to as "deviation") between the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the value of the left-side error and the value obtained by subtracting the estimator from the true value is equal to or less than the value of the right-side error, for a fixed sample size, and the value obtained by approximating this probability using the asymptotic normality of the estimator distribution.

[0019] The size determination unit 143 evaluates data related to the calculation of the estimator from the result of the approximation process by the normal approximation unit 141, i.e., the asymptotic approximation probability and the deviation calculated by the deviation evaluation unit 142. For example, the size determination unit 143 sets the initial value of the sample size n to 2 and repeats the following procedure until a sample size that satisfies a predetermined condition is determined. Specifically, for the sample size n, the value calculated by the deviation evaluation unit 142 is subtracted from the value calculated by the normal approximation unit 141, and if this value is equal to or greater than the reliability rate, the sample size required for estimator calculation is determined to be n at that time. If not, the sample size is updated to n+1.

[0020] [Explanation of operation] Next, the operation of the sample size determination device of this embodiment will be described with reference to the flowchart of FIG.

[0021] First, the estimator type determining unit 100 determines the type of the input calculated estimator (the estimator to be calculated) (step S101).

[0022] The sample size evaluation unit 140 receives each parameter (step S102). In this embodiment, in the process of step S102, the sample size evaluation unit 140 receives the left error ε1 and the right error ε2 via the left error input unit 110 and the right error input unit 111. In addition, sample size evaluation unit 140 inputs the standard deviation lower bound σ1, the standard deviation upper bound σ2, the third-moment upper bound A, the fourth-moment lower bound B, the fourth-moment upper bound C, the sixth-moment upper bound D, the left-side distribution function lower bound l1, the left-side distribution function upper bound u1, the right-side distribution function lower bound l2, and the right-side distribution function upper bound u2 via standard deviation lower bound input unit 130, standard deviation upper bound input unit 131, third-moment upper bound input unit 132, fourth-moment lower bound input unit 133, fourth-moment upper bound input unit 134, sixth-moment upper bound input unit 135, left-side distribution function lower bound input unit 136, left-side distribution function upper bound input unit 137, right-side distribution function lower bound input unit 138, and right-side distribution function upper bound input unit 139.

[0023] Each parameter is set to satisfy the following condition: for a random number X that follows a distribution that generates an independent and identically distributed finite sample used to calculate the estimator, the expected value is μ = E[X], the standard deviation is σ (see equation (4)), the cumulative distribution function is F, and the 100p% point of F is ξ p =inf{t|F(t)≧p}, the following conditions are met. However, 0 <p<1である。

[0024]

number

[0025] σ1≦σ≦σ2(5) E[|(X-μ)| 3 ]≦A (6) B≦E[|(X-μ) 2 -σ 2 | 2 ]≦C (7) E[|(X-μ) 2 -σ 2 | 3 ]≦D (8) l1≦F(ξ p -ε1) ≤ u1(9) l2≦F(ξ p+ε2)≦u2(10)

[0026] The sample size evaluation unit 140 also receives the reliability rate 1-δ via the reliability rate input unit 120 (step S102). The reliability rate 1-δ corresponds to the probability (proportion) that the estimator will adequately estimate the true value.

[0027] The size determination unit 143 sets 2 as the initial value of the sample size n (step S103). The normal approximation unit 141 calculates a value (asymptotic approximation probability) P , which is an approximation of the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimator from the true value is equal to or less than the right-side error value, by the asymptotic normality of the estimator distribution. n (Step S104). That is, the normal approximation unit 141 performs approximation processing.

[0028] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is the sample mean, the normal approximation unit 141 calculates P n The following equation (11) is used: Φ is the cumulative distribution function of the standard normal distribution.

[0029]

number

[0030] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is unbiased variance, the normal approximation unit 141 calculates P n As such, the following equation (12) is used.

[0031]

number

[0032] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is the 100p% point of the sample, which is an example of the sample quantile, the normal approximation unit 141 calculates P nThe following equation (13) is used as the equation: Note that equations (11) to (13) each correspond to an approximation equation.

[0033]

number

[0034] In formula (13), the values ​​represented by the following symbols indicate the maximum integers not exceeding np.

[0035]

number

[0036] The deviation evaluation unit 142 calculates an upper bound of the absolute value (hereinafter also referred to as "normal approximation error") E between the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimator from the true value is equal to or less than the right-side error value, and the value obtained by approximating this probability using the asymptotic normality of the estimator distribution. n is calculated (step S105). n corresponds to the deviation that occurs in the approximation process by the normal approximation unit 141. n The process of calculating the difference is also called a deviation evaluation process.

[0037] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is the sample mean, the deviation evaluation unit 142 performs the process of step S105 by calculating E n As such, the following equation (14) is used.

[0038]

number

[0039] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is unbiased variance, the deviation evaluation unit 142 performs the process of step S105 by calculating E n As such, the following equation (15) is used.

[0040]

number

[0041] In this embodiment, when the estimator type determination unit 100 determines that the type of the calculated estimator is the 100p% point of the sample, the deviation evaluation unit 142 performs the process of step S105 by using E n The following equation (16) is used as the above equation. Note that equations (14) to (16) each correspond to an evaluation equation (deviation evaluation equation). In equations (14) to (16), C0=0.4748.

[0042]

number

[0043] The size determination unit 143 determines whether P n -E n The value of P is calculated (step S106). n -E n If P is less than the reliability rate 1-δ, the size determination unit 143 increments the value of the sample size by 1 and returns to the state of repeating the processes from step S104 onwards (step S107). n -E n When the reliability rate is equal to or greater than 1-δ, the size determination unit 143 determines the sample size n at that time as the sample size required for calculating the estimator of the determined type (step S108).

[0044] [Effect description] In this embodiment, the sample size determination device can determine the sample size required to calculate the estimator without assuming normality of the distribution followed by the samples. Specifically, the sample size determination device can determine the sample size required to ensure that the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the input left-hand error and that the value obtained by subtracting the estimator from the true value is equal to or less than the input right-hand error is equal to or greater than the input confidence rate. The reason why it is not necessary to assume normality of the distribution followed by the samples is that the processing by the normal approximation unit 141 and the deviation evaluation unit 142 makes it possible to evaluate the distribution of the estimator without using properties inherent to normal distributions.

[0045] [Second embodiment] [Configuration Description] Next, a reliability rate determination device as a second embodiment of the information processing device will be described.

[0046] 3 is a block diagram showing an example of the configuration of a reliability rate determination device. As shown in Fig. 3, the reliability rate determination device of the second embodiment includes an estimator type determination unit 100, a left-side error input unit 110, a right-side error input unit 111, a sample size input unit 121, a standard deviation lower-bound input unit 130, a standard deviation upper-bound input unit 131, a third-order moment upper-bound input unit 132, a fourth-order moment lower-bound input unit 133, a fourth-order moment upper-bound input unit 134, a sixth-order moment upper-bound input unit 135, a left-side distribution function lower-bound input unit 136, a left-side distribution function upper-bound input unit 137, a right-side distribution function lower-bound input unit 138, a right-side distribution function upper-bound input unit 139, and a reliability rate evaluation unit 150.

[0047] The configurations and functions of the estimator type determination unit 100, left-side error input unit 110, right-side error input unit 111, standard deviation lower bound input unit 130, standard deviation upper bound input unit 131, third-order moment upper bound input unit 132, fourth-order moment lower bound input unit 133, fourth-order moment upper bound input unit 134, sixth-order moment upper bound input unit 135, left-side distribution function lower bound input unit 136, left-side distribution function upper bound input unit 137, right-side distribution function lower bound input unit 138, and right-side distribution function upper bound input unit 139 are the same as those in the first embodiment. The sample size input unit 121 inputs a sample size used for calculating the estimator.

[0048] The reliability rate evaluation unit 150 includes a normal approximation unit 151 , a deviation evaluation unit 152 , and a reliability rate determination unit 153 .

[0049] Assuming that an estimator of the type input to the estimator type determination unit 100 is calculated for the sample size input to the sample size input unit 121, the normal approximation unit 151 calculates a value (i.e., asymptotic approximation probability) obtained by approximating the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the left-side error value and that the value obtained by subtracting the estimator from the true value is equal to or less than the right-side error value, using the asymptotic normality of the estimator distribution. That is, the normal approximation unit 151 approximates the estimator distribution with a normal distribution. Note that in this embodiment as well, the type of estimator is the sample mean, unbiased variance, or sample quantile.

[0050] The deviation evaluation unit 152 evaluates the deviation occurring in the approximation process by the normal approximation unit 151. Specifically, assuming that an estimator of the type input to the estimator type determination unit 100 is calculated for the sample size input to the sample size input unit 121, the deviation evaluation unit 152 calculates the upper bound of the absolute value (i.e., normal approximation error) of the difference (i.e., deviation) between the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimator from the true value is equal to or less than the right-side error value, and the value obtained by approximating this probability using the asymptotic normality of the estimator distribution. The reliability rate determination unit 153 determines the value obtained by subtracting the value calculated by the deviation evaluation unit 152 from the value calculated by the normal approximation unit 151 as the reliability rate.

[0051] [Explanation of operation] Next, the operation of the reliability rate determination device of this embodiment will be described with reference to the flowchart of FIG.

[0052] First, the estimator type determination unit 100 determines the type of the input calculated estimator (step S101). The reliability rate evaluation unit 150 inputs each parameter (step S112), similarly to the sample size evaluation unit 140 in the first embodiment (see step S102 in FIG. 2). However, while in the first embodiment the sample size evaluation unit 140 received the reliability rate 1-δ via the reliability rate input unit 120, in this embodiment the reliability rate evaluation unit 150 inputs the sample size via the sample size input unit 121 in the processing of step S112.

[0053] As in the first embodiment, each parameter satisfies the conditions of the above formulas (5) to (10).

[0054] The normal approximation unit 151, like the normal approximation unit 141 in the first embodiment, calculates the asymptotic approximation probability P n (Step S104). The deviation evaluation unit 152, like the deviation evaluation unit 142 in the first embodiment, calculates the normal approximation error E n (Step S105). Note that, unlike the normal approximation unit 141 and the deviation evaluation unit 142 in the first embodiment, the normal approximation unit 151 and the deviation evaluation unit 152 in this embodiment calculate the asymptotic approximation probability P n and the normal approximation error E n Calculate.

[0055] The reliability rate determination unit 153 determines the P calculated by the normal approximation unit 151. n The deviation evaluation unit 152 calculates E n The value obtained by subtracting the above is determined as the reliability rate (step S116).

[0056] [Effect description] In this embodiment, the reliability rate determination device can determine the lower bound of the probability that, when the estimator is calculated from samples of an input sample size, the value obtained by subtracting the estimator from the true value is equal to or less than the input left-side error and the value obtained by subtracting the estimator from the true value is equal to or less than the input right-side error, without assuming normality of the distribution that the samples follow. The reason why it is not necessary to assume normality of the distribution that the samples follow is that the processing by the normal approximation unit 151 and the deviation evaluation unit 152 makes it possible to evaluate the distribution of the estimator without using properties inherent to normal distributions.

[0057] [Third embodiment] [Configuration Description] Next, an error determination device as a third embodiment of the information processing device will be described.

[0058] Fig. 5 is a block diagram showing an example of the configuration of an error determination device. As shown in Fig. 5, the error determination device of the third embodiment includes an estimator type determination unit 100, a reliability rate input unit 120, a sample size input unit 121, a standard deviation lower bound input unit 130, a standard deviation upper bound input unit 131, a third-order moment upper bound input unit 132, a fourth-order moment lower bound input unit 133, a fourth-order moment upper bound input unit 134, a sixth-order moment upper bound input unit 135, a left-side distribution function lower bound input unit 136, a left-side distribution function upper bound input unit 137, a right-side distribution function lower bound input unit 138, a right-side distribution function upper bound input unit 139, an error evaluation unit 160, a left-side error initial value input unit 165, a right-side error initial value input unit 166, a left-side error increment input unit 167, and a right-side error increment input unit 168.

[0059] The configurations and functions of the estimator type determination unit 100, the reliability rate input unit 120, the sample size input unit 121, the standard deviation lower bound input unit 130, the standard deviation upper bound input unit 131, the third-order moment upper bound input unit 132, the fourth-order moment lower bound input unit 133, the fourth-order moment upper bound input unit 134, the sixth-order moment upper bound input unit 135, the left-side distribution function lower bound input unit 136, the left-side distribution function upper bound input unit 137, the right-side distribution function lower bound input unit 138, and the right-side distribution function upper bound input unit 139 are the same as those in the first or second embodiment.

[0060] The left error initial value input unit 165 inputs an initial value ε1 of the left error. The right error initial value input unit 166 inputs an initial value ε2 of the right error. The left error increment input unit 167 inputs an increment η1 of the left error. It inputs an increment η2 of the right error. The left error corresponds to an error when the estimated amount deviates to the left of the true value. The right error corresponds to an error when the estimated amount deviates to the right of the true value.

[0061] The error evaluation unit 160 includes a normal approximation unit 161 , a deviation evaluation unit 162 , and an error determination unit 163 .

[0062] Assuming that an estimator of a type input to the estimator type determination unit 100 is calculated from a sample of a sample size input to the sample size input unit 121 for a fixed left-side error and a fixed right-side error, the normal approximation unit 161 calculates a value (i.e., an asymptotic approximation probability) that approximates the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the fixed left-side error and the value obtained by subtracting the estimator from the true value is equal to or less than the fixed right-side error, using the asymptotic normality of the estimator distribution. That is, the normal approximation unit 161 approximates the estimator distribution with a normal distribution. Note that in this embodiment, the type of estimator is, for example, the sample mean, unbiased variance, or sample quantile.

[0063] The deviation evaluation unit 162 evaluates the deviation occurring in the approximation process by the normal approximation unit 161. Specifically, assuming a case where an estimator of a type input to the estimator type determination unit 100 is calculated from a sample of a sample size input to the sample size input unit 121 for a fixed left-side error and a fixed right-side error, the deviation evaluation unit 162 calculates an upper bound of the absolute value (i.e., normal approximation error) of the difference (i.e., deviation) between the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the fixed left-side error and the value obtained by subtracting the estimator from the true value is equal to or less than the fixed right-side error, and the value obtained by approximating this probability using the asymptotic normality of the estimator distribution.

[0064] The error determination unit 163 increases the fixed value of the left error by η1 and increases the fixed value of the right error by η2 until the value obtained by subtracting the value calculated by the deviation evaluation unit 162 from the value calculated by the normal approximation unit 161 becomes equal to or greater than the value input to the reliability rate input unit 120. Then, the error determination unit 163 determines the left error and right error when a predetermined condition is satisfied as errors.

[0065] [Explanation of operation] Next, the operation of the error determination device of this embodiment will be described with reference to the flowchart of FIG.

[0066] First, the estimator type determining unit 100 determines the type of the input calculated estimator (step S101).

[0067] The error evaluation unit 160 inputs each parameter (step S122). In this embodiment, in the processing of step S122, the error evaluation unit 160 inputs the left-side error initial value ε1 and the right-side error initial value ε2 via the left-side error initial value input unit 165 and the right-side error initial value input unit 166. The error evaluation unit 160 also inputs the standard deviation lower bound σ1, the standard deviation upper bound σ2, the third-order moment upper bound A, the fourth-order moment lower bound B, the fourth-order moment upper bound C, and the sixth-order moment upper bound D via the standard deviation lower bound input unit 130, the standard deviation upper bound input unit 131, the third-order moment upper bound input unit 132, the fourth-order moment lower bound input unit 133, the fourth-order moment upper bound input unit 134, and the sixth-order moment upper bound input unit 135.

[0068] In addition, in the processing of step S122, the error evaluation unit 160 inputs the initial value ε1 of the left error, the initial value ε2 of the right error, the increase width η1 of the left error, and the increase width η2 of the right error via the initial value input unit 165 of the left error, the initial value input unit 166 of the right error, the increase width input unit 167 of the left error, and the increase width input unit 168 of the right error.

[0069] Each parameter satisfies the conditions of the above formulas (5) to (8).

[0070] In addition, in the first embodiment, the sample size evaluation unit 140 receives the reliability rate 1-δ via the reliability rate input unit 120, and in the second embodiment, the reliability rate evaluation unit 150 receives the sample size via the sample size input unit 121. However, in this embodiment, the error evaluation unit 160 inputs both the reliability rate 1-δ and the sample size in the processing of step S122.

[0071] The error evaluation unit 160 inputs the left-hand distribution function lower bound l1, the left-hand distribution function upper bound u1, the right-hand distribution function lower bound l2, and the right-hand distribution function upper bound u2 via the left-hand distribution function lower bound input unit 136, the left-hand distribution function upper bound input unit 137, the right-hand distribution function lower bound input unit 138, and the right-hand distribution function upper bound input unit 139 (step S123).

[0072] The conditions of the above equations (9) to (10) are satisfied for each parameter input to the error evaluation unit 160 via the left-side distribution function lower bound input unit 136, the left-side distribution function upper bound input unit 137, the right-side distribution function lower bound input unit 138, and the right-side distribution function upper bound input unit 139.

[0073] Similar to the normal approximation unit 141 in the first embodiment, the normal approximation unit 161 calculates the asymptotic approximation probability P n is calculated (step S104).

[0074] The deviation evaluation unit 162, like the deviation evaluation unit 142 in the first embodiment, calculates the normal approximation error E n is calculated (step S105).

[0075] The error determination unit 163 determines P n -E n (Step S106). The error determination unit 163 calculates the value of P n -E nIf the reliability rate is less than 1-δ, the left error ε1 and the right error ε2 are increased by η1 and η2, respectively. Then, the process returns to the state where the processes from step S123 onward are repeated (step S127). n -E n becomes equal to or greater than the reliability rate 1-δ, the error determiner 163 determines the left error ε1 and the right error ε2 at that time as the errors when the determined type of estimated quantity is calculated (step S128).

[0076] [Effect description] In this embodiment, the error determination device can determine the left-hand error and the right-hand error without assuming normality of the distribution that the samples follow so that the probability that the value obtained by subtracting the estimator from the true value is equal to or less than the left-hand error and that the value obtained by subtracting the estimator from the true value is equal to or less than the right-hand error is equal to or greater than the confidence rate. The reason why it is not necessary to assume normality of the distribution that the samples follow is that the distribution of the estimator can be evaluated by the processing of the normal approximation unit 161 and the deviation evaluation unit 162 without using properties inherent to the normal distribution. [Example]

[0077] Next, a specific example will be described.

[0078] [First Example] 7 is a block diagram showing Example 1. Example 1 is an example of the first embodiment.

[0079] As shown in FIG. 7, the device of the first example includes the sample size assessment unit 140 in the first embodiment, a dataset input unit 400, a sample utilization determination unit 410, and a model construction unit 420.

[0080] The dataset input unit 400 inputs a dataset consisting of multiple samples, each of which may have a different sample size. The sample size evaluation unit 140 determines the sample size required to calculate the sample mean, unbiased variance, or sample quantile. The sample utilization determination unit 410 extracts a number of samples from the dataset that is equal to or greater than the sample size determined by the sample size evaluation unit 140.

[0081] The model construction unit 420 constructs a model by machine learning using the sample mean, unbiased variance, or sample quantile as feature values. In order to reduce the dispersion of the feature value distribution and perform robust learning, the model construction unit 420 uses a dataset consisting of only samples of a sufficient size extracted by the sample utilization determination unit 410 for model training. Note that, although the selection of data to be used for model construction has been described in this embodiment, the results of the sample utilization determination unit 410 can also be used to select test data for the constructed model.

[0082] [Second Example] 8 is a block diagram showing Example 2. Example 2 is an example of the second embodiment.

[0083] As shown in FIG. 8, the device of the second example includes the reliability rate evaluation unit 150 in the second embodiment, a dataset input unit 500, a sample usage determination unit 510, a model construction unit 520, and a threshold input unit 530.

[0084] The dataset input unit 500 inputs a dataset consisting of multiple samples, each of which may have a different sample size. The confidence rate evaluation unit 150 determines a confidence rate when the sample mean, unbiased variance, or sample quantile is calculated for each sample in the dataset. The sample utilization determination unit 510 compares the confidence rate with a threshold input to the threshold input unit 530. The sample utilization determination unit 510 extracts only samples from the dataset whose confidence rate is equal to or greater than the threshold. The model construction unit 520 constructs a model using machine learning, using the sample mean, unbiased variance, or sample quantile as a feature. To reduce the dispersion of the feature distribution and perform robust learning, the model construction unit 520 uses a dataset consisting only of samples extracted by the sample utilization determination unit 510 from which features can be extracted with sufficient confidence rate for model training. Note that while this embodiment describes the selection of data to be used in model construction, the results of the sample utilization determination unit 510 can also be used to select test data for the constructed model.

[0085] [Third Example] 9 is a block diagram showing a third example, which is also an example of the second embodiment.

[0086] As shown in FIG. 9, the device of the third example includes the reliability rate evaluation unit 150 in the second embodiment, a data set input unit 501, a weight calculation unit 540, and a model construction unit 550.

[0087] The dataset input unit 501 inputs a dataset consisting of multiple samples with a common sample size. The reliability evaluation unit 150 determines a reliability rate when the sample mean, unbiased variance, or sample quantile is calculated for a sample size common to each sample in the dataset. The weight calculation unit 540 determines a weight to assign to each estimator depending on the level of the determined reliability rate. The model construction unit 550 assigns the weight determined by the weight calculation unit 540 to the feature values, i.e., the sample mean, unbiased variance, or sample quantile, thereby constructing a model that emphasizes feature values ​​with high reliability rates. Note that, although the present embodiment has described the selection of data used to construct a model, the results of the weight calculation unit 540 can also be used when using test data for the constructed model.

[0088] [Fourth Example] 10 is a block diagram showing a fourth example, which is an example of the third embodiment.

[0089] As shown in FIG. 10, the device of the fourth example includes the error evaluation unit 160 in the third embodiment, a data set input unit 600, a sample usage determination unit 610, a model construction unit 620, and a threshold input unit 630.

[0090] The dataset input unit 600 inputs a dataset consisting of multiple samples, each of which may have a different sample size. The error evaluation unit 160 determines the error when calculating the sample mean, unbiased variance, or sample quantile for each sample in the dataset. The sample utilization determination unit 610 compares the error with a threshold input to the threshold input unit 630. The sample utilization determination unit 610 extracts only samples from the dataset whose error is equal to or less than the threshold. The model construction unit 620 constructs a model using machine learning, using the sample mean, unbiased variance, or sample quantile as a feature. To reduce the dispersion of the feature distribution and perform robust learning, the model construction unit 620 uses a dataset consisting only of samples from which features with sufficiently small errors from the true value extracted by the sample utilization determination unit 610 can be extracted for model training. Note that while this embodiment describes the selection of data used to construct a model, the results of the sample utilization determination unit 610 can also be used to select test data for the constructed model.

[0091] [Fifth Example] 11 is a block diagram showing a fifth example, which is also an example of the third embodiment.

[0092] As shown in FIG. 11, the device of the fifth example includes the error evaluation unit 160 in the third embodiment, a data set input unit 601, a weight calculation unit 640, and a model construction unit 650.

[0093] The dataset input unit 601 inputs a dataset consisting of multiple samples with a common sample size. The error evaluation unit 160 determines the error when calculating the sample mean, unbiased variance, or sample quantile for a sample size common to each sample in the dataset. The weight calculation unit 640 determines the weight to assign to each estimator depending on the smallness of the determined error. The model construction unit 650 assigns the weight determined by the weight calculation unit 640 to the feature values, namely the sample mean, unbiased variance, or sample quantile, thereby enabling model construction that emphasizes feature values ​​with small errors from the true value. Note that, although the present embodiment has described the selection of data used to construct a model, the results of the weight calculation unit 640 can also be used when using test data for the constructed model.

[0094] The device of the above embodiment can be applied to applications such as improving a model by excluding samples with an insufficient sample size from a training dataset when constructing a machine learning model that includes a sample mean, unbiased variance, or sample quantile as a feature. Furthermore, the information processing device of the above embodiment can also be applied to applications such as determining in advance the sample size required for calculation and using it as a reference for experimental planning for data acquisition when data analysis is expected to be performed using a sample mean, unbiased variance, or sample quantile.

[0095] Each component in the above embodiments and examples can be configured as a single piece of hardware, or as a single piece of software. Each component can also be configured as multiple pieces of hardware, or as multiple pieces of software. Furthermore, some of the components can be configured as hardware, and the other parts can be configured as software.

[0096] Each function (each process) in the above-described embodiments can be realized by a computer having a processor such as a CPU (Central Processing Unit), a memory, etc. For example, a program for implementing the method (process) in the above-described embodiments may be stored in a storage device (storage medium), and each function may be realized by executing the program stored in the storage device by a CPU.

[0097] FIG. 12 is a block diagram showing an example of a computer having a CPU. The computer is implemented in the devices of the above-described embodiments and examples. The CPU 1000 executes processing according to a program stored in the storage device 1001, thereby realizing the functions of the above-described embodiments and examples. For example, the CPU 1000 can realize the functions of the sample size determination device, the reliability rate determination device, and the error determination device shown in FIGS. 1, 3, and 5. In other words, the CPU 1000 can realize the functions of the sample size evaluation unit 140 and the functions of each input unit shown in FIG. 1. The CPU 1000 can also realize the functions of the reliability rate determination device and the functions of each input unit shown in FIG. 3. The CPU 1000 can also realize the functions of the error determination device and the functions of each input unit shown in FIG. 5.

[0098] Furthermore, a computer can realize the functions of the devices in the above-described embodiments. That is, the CPU 1000 can realize the functions of the blocks in the devices shown in FIGS.

[0099] The storage device 1001 is, for example, a non-transitory computer-readable medium. The non-transitory computer-readable medium includes various types of tangible storage media. Specific examples of non-transitory computer-readable media include magnetic recording media (e.g., hard disks), magneto-optical recording media (e.g., magneto-optical disks), CD-ROMs (Compact Disc-Read Only Memory), CD-Rs (Compact Disc-Recordable), CD-R / Ws (Compact Disc-ReWritable), and semiconductor memories (e.g., mask ROMs, PROMs (Programmable ROMs), EPROMs (Erasable PROMs), and flash ROMs).

[0100] The program may also be stored in various types of transitory computer-readable media, to which the program is supplied, for example, via a wired or wireless communication path, i.e., via an electrical signal, an optical signal, or an electromagnetic wave.

[0101] The memory 1002 is realized by, for example, a random access memory (RAM), and is a storage means for temporarily storing data when the CPU 1000 executes processing. A configuration is also conceivable in which a program held in the storage device 1001 or a temporary computer-readable medium is transferred to the memory 1002, and the CPU 1000 executes processing based on the program in the memory 1002.

[0102] Fig. 13 is a block diagram showing the main components of an information processing device. The device 10 for calculating an estimator shown in Fig. 13 includes normal approximation means (normal approximation unit) 11 (realized by normal approximation units 141, 151, and 161 in the embodiments) that performs approximation processing to approximate the estimator distribution with a normal distribution, deviation evaluation means (deviation evaluation unit) 12 (realized by deviation evaluation units 142, 152, and 162 in the embodiments) that evaluates deviations that occur in the approximation processing, and data evaluation means (data evaluation unit) 13 (realized by a size determination unit 143, a reliability rate determination unit 153, or an error determination unit 163 in the embodiments) that evaluates data related to calculation of the estimator from the result of the approximation processing and the deviations.

[0103] The data evaluation means 13 is, for example, a sample size determination means (implemented by the size determination unit 143 in the embodiment) that determines a sample size for calculating an estimator. The sample size is an example of data related to the calculation of an estimator. The sample size determination means, for example, determines the size of a sample to be used for calculating an estimator by repeating the calculation of a sample size (for example, the processing of steps S104 to S107 in the first embodiment). n -E n The sample size when the confidence level is 1-δ or more is the final sample size.

[0104] The data evaluation means 13 is, for example, a reliability rate determination means for determining a reliability rate (implemented by the reliability rate determination unit 153 in the embodiment). The reliability rate is an example of data related to the calculation of the estimator. In the second embodiment, the reliability rate determination unit 153, which is an example of the reliability rate determination means, determines the reliability rate of P n -E n is the reliability rate.

[0105] The data evaluation means 13 is, for example, an error determination means (implemented by the error determination unit 163 in the embodiment) that determines the error between the estimated amount and the true value. The error is an example of data related to the calculation of the estimated amount.

[0106] Some or all of the above-described embodiments and examples can be described as follows, but the present invention is not limited to the following configurations.

[0107] (Appendix 1) A normal approximation means for performing approximation processing to approximate the estimator distribution with a normal distribution; a deviation evaluation means for evaluating a deviation occurring in the approximation process; a data evaluation means for evaluating data relating to calculation of an estimated quantity from the result of the approximation processing and the deviation; An information processing device comprising:

[0108] (Supplementary Note 2) The data evaluation means is a sample size determination means for determining a sample size for calculating the estimator as data related to the calculation of the estimator. The information processing device of Appendix 1.

[0109] (Supplementary Note 3) The normal approximation means uses an approximation formula including a sample size as a parameter, and performs the approximation process while changing the parameter; the deviation evaluation means uses an evaluation formula including a sample size as a parameter, and performs the deviation evaluation process while changing the parameter; The sample size determination means determines, as the sample size, the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a confidence rate. The information processing device of Appendix 2.

[0110] (Supplementary Note 4) The data evaluation means is a reliability rate determination means for determining a reliability rate of data related to the calculation of the estimator. The information processing device of Appendix 1.

[0111] (Supplementary Note 5) The normal approximation means performs the approximation process using an approximation formula including a sample size as a parameter, the deviation evaluation means performs the deviation evaluation process using an evaluation formula including a sample size as a parameter; The reliability rate determining means determines the difference between the result of the approximation process and the deviation as a reliability rate. The information processing device of Appendix 4.

[0112] (Appendix 6) The data evaluation means is an error determination means for determining an error between the estimated quantity as data related to the calculation of the estimated quantity and a true value, which is a value to be estimated. The information processing device of Appendix 1.

[0113] (Supplementary Note 7) The normal approximation means performs the approximation process while changing a left error corresponding to an error when the estimated value deviates to the left of the true value and a right error corresponding to an error when the estimated value deviates to the right of the true value, the deviation evaluation means performs the deviation evaluation process while changing the left-side error and the right-side error, The error determining means determines the left error and the right error as errors between the estimated quantity and the true value when the difference between the result of the approximation processing and the deviation is equal to or greater than a reliability rate. The information processing device of Appendix 6.

[0114] (Appendix 8) The estimator is the sample mean, unbiased variance, or sample quantile. 8. An information processing device according to any one of appendix 1 to appendix 7.

[0115] (Appendix 9) Approximation processing is performed to approximate the estimator distribution with a normal distribution. Evaluating the deviation caused by the approximation process; Evaluating data related to the calculation of the estimated amount from the result of the approximation process and the deviation Information processing methods.

[0116] (Appendix 10) Determine the sample size for calculating the estimator as data related to the calculation of the estimator Information processing method of Appendix 9.

[0117] (Appendix 11) Determine the reliability of the data for the calculation of the estimator Information processing method of Appendix 9.

[0118] (Appendix 12) Determine the error between the estimated quantity and the true value, which is the value you want to estimate, as data related to the calculation of the estimated quantity. Information processing method of Appendix 9.

[0119] (Appendix 13) The estimator is the sample mean, unbiased variance, or sample quantile. 12. An information processing method according to any one of claims 9 to 12.

[0120] (Appendix 14) A computer-readable recording medium storing an information processing program, The information processing program is installed on a computer. An approximation process is performed to approximate the estimator distribution with a normal distribution. Evaluating the deviation occurring in the approximation process; Data relating to the calculation of the estimated amount is evaluated from the result of the approximation process and the deviation. A computer-readable recording medium.

[0121] (Supplementary Note 15) The information processing program is configured to: determining a sample size for calculating the estimator as data related to the calculation of the estimator; 15. The computer-readable storage medium of claim 14.

[0122] Although the present invention has been described above with reference to the embodiments and examples, the present invention is not limited to the above-described embodiments and examples. Various modifications that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the present invention. [Explanation of symbols]

[0123] 10. Information processing equipment 11 Normal approximation means 12 Deviation assessment methods 13 Data evaluation methods 100 Estimator type determination section 120 Reliability rate input section 121 Sample size input section 140 Sample Size Assessment Section 141,151,161 Normal approximation part 142,152,162 Deviation evaluation unit 143 Size determination section 150 Reliability Evaluation Unit 153 Reliability Rate Determination Unit 160 Error evaluation section 163 Error determination section 400 Dataset Input Section 410 Sample Use Judgment Unit 420 Model Construction Department 500,501 Dataset input section 510 Sample Use Judgment Unit 520,550 Model Construction Department 530 Threshold input section 540 Weight calculation unit 600,601 Dataset input section 610 Sample Use Judgment Unit 620,650 Model Construction Department 630 Threshold input section 640 Weight calculation unit 1000 CPU 1001 Storage device 1002 memory

Claims

1. a normal approximation means for performing an approximation process to approximate the probability distribution according to the estimator with a normal distribution; a deviation evaluation means for performing a deviation evaluation process in which the difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the right-side error value and a value obtained by approximating the probability using the asymptotic normality of the probability distribution is defined as a deviation, and the deviation evaluation means evaluates the deviation occurring in the approximation process; a sample size determination means for determining a sample size for calculating an estimator based on the result of the approximation process and the deviation; The sample size determination means determines, as the sample size, the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined reliability rate. An information processing device comprising:

2. the normal approximation means uses an approximation formula including a sample size as a parameter, and performs the approximation process while changing the parameter; The deviation evaluation means uses an evaluation formula including a sample size as a parameter, and performs the deviation evaluation process while changing the parameter. The information processing device according to claim 1 .

3. A normal approximation means for performing approximation processing to approximate the probability distribution according to the estimator with a normal distribution; a deviation evaluation means for performing a deviation evaluation process in which the difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the right-side error value and a value obtained by approximating the probability using the asymptotic normality of the probability distribution is defined as a deviation, and the deviation evaluation means evaluates the deviation occurring in the approximation process; and a reliability rate determining means for determining the difference between the result of the approximation process and the deviation as a reliability rate. Information processing device.

4. the normal approximation means performs the approximation process using an approximation formula including a sample size as a parameter; The deviation evaluation means performs the deviation evaluation process using an evaluation formula that includes the sample size as a parameter. The information processing device according to claim 3 .

5. A normal approximation means for performing an approximation process to approximate a probability distribution according to the estimator with a normal distribution; a deviation evaluation means for performing a deviation evaluation process in which the difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or smaller than the right-side error value and a value obtained by approximating the probability using the asymptotic normality of the probability distribution is defined as a deviation, and the deviation evaluation means evaluates the deviation occurring in the approximation process; an error determining means for determining an error between the estimated quantity and a true value, which is a value to be estimated, based on the result of the approximation process and the deviation; The error determining means determines the left error and the right error as errors between the estimated quantity and the true value when the difference between the result of the approximation processing and the deviation is equal to or greater than a predetermined reliability rate. Information processing device.

6. the normal approximation means performs the approximation process while varying a left error corresponding to an error when the estimated value deviates to the left of the true value and a right error corresponding to an error when the estimated value deviates to the right of the true value; The deviation evaluation means performs the deviation evaluation process while changing the left-side error and the right-side error. The information processing device according to claim 5 .

7. The estimator is the sample mean, unbiased variance, or sample quantile The information processing device according to any one of claims 1 to 6.

8. An approximation process is performed to approximate the probability distribution according to the estimator with a normal distribution, a deviation is defined as the difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or less than the right-side error value, and a value obtained by approximating the probability using the asymptotic normality of the probability distribution, and the deviation occurring in the approximation process is evaluated; determining a sample size for calculating an estimator based on the result of the approximation process and the deviation; When determining the sample size, the value of the parameter when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined reliability is determined as the sample size. Information processing methods.

9. Performing an approximation process to approximate the probability distribution according to the estimator with a normal distribution, a deviation is defined as the difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or less than the right-side error value, and a value obtained by approximating the probability using the asymptotic normality of the probability distribution, and the deviation occurring in the approximation process is evaluated; The difference between the result of the approximation process and the deviation is determined as a reliability rate. Information processing methods.

10. On the computer, An approximation process is performed to approximate the probability distribution according to the estimator with a normal distribution, a difference between the probability that the value obtained by subtracting the estimated quantity from the true value is equal to or less than the left-side error value and the value obtained by subtracting the estimated quantity from the true value is equal to or less than the right-side error value, and a value obtained by approximating the probability by the asymptotic normality of the probability distribution, and evaluating the deviation occurring in the approximation process; determining a sample size for calculating an estimator based on the result of the approximation process and the deviation; When determining the sample size, the parameter value when the difference between the result of the approximation process and the deviation is equal to or greater than a predetermined reliability rate is determined as the sample size. Information processing program for.

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