JP2014211761A - Analyzer, analysis method, and analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the accuracy of statistical data analysis in which security is enhanced, and achieve improvement of the accuracy of hypothesis testing to concealed data.SOLUTION: An analyzer 10 extracts sample data from among data items to be analyzed. Then, the analyzer 10 asymptotically expands an inverse function of a cumulative distribution function by using the reliability of standard normal distribution of the extracted sample data, and performs a single-sample average match test for testing whether or not the average of the sample data matches a predetermined value by using the expanded inverse function.

Description

  The present invention relates to an analysis apparatus, an analysis method, and an analysis program.

  In recent years, a large amount of data called BigData has attracted attention. Attempts have been made to perform statistical data analysis such as hypothesis testing on such a large amount of data and use the results. On the other hand, security enhancement such as protection of personal information for analysis target data is also required, and a hypothesis test is also required for disturbance data in which analysis target data is concealed. In the hypothesis test, a statistic can be obtained from a sample sampled from the population, and the property related to the sample (for example, whether the average value is greater than 100) can be statistically evaluated.

  There are various hypothesis tests. Among them, a one-sample average coincidence test technique using the central limit theorem is known as a basic test technique with a wide range of applications. Here, the one-sample mean-match test method refers to whether or not the mean agrees with a certain value when a sample is extracted from a single population assumed to have mean and variance, and the variance is assumed to be known. It is a method to judge.

  In addition, when the data to be analyzed is data including personal information, it is known to perform an irreversible stochastic operation on the data to prevent leakage of personal information. For example, as a technique for preventing leakage of personal information, “Pk” is an extension of k-anonymity to a stochastic index, in which any attacker cannot associate secret data with disturbance data with a probability of 1 / k or more. A privacy index called “anonymity” has been proposed.

  In addition, as a technique for preventing leakage of personal information, for example, a random variable according to a Laplace distribution having a specific parameter with respect to numerical attribute data among data to be analyzed is a value (hereinafter referred to as noise). The technology to add as is known.

JP 2011-100116 A

P. Samarati and L. Sweeney. Generalizing Data to Provide Anonymity When Disclosing Information (Extended abstract). Proc. Of the 17 th ACM-SIGMOD-SIGACT-SIGART Symposium on the Principles of Database Systems, p. 188, Seattle, WA, 1998. Dai Igarashi, Koji Senda, Katsumi Takahashi. Extension to the probabilistic index of k-anonymity and its application example. CSS2009, 2009 Dai Igarashi, Koji Senda, Katsumi Takahashi. Randomization method for satisfying k-anonymity in numerical attributes. CSS2011, 2011 Ryo Kikuchi, Akihiro Yamanaka, Dai Igarashi. A t-test method for privacy-protected data. LOIS2012, 2012 Takeuchi Kei et al. Statistical Dictionary. Toho Keizai Shinposha, 1989 E.A.Cornish and R.A.Fisher. Moments and cumulants in the specification of distributions. Revue de l´Institut International de Statistique, 5: 307-320, 1937

  However, in the conventional one-sample average coincidence test method using the central limit theorem, the number of samples to be analyzed may affect the calculated risk factor, and there is a problem in the accuracy of the hypothesis test. There was a case. In addition, there is a case where security cannot be strengthened because a highly accurate one-sample average coincidence test method for disturbance data has not been established.

  Therefore, an object of the present invention is to provide a statistical data analysis technique that improves the accuracy of statistical data analysis with enhanced security and realizes an improvement in accuracy of hypothesis testing for concealed data.

  In order to solve the above-described problems and achieve the object, the analysis apparatus includes an extraction unit that extracts sample data from the data to be analyzed, and the reliability of the standard normal distribution of the sample data extracted by the extraction unit. Analysis that performs asymptotic expansion of the inverse function of the cumulative distribution function using degree, and uses the expanded inverse function to test whether the average of the sample data matches a predetermined value And a section.

  The analysis method includes an extraction step of extracting sample data from the data to be analyzed, and an inverse function of the cumulative distribution function using the reliability of the standard normal distribution of the sample data extracted by the extraction step. And an analysis step of performing a one-sample average match test for testing whether or not the average of the sample data matches a predetermined value using the expanded inverse function. .

  The analysis program also includes an extraction step for extracting sample data from the data to be analyzed, and an inverse function of the cumulative distribution function using the reliability of the standard normal distribution of the sample data extracted by the extraction step. And an analysis step for performing a one-sample average match test for testing whether or not the average of the sample data matches a predetermined value using the developed inverse function.

  The analysis device, analysis method, and analysis program disclosed in the present application provide statistical data analysis technology that improves the accuracy of statistical data analysis with enhanced security and improves the accuracy of hypothesis testing for concealed data. It is possible.

FIG. 1 is a diagram for explaining the configuration of the analysis apparatus according to the first embodiment. FIG. 2 is a diagram illustrating an example of analysis target data stored in the analysis target data storage unit. FIG. 3 is a diagram illustrating a disturbance process that satisfies Pk anonymity. FIG. 4 is a diagram showing a disturbance process for adding a random variable to secret data. FIG. 5 is a diagram for explaining a processing example of the one-sample average match test. FIG. 6 is a diagram for explaining two errors in the hypothesis test. FIG. 7 is a diagram illustrating an example of an experimental result of a one-sided test. FIG. 8 is a flowchart for explaining the flow of analysis processing in the analysis apparatus according to the first embodiment. FIG. 9 is a diagram illustrating a computer that executes an analysis program.

  Exemplary embodiments of an analysis apparatus, an analysis method, and an analysis program according to the present invention will be described below in detail with reference to the accompanying drawings. In addition, this invention is not limited by this embodiment.

[First embodiment]
In the following embodiments, the configuration of the analysis apparatus according to the first embodiment and the flow of processing by the analysis apparatus will be described in order, and finally the effects of the first embodiment will be described.

[Configuration of analyzer]
Initially, the structure of the analyzer 10 is demonstrated using FIG. FIG. 1 is a diagram for explaining a configuration of an analysis apparatus 10 according to the first embodiment. As illustrated in FIG. 1, the analysis device 10 includes a communication processing unit 11, a control unit 12, and a storage unit 13.

  The communication processing unit 11 controls communication related to various types of information exchanged with the connected terminal device 20. For example, the communication processing unit 11 receives a request for analysis processing for the analysis target data from the terminal device 20. For example, the communication processing unit 11 transmits the processing result of the analysis process to the terminal device 20.

  As shown in FIG. 1, the storage unit 13 includes an analysis target data storage unit 13a and a disturbance data storage unit 13b. The storage unit 13 is, for example, a semiconductor memory device such as a RAM (Random Access Memory) or a flash memory, or a storage device such as a hard disk or an optical disk.

  The analysis target data storage unit 13a stores analysis target data to be analyzed (hereinafter referred to as secret data as appropriate). For example, as shown in FIG. 2, the analysis target data storage unit 13a includes an “employee ID” that uniquely identifies an employee, an “address” that indicates the address of the employee, an “age” that indicates the age of the employee, Are stored in association with “maximum blood pressure” indicating the numerical value of the maximum blood pressure.

  The secret data stored in the analysis target data storage unit 13a is divided into, for example, “identifier”, “quasi-identifier”, and “sensitive attribute”. The identifier uniquely associates one record with its owner, and corresponds to, for example, “employee ID” in FIG. The identifier is usually deleted before the disturbance process.

  The quasi-identifier is one that can identify the owner of a record by combining a plurality of quasi-identifiers, such as “address” and “age” in FIG. The quasi-identifier is subject to disturbance processing. Since information on quasi-identifiers is easy to obtain, it is generally impossible to keep them secret. However, combining them may lead to the identification of the record owner even if the identifiers are deleted. is there. Therefore, the quasi-identifier is disturbed by the method shown in the left figure so that the owner of the record cannot be specified. Since the quasi-identifier is considered to be indispensable in the data analysis after the disturbance data is disclosed, if it is completely deleted, the meaning of the data disclosure may be lost.

  The sensitive attribute is data to be kept secret, for example, “blood pressure” in FIG. 2, and the sensitive attribute may be a target of the disturbance operation, but may not be disturbed. That is, whether an attribute is a quasi-identifier or a sensitive attribute is determined according to the problem, and may be “a quasi-identifier and a sensitive attribute” in some cases. In addition, since the disturbance operation basically loses the usefulness of data analysis, if it is difficult to consider it as a quasi-identifier, it is better to leave it undisturbed. In this embodiment, “quasi-identifier” and “sensitive attribute” are targets of the disturbance operation. However, it is assumed that only the “sensitive attribute” is used in the hypothesis test, and the sensitive attribute is a numerical attribute. For example, when a quasi-identifier (such as age) of a numerical attribute exists, a hypothesis test can be performed on the quasi-identifier, but this is not general for the purpose of data analysis.

  The disturbance data storage unit 13b stores disturbance data to which noise is added by a disturbance process by a disturbance unit 12a described later. The disturbing process will be described in detail in the description of the disturbing unit 12a later.

  Returning to the description of FIG. 1, the control unit 12 includes a disturbance unit 12a, an extraction unit 12b, and an analysis unit 12c. Here, the control unit 12 is an electronic circuit such as a CPU (Central Processing Unit) or MPU (Micro Processing Unit), or an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array).

  The disturbing unit 12a adds a random variable according to a distribution having a specific parameter to data relating to a numerical value among the secret data. For example, as shown in FIG. 3, the disturbing unit 12a performs a disturbing process of adding a random variable according to a Laplace distribution having a specific parameter as data (noise) among the secret data, as shown in FIG. Disturbance data that satisfies Pk anonymity is generated. Thereafter, the disturbance unit 12a stores the generated disturbance data in the disturbance data storage unit 13b.

  Here, a disturbance processing example for adding a random variable to secret data will be described with reference to FIG. As shown in FIG. 4, it is assumed that secret data values include “10”, “15”, “13”, “9”, and “21”. Then, X is added to each secret data, where X is a random variable. As a result, “8”, “17”, “13”, “9”, and “18” are generated as the disturbance data. Here, for example, if the probability distribution followed by X is μ, the probability that secret data “10” changes to disturbance data “8” is P (10 + X = 8) = P (X = −2) = μ (− 2).

  The extraction unit 12b extracts sample data from the data to be analyzed. Specifically, the extraction unit 12b extracts n sample data from the disturbance data stored in the disturbance data storage unit 13b, and notifies the analysis unit 12c of the sample data.

The analysis unit 12c uses the reliability of the standard normal distribution of the sample data extracted by the extraction unit 12a (for example, z (δ) to be described later) (for example, F _n (δ to be described later). ) ^-1 ) Asymptotically expanded, and using the expanded inverse function, a one-sample average match test is performed to test whether the average of the sample data matches a predetermined value.

For example, the analysis unit 12c expands the inverse function F _n (δ) ⁻¹ of the cumulative distribution function by Cornish-Fisher expansion using the reliability z (δ) of the standard normal distribution of the sample data. Then, a one-sample average match test is performed using the inverse function F _n (δ) ⁻¹ . Further, for example, the analysis unit 12c performs a one-sample average coincidence test using 100 × (1-α)% points obtained by subtracting the value of 1 by the value of the significance level α as the reliability.

  Here, before describing the processing executed by the analysis unit 12c, the one-sample average match test will be described. Here, the one-sample mean-match test is a sample from a single population that is assumed to have a mean and variance, and determines whether the mean matches a certain value when the variance is assumed to be known. It is a technique to do.

  Conventionally, it has been common to use the central limit theorem in the one-sample mean agreement test. The central limit theorem makes use of the fact that when the number of samples n is infinite, the error between the sample mean and the true mean follows a standard normal distribution. If it is small, it is unclear how much the sample average deviates from the true average.

  In particular, when performing the above-described disturbance processing, even if it can be assumed that the secret data follows a normal distribution, the disturbance data generally deviates from the normal distribution due to the influence of noise applied for the disturbance operation. For this reason, the use of the central limit theorem in the one-sample average coincidence test when the number of sample data is small may not be appropriate.

Here, a processing example of a general one-sample average match test will be described using the example of FIG. In the example of FIG. 5, it is assumed that the standard deviation σ of the distribution that the secret data follows is known. Then, n sample data Z ₁ , Z ₂ ,..., Z _n are extracted from the secret data. Then, the following equations (1) and (2) are calculated. Here, it is a value assumed to be the average of μ ₀ . μ ₀ is given according to the problem. Since μ ₀ is not actually given in many cases, some value is substituted. For example, if the data to be analyzed is data related to annual income, an average of annual income for Japan as a whole is given.

Then, the value of the significance level α is determined, and the sample statistic s _n is compared with the magnitude of z (1-α). Here, z (1-α) is “100 × (1-α)% point” which is the reliability of the standard normal distribution. For example, when α = 0.05, z (0.95). ) ≈1.64.

From the comparison result, it is determined whether the null hypothesis μ = μ ₀ or the alternative hypothesis μ> μ ₀ is correct. Here, μ ₀ is a value assumed to be the average of secret data, as described above, and μ is an average value of n extracted data. That is, if s _n > z (1-α) as a result of comparison, “if the average of the secret data is μ ₀ , the probability that s _n > z (1-α) is at most α Therefore, in practice, the average of secret data is not μ ₀ , that is, it is determined that the null hypothesis is not correct, which is usually the proposition that the alternative hypothesis wants to claim.

  Here, two errors in the hypothesis test will be described with reference to FIG. As shown in FIG. 6, the two errors in the hypothesis test include a first type error and a second type error. In other words, type I error is when the null hypothesis is correct as a true state, and the test result regards the alternative hypothesis as correct, that is, the null hypothesis is correct but the alternative hypothesis is correct. This is an error in judgment when it is judged. The probability that this type 1 error will occur is called the risk factor, and the upper limit of the risk factor is called the significance level.

  The second type error is when the alternative hypothesis is correct as a true state and the test result regards the null hypothesis as correct, that is, the alternative hypothesis is correct but the null hypothesis is correct. This is an error in judgment when it is judged. This is a so-called trade-off relationship in which the probability of the first type error and the probability of the second type error are not lowered at the same time. However, it is usually desirable to perform a test that maximizes the power of detection while keeping the upper limit (significance level) of the risk factor constant.

As described above, the use of the central limit theorem in the one-sample average coincidence test when the number of sample data is small may not be appropriate. This is because when the number of sample data is sufficiently large, it can be said that s _n follows the standard normal distribution by the central limit theorem for a given significance level α, and therefore, 100 × (1-α)% points of the standard normal distribution The magnitudes of s _n calculated from the sample data may be compared, but when the number of sample data is small, it cannot be said that s _n follows the standard normal distribution. That is, when the number of sample data is small, it is unclear whether or not the superiority level not given by the central limit theorem is achieved, and the reliability of the test is low. That is, since it can not assume the distribution of s _n, it is impossible to exactly determine the 100 × (1-α)% point of the distribution of s _n. Here, the power is the probability that the alternative hypothesis is correct as a true state and the alternative hypothesis is correct as a test result (for example, in the example of FIG. 6, it corresponds to the “o” portion at the lower right). .

For example, the alpha = 0.05, the results using a 95% point of the standard normal distribution in accordance with the central limit theorem, to might take 90% point to the point s _n, may 99% point. That is, since the risk factor cannot be obtained, the reliability of the test is impaired.

  Therefore, the analysis unit 12c obtains 100 (1-α)% points in the hypothesis test by developing an inverse function of the cumulative distribution function of the disturbance data by a method called Cornish-Fisher expansion.

First, the analysis unit 12c receives n sample data for hypothesis testing extracted by the extraction unit 12b. Then, the analysis unit 12c sets X _i (i = 1... N) as a random variable representing data (general data regardless of secret data, disturbance data, etc.), and the average and standard deviation (both are the mother data). The following formulas (3) and (4) are calculated by setting the mean μ and standard deviation σ from the group mean / standard deviation, ie, the distribution followed by the population, not obtained from sampling, respectively.

Analyzing unit 12c, the cumulative distribution function of the distribution of the _{S n} follows the _{F n.} That is, when the probability density function of S _n and fn, and those represented by the following equation (5). Note that the leftmost P [S _n ≦ τ] in the equation (5) means the probability of S _n ≦ τ.

Here, the analysis unit 12c, when the Cornish-Fisher expansion on _{F n,} as [delta] = 1-alpha, by the following equation (6), representing the 100 × (1-α)% point _{S n} can do.

Here, the cumulant in the above equation (6) will be described. First, define the moment. For the random variable X, the n-th moment is defined as the following equation (7), where x is the expected value of ^Xn , that is, the probability density function of X is f. Hereinafter, μ _n = E [X ⁿ ] is expressed. At this time, cumulants k _i up to the fourth order (i = 1, 2, 3, 4) are defined by the following formulas (8) to (11).

With regard to the above equation (6), it is considered that the central limit theorem is approximated to higher order terms. That is, n → ∞ converges to the 100 × δ% point z (δ) of the standard normal distribution as in the central limit theorem. However, using the formula (6) as it is does not necessarily have the effect of reducing the risk factor. That is, in order to lower the risk factor compared to the central limit theorem, it is necessary to satisfy F _n (δ) ⁻¹ > z (δ). The sign of may be positive or negative depending on the magnitude of z (δ).

  Therefore, the analysis unit 12c uses the following equation (12) instead of the equation (6) in the case of a one-sided test problem. Expression (7) is also n → ∞, and converges to z (δ) at the same speed as Expression (6). The analysis unit 12c uses the following equation (13) instead of the equation (6) in the case of a two-sided test problem.

Further, if the random variable representing the secret data is X, the random variable representing the noise added by the disturbance operation is Y, and the respective i-th order cumulants are ι _i and λ _i , the i-th order cumulant κ _{i of the} disturbance data Z = X + Y is obtained. It can be expressed as κ _i = ι _i + λ _i .

  Using this, the average 100 × (1-α)% point of Sn and disturbance data Z expressed by the following formulas (14) and (15) is approximated by the above formula (12) or formula (13). By doing so, it is possible to realize a one-sample average test for disturbance data.

  As described above, the analysis apparatus 10 according to the first embodiment can improve the reliability of the sample average test. In other words, in the central limit theorem, approximation is performed using only the first term on the right side in the above equation (6), whereas in the analysis apparatus 10 according to the first embodiment, the terms after the second term are absolute values. By using the above-mentioned formulas (6) and (7) and using the second and subsequent terms, the risk factor can be lowered and the reliability of the sample average test can be improved.

  In the analysis apparatus 10 according to the first embodiment, the cumulative distribution function is developed by a technique called Cornish-Fisher expansion. The Cornish-Fisher expansion is effective when it is difficult to obtain the cumulative distribution function explicitly as in this case, but if used as it is, the effect of “lowering the risk factor in the hypothesis test” may not occur. As described above, correction is performed so that the risk rate decreases.

  In the following, the hypothesis testing process will be described, but a processing example in the case of handling a one-sided test problem and a case of handling a two-sided test problem will be described. As a premise, the secret data is assumed to follow a normal distribution, and the noise added by the disturbance processing is assumed to be Laplace noise.

First, a processing example when handling a one-sided test problem will be described. When a random variable representing secret data is X, the normal distribution followed by X is represented by N (μ, σ ² ), that is, the probability density function f _X of the following equation (16).

Further, when a random variable representing noise added by the disturbance operation is Y, Laplace noise followed by _Y is represented by a probability density function fY of the following equation (17).

  At this time, if “b” in the above equation (17) is also obtained by the following equation (18), Pk anonymity is satisfied. That is, no attacker can associate secret data with disturbance data with a probability of 1 / k or more. In equation (18), | R | is the number of rows in the table, and ν is the range of secret data (numerical values). Further, Z = X + Y obtained by adding the random variable X and the random variable Y becomes disturbance data.

Let n samples be taken from the disturbance data. We define a _{s n} below (19) and (20). Here, μ ′ = μ, μ is defined as an average value of Z, and σ ′ is defined as a standard deviation of Z expressed by the following equation (21).

At this time, the above expression (12) becomes the following expression (22). Here, γ ₄ in the following equation (22) is obtained by the following equation (23).

Using the above equation (22), as a one-sided test problem of significance level α, a hypothesis test consisting of two hypotheses of null hypothesis H ₀ : μ ′ = μ ₀ and alternative hypothesis H ₁ : μ ′> μ ₀ Can be built. The actually sampled data is defined as z _i (i = 1,..., N), and s _n is defined by the following equation (24). At this time, if s ₀ > F _n (δ) ⁻¹ (δ = 1−α), the null hypothesis is rejected and the alternative hypothesis is accepted. Otherwise, accept the null hypothesis.

For example, in the case of a test whether or not the systolic blood pressure significantly increased after administration of a specific drug, μ ₀ is the average of the systolic blood pressure (average before administration of the drug, general average value, etc. And μ ′ is the average of the systolic blood pressure of the sample data. If s ₀ > F _n (δ) ⁻¹ , the null hypothesis is rejected, and s ₀ > F _n (δ) ⁻¹ Accepts the null hypothesis. In other words, the rejection of the null hypothesis is an event that occurs only with a probability of 100 × (1-α)% if the average before and after administration is the same. Therefore, it means that it is judged that the systolic blood pressure after administration has increased significantly compared to before administration, and acceptance of the null hypothesis means that the systolic blood pressure after administration has not changed compared to before administration. It means to do.

Here, FIG. 7 shows an example of an experimental result when the above-described test processing is performed for the one-side test. FIG. 7 is a diagram illustrating an example of an experimental result of a one-sided test. In the example of FIG. 7, the 95% point of the disturbance data generated from the random number is indicated by a rhombus, the 95% point of the central limit theorem (the 95% point of the standard distribution) is indicated by a square, and the analysis apparatus 10 according to the present embodiment The 95% point by the method is indicated by a triangle. Moreover, 95% point of the disturbance data generated from random numbers, and calculates a 10000 _{S n,} displaying the 9500 th values. In FIG. 7, the vertical axis indicates the value of the 95% point, and the horizontal axis indicates the number of samples.

  As shown in FIG. 7, regardless of the number of samples, it can be seen that the 95% point value obtained by the method of the analysis apparatus 10 according to the present embodiment is larger than the 95% point value of the central limit theorem. The larger the value, the lower the risk factor. Therefore, in the analysis apparatus 10 according to the present embodiment, it is possible to always reduce the risk factor as compared with the case where the central limit theorem is used.

Next, a processing example when dealing with a two-sided test problem will be described. Also in the case of dealing with the two-sided test problem, the parameter b in the above equation (17) is determined by the above equation (18) as in the case of dealing with the above one-sided test problem, and the above equations (19) and (20 ) Define Sn. At this time, the above expression (13) becomes the following expression (25). Here, γ ₄ in the above equation (22) is obtained by the following equation (26).

Using the above equation (25), as a two-sided test problem of significance level α, a hypothesis test consisting of two hypotheses: null hypothesis H ₀ : μ ′ = μ ₀ and alternative hypothesis H ₁ : μ ′ ≠ μ ₀ Can be built. And _S0 is calculated and it is determined whether the following (27) Formula or (28) Formula is satisfied. In the equations (27) and (28), δ = 1−α / 2. If the following formula (27) or the following formula (28) holds, the null hypothesis is rejected, and if it does not hold, the null hypothesis is accepted. For example, it can be used for the test problem of whether or not there is a significant difference in blood pressure after administration of a specific drug compared to before administration.

  As described above, in the analysis apparatus 10 according to the first embodiment, “anonymized (disturbed) data can be accurately statistical data analyzed (hypothesis test). For example, in the medical field, Pk anonymity is obtained. It is possible to accurately test the accuracy of hypotheses based on sample data within the guaranteed range.

[Processing by analyzer]
Next, processing of the analysis apparatus 10 according to the first embodiment will be described with reference to FIG. FIG. 8 is a flowchart for explaining the flow of analysis processing in the analysis apparatus 10 according to the first embodiment.

  As shown in FIG. 8, when the disturbance unit 12a of the analysis device 10 receives an analysis request from the terminal device 20 (step S101), the disturbing unit 12a reads secret data to be analyzed from the analysis target data storage unit 13a (step S102).

And the disturbance part 12a adds a Laplace noise with respect to the read secret data, and produces | generates disturbance data (step S103). And the analysis part 12c extracts n sample data from disturbance data (step S104). Then, the analysis unit 12c calculates the test statistic “s _n ” using the above-described equations (1) and (2) (step S105).

Then, the analysis unit 12c compares the magnitude of _{s n} and z (1-α) (step S106). As a result, if the analysis unit 12c determines that s _n > z (1-α) (Yes in step S107), the analysis unit 12c determines that the alternative hypothesis is correct (step S108). If it is determined that s _n > z (1-α) is not satisfied (No at Step S107), it is determined that the null hypothesis is correct (Step S109). And the analysis part 12c outputs an analysis result with respect to the terminal device 20 (step S110).

  For example, the analysis unit 12c analyzes whether the blood pressure of people suffering from a specific disease has a significant difference compared to the average value of the blood pressure, Whether the blood pressure is significantly different from the average value of the blood pressure is output.

[Effect of the first embodiment]
As described above, in the analysis apparatus 10 according to the first embodiment, sample data is extracted from data to be analyzed, and accumulated using the reliability of the standard normal distribution of the extracted sample data. An asymptotic expansion is performed on the inverse function of the distribution function, and a one-sample average match test is performed to test whether the average of the sample data matches a predetermined value using the expanded inverse function. As a result, the accuracy of statistical data analysis with enhanced security can be improved, and the accuracy of hypothesis testing for concealed data can be improved.

  Further, in the analysis apparatus 10 according to the first embodiment, the analysis target data in which a random variable according to a distribution having a specific parameter is added to data related to a numerical value among the data to be analyzed, and the random variable is added. Extract sample data from. For this reason, it is possible to conceal data and strengthen security.

  Further, in the analysis apparatus 10 according to the first embodiment, the inverse function of the cumulative distribution function is developed by Cornish-Fischer expansion, and a one-sample average match test is performed. For this reason, it is possible to obtain the cumulative function explicitly.

  Further, in the analysis apparatus 10 according to the first embodiment, as the reliability, the inverse function of the cumulative distribution function is asymptotically developed using the reliability obtained from the arbitrarily set significance level α, and the one-sample average match Perform the test. For example, the analysis apparatus 10 obtains 100 × (1-α)% points of the standard normal distribution, and performs a one-sample average coincidence test using the 100 × (1-α)% points. For this reason, it is possible to improve the accuracy of statistical data analysis with enhanced security and to improve the accuracy of hypothesis testing for concealed data.

[System configuration, etc.]
Further, each component of each illustrated apparatus is functionally conceptual, and does not necessarily need to be physically configured as illustrated. In other words, the specific form of distribution / integration of each device is not limited to that shown in the figure, and all or a part thereof may be functionally or physically distributed or arbitrarily distributed in arbitrary units according to various loads or usage conditions. Can be integrated and configured. For example, the disturbance unit 12a and the analysis unit 12b may be integrated. Further, all or any part of each processing function performed in each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware by wired logic.

  Also, among the processes described in the present embodiment, all or part of the processes described as being performed automatically can be performed manually, or the processes described as being performed manually can be performed. All or a part can be automatically performed by a known method. In addition, the processing procedure, control procedure, specific name, and information including various data and parameters shown in the above-described document and drawings can be arbitrarily changed unless otherwise specified.

[program]
In addition, it is possible to create a program in which processing executed by the analysis apparatus 10 described in the above embodiment is described in a language that can be executed by a computer. For example, an analysis program in which processing executed by the analysis apparatus 10 according to the first embodiment is described in a language that can be executed by a computer can be created. In this case, when the computer executes the analysis program, the same effect as that of the above embodiment can be obtained. Furthermore, the same processing as that of the first embodiment may be realized by recording the analysis program on a computer-readable recording medium, recording the analysis program on the recording medium, and reading and executing the analysis program on the computer. Good. Hereinafter, an example of a computer that executes an analysis program that realizes the same function as the analysis apparatus 10 illustrated in FIG. 2 will be described.

  FIG. 9 is a diagram illustrating a computer 1000 that executes an analysis program. As illustrated in FIG. 9, the computer 1000 includes, for example, a memory 1010, a CPU 1020, a hard disk drive interface 1030, a disk drive interface 1040, a serial port interface 1050, a video adapter 1060, and a network interface 1070. These units are connected by a bus 1080.

  The memory 1010 includes a ROM (Read Only Memory) 1011 and a RAM 1012 as illustrated in FIG. The ROM 1011 stores a boot program such as BIOS (Basic Input Output System). The hard disk drive interface 1030 is connected to the hard disk drive 1031 as illustrated in FIG. The disk drive interface 1040 is connected to the disk drive 1041 as illustrated in FIG. For example, a removable storage medium such as a magnetic disk or an optical disk is inserted into the disk drive 1041. The serial port interface 1050 is connected to a mouse 1051 and a keyboard 1052, for example, as illustrated in FIG. The video adapter 1060 is connected to a display 1061, for example, as illustrated in FIG.

  Here, as illustrated in FIG. 9, the hard disk drive 1031 stores, for example, an OS 1091, an application program 1092, a program module 1093, and program data 1094. That is, the above analysis program is stored in, for example, the hard disk drive 1031 as a program module in which a command executed by the computer 1000 is described.

  The various data described in the above embodiment is stored as program data, for example, in the memory 1010 or the hard disk drive 1031. Then, the CPU 1020 reads the program module 1093 and the program data 1094 stored in the memory 1010 and the hard disk drive 1031 to the RAM 1012 as necessary, and executes various processing procedures.

  Note that the program module 1093 and the program data 1094 related to the analysis program are not limited to being stored in the hard disk drive 1031, but may be stored in, for example, a removable storage medium and read out by the CPU 1020 via the disk drive or the like. Good. Alternatively, the program module 1093 and the program data 1094 related to the analysis program are stored in another computer connected via a network (LAN (Local Area Network), WAN (Wide Area Network), etc.), and via the network interface 1070. May be read by the CPU 1020.

DESCRIPTION OF SYMBOLS 10 Analysis apparatus 11 Communication processing part 12 Control part 12a Disturbing part 12b Extraction part 12c Analyzing part 13 Storage part 13a Analysis object data storage part 13b Disturbing data storage part 20 Terminal device

Claims (6)

An extractor that extracts sample data from the data to be analyzed;
The inverse function of the cumulative distribution function is asymptotically expanded using the reliability of the standard normal distribution of the sample data extracted by the extraction unit, and the average of the sample data matches a predetermined value using the expanded inverse function An analysis unit that performs a one-sample average match test to test whether or not
An analysis device characterized by comprising: Among the data to be analyzed, further comprising a disturbance unit for adding a random variable according to a distribution having a specific parameter to data relating to a numerical value,
The analysis apparatus according to claim 1, wherein sample data is extracted from data to which a random variable is added by the disturbance unit.   The analysis apparatus according to claim 1, wherein the analysis unit expands an inverse function of the cumulative distribution function by Cornish finisher expansion as the asymptotic expansion, and performs the one-sample mean match test.   The analysis unit performs asymptotic expansion of an inverse function of a cumulative distribution function using the reliability obtained from an arbitrarily set significance level as the reliability, and performs the one-sample mean match test The analysis device according to claim 1. An analysis method executed by an analysis device,
An extraction process for extracting sample data from the data to be analyzed;
Asymptotic expansion of the inverse function of the cumulative distribution function is performed using the reliability of the standard normal distribution of the sample data extracted by the extraction step, and the average of the sample data matches a predetermined value using the expanded inverse function An analysis step of performing a one-sample average match test to test whether or not
The analysis method characterized by including. An extraction step for extracting sample data from the data to be analyzed;
Using the reliability of the standard normal distribution of the sample data extracted by the extraction step, the inverse function of the cumulative distribution function is asymptotically expanded, and the average of the sample data matches a predetermined value using the expanded inverse function An analysis step for performing a one-sample mean match test to test whether or not
An analysis program that causes a computer to execute.

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