JP7075362B2 - Judgment device, judgment method and judgment program - Google Patents

Description

The present invention relates to a device for determining a data poisoning attack.

In collaborative filtering used in recommender systems and the like, evaluation values for unrated items are predicted using evaluation data for a plurality of items by users in the same system. As an attack against collaborative filtering, there is a data poisoning attack in which an attacker illegally evaluates an item while pretending to be a legitimate user and mixes malicious data into the evaluation data. Data poisoning attacks aim to reduce predictive performance or increase or decrease the popularity of specific items.

As a countermeasure against data poisoning attacks against collaborative filtering, for example, there is a method using the t-test proposed in Non-Patent Document 1. In this method, it is assumed that the distribution of the evaluation values is a normal distribution, and the difference in the distribution is detected by the t-test to determine that the additionally given evaluation data is malignant data.

B. Li, Y. Wang, A. Singh, and Y. Vorobeychik: Data Poisoning Attacks on Factorization-Based Collaborative Filtering, Proceedings of the 3rd Conference on Neural Information Processing Systems (IPS16). 1-13, 2016.

In the above method, it is assumed that the distribution of the evaluation values of the normal user and the malignant user is a normal distribution, but the distribution of the evaluation values does not always follow the normal distribution. For this reason, it was often the case that the additional malignant data given could not be detected correctly.

An object of the present invention is to provide a determination device, a determination method, and a determination program capable of determining malignant data regardless of the distribution of evaluation data.

The determination device according to the present invention includes a calculation unit that calculates a cumulative probability distribution for a sample of the evaluation value in an evaluation matrix that stores evaluation values for a plurality of items for each user, and two evaluation matrices that are different from each other. A determination unit that determines that the populations of the two evaluation matrices are not the same when the difference in the cumulative probability distribution and the index based on the number of users in each of the two evaluation matrices satisfy the conditions based on the predetermined significance level. To prepare for.

The calculation unit may calculate the cumulative probability distribution representing the histogram of the evaluation values by using the set of the evaluation values stored in the evaluation matrix as the sample.

The calculation unit may calculate the cumulative probability distribution representing a histogram of the presence or absence of the evaluation value in the sample, with the parts corresponding to each other in the two evaluation matrices as the sample.

The calculation unit may use the submatrix of the unit of the item in the evaluation matrix as the sample.

In the two evaluation matrices, the determination unit may determine that the populations of the two evaluation matrices are not the same when the number of the items satisfying the above conditions is a predetermined number or more.

The determination method according to the present invention includes a calculation step for calculating a cumulative probability distribution for a sample of the evaluation values in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, and the above-mentioned two evaluation matrices that are different from each other. A determination step for determining that the populations of the two evaluation matrices are not the same when the difference in the cumulative probability distribution and the index based on the number of users in each of the two evaluation matrices satisfy the conditions based on the predetermined significance level. Is executed by the computer.

The determination program according to the present invention includes a calculation step for calculating a cumulative probability distribution for a sample of the evaluation values in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, and the above-mentioned two evaluation matrices that are different from each other. A determination step for determining that the populations of the two evaluation matrices are not the same when the difference in the cumulative probability distribution and the index based on the number of users in each of the two evaluation matrices satisfy the conditions based on a predetermined significance level. Is for letting the computer execute.

According to the present invention, malignant data can be determined regardless of the distribution of evaluation data.

It is a block diagram which shows the functional structure of the determination apparatus which concerns on embodiment. It is a flowchart which shows the procedure of the 1st determination method which concerns on embodiment. It is a flowchart which shows the procedure of the 2nd determination method which concerns on embodiment.

Hereinafter, an example of the embodiment of the present invention will be described.
In the method for determining malignant data according to the present embodiment, it is determined by using the Kolmogorov-Smirnov test that the evaluation matrix additionally given is malignant data with respect to the normal evaluation matrix used for emphasis filtering.
The Kolmogorov-Smirnov test is one of the non-parametric test methods that does not depend on the distribution, unlike the t-test that assumes a normal distribution. A distinction is made between the matrix and the evaluation matrix by malicious users.

Here, M is an evaluation matrix for n items by m regular users. M _{i and j} indicate the evaluation of the j-th column (item) of the i-th row (user) of the evaluation matrix M. However, M is a sparse matrix and includes elements whose evaluation has not been observed.
In collaborative filtering, the value of an unobserved element in M is estimated by analyzing the evaluation matrix M.

In a data poisoning attack against collaborative filtering, the attacker becomes a legitimate user, fraudulently evaluates items according to the purpose of the attack, and adds malicious evaluation data to the learning system. Let M'be the evaluation matrix for n items by m'malignant users.
In the determination device 1 of the present embodiment, when the evaluation matrix M'is additionally given to the evaluation matrix M of the regular user, the evaluation matrix M'is by the regular user or is mixed by the malicious user. Determine if it is a thing.

FIG. 1 is a block diagram showing a functional configuration of the determination device 1 according to the present embodiment.
The determination device 1 is an information processing device (computer) such as a server device or a personal computer, and includes a control unit 10 and a storage unit 20, as well as various data input / output devices and communication devices.

The control unit 10 is a part that controls the entire determination device 1, and realizes each function in the present embodiment by appropriately reading and executing various programs stored in the storage unit 20. The control unit 10 may be a CPU.

The storage unit 20 is a storage area for various programs and various data for making the hardware group function as the determination device 1, and may be a ROM, RAM, flash memory, hard disk (HDD), or the like. Specifically, the storage unit 20 stores a program (determination program) for causing the control unit 10 to execute each function of the present embodiment, various data in the process of processing, and the like.

The control unit 10 includes a calculation unit 11 and a determination unit 12. By operating these functional units, the control unit 10 determines whether the newly added evaluation matrix M'is derived from the same population as the existing evaluation matrix M, that is, whether it is normal evaluation data. Determine if it is malignant evaluation data.

The calculation unit 11 calculates a cumulative probability distribution for a sample of evaluation values in the evaluation matrices M and M'where evaluation values for a plurality of items for each user are stored.
The calculation unit 11 uses, for example, a set of observed evaluation values stored in the evaluation matrices M and M'as a sample, and calculates a cumulative probability distribution representing a histogram of the evaluation values.
Further, the calculation unit 11 uses, for example, the parts corresponding to each other in the two evaluation matrices M and M'as samples, and calculates the cumulative probability distribution representing the histogram of the presence / absence of the evaluation values in these samples. Specifically, the calculation unit 11 may sample the submatrix of the unit of the item in the evaluation matrix M and M'.

The determination unit 12 determines the condition that the difference between the two evaluation matrices M and M'that are different from each other and the cumulative probability distribution of each, and the index based on the number of users m and m'in each of the evaluation matrices M and M'is based on a predetermined significance level. If so, it is determined that the populations of the two evaluation matrices M and M'are not the same.
Further, in the two evaluation matrices M and M', the determination unit 12 does not have the same population of the two evaluation matrices M and M'when the number of subsets (number of items) satisfying the conditions is equal to or more than a predetermined value. May be determined.

Next, the procedure of the method for determining malicious data by the determination device 1 will be described in detail.
The determination device 1 employs, for example, the first determination method or the second determination method shown below. Further, the determination device 1 executes both the first determination method and the second determination method, and when it is determined that the populations are not the same in either method, the evaluation matrix M'is malignant evaluation data. It may be determined that there is.

[First determination method]
In the first determination method, the determination device 1 uses the Kolmogorov-Smirnov test, and M'is malignant based on the difference in the cumulative probability distribution of the observed evaluation values included in each of the evaluation matrices M and M'. Determine if it is a user evaluation matrix.

FIG. 2 is a flowchart showing the procedure of the first determination method according to the present embodiment.
In using the Kolmogorov-Smirnov test, X is a sample of the evaluation value of a regular user, and X'is a sample of the evaluation value of a malignant user. Further, the null hypothesis is that "the population of X and X'is the same".

In step S1, the calculation unit 11 calculates the cumulative probability distribution P (x) of the sample X using the evaluation matrix M of the normal user. Further, the calculation unit 11 calculates the cumulative probability distribution Q (x) of the sample X'using the evaluation matrix M'of the malignant user.
Here, x is an observed evaluation value included in the evaluation matrices M and M'. For example, when the actual evaluation values 1 to 5 for each item and 0 indicating no evaluation are mixed as the elements of the evaluation matrices M and M', the calculation unit 11 determines the evaluation value x (excluding 0 of no evaluation). The cumulative probability distribution is calculated from the histograms of = 1 to 5).

In step S2, the determination unit 12 calculates the Kolmogorov-Smirnov statistic D by the following equation based on the cumulative probability distributions P (x) and Q (x).
D = max _x | P (x) -Q (x) |

In step S3, the determination unit 12 calculates D [mm'/ (m + m')] ^1/2 as an index for determining malignant data from the number of regular users m, the number of malignant users m', and the statistic D. do.

In step S4, the determination unit 12 determines whether or not the value of D [mm'/ (m + m')] ^1/2 is larger than K _α with respect to the significance level α. However, K _α is a number that satisfies Pr [D [mm'/ (m + m')] ^1/2 ≤ K _α ] = 1-α. If this determination is YES, the process proceeds to step S5, and if the determination is NO, the process proceeds to step S6.

In step S5, the determination unit 12 rejects the null hypothesis and determines that the populations of X and X'are not the same, that is, the evaluation matrix M'is malignant data contaminated by a malignant user.

In step S6, the determination unit 12 determines that the population of X and X'is the same, and the evaluation matrix M'is regular data given by the regular user.

[Second judgment method]
In the second determination method, the determination device 1 uses the Kolmogorov-Smirnov test, and M'is the evaluation matrix of the malignant user based on the difference in the evaluation method for each item in each of the evaluation matrices M and M'. Determine if it exists.

FIG. 3 is a flowchart showing the procedure of the second determination method according to the present embodiment.
In using the Kolmogorov-Smirnov test, X _j is a sample of the evaluation value for the j-th item by a regular user, and X j'is a sample of the evaluation value for the _j -th item by a malignant user. However, the evaluation value is a binary value of 0 or 1, that is, 1 regardless of whether the evaluation is high or low if the user evaluates the jth item, and 0 if the user does not evaluate the item. Further, the null hypothesis is that "the population of X _j and X _j'is the same".

In step S11, the control unit 10 initializes the index j of n items and the number of items k for determining malicious data to 0.

In step S12, the determination unit 12 counts up the index j (j = j + 1).

In step S13, the calculation unit 11 obtains the cumulative probability distribution P (x) of the sample X _j using the evaluation matrix M of the normal user. Further, the calculation unit 11 obtains the cumulative probability distribution Q (x) of the sample X _j'using the evaluation matrix M'of the malignant user.
Here, x is the above-mentioned evaluation value of 0 or 1. For example, when the actual evaluation values 1 to 5 for each item and 0 indicating no evaluation are mixed as elements of the evaluation matrices M and M', the calculation unit 11 evaluates as no evaluation (x = 0). The cumulative probability distribution is obtained from the histogram of (x = 1).

In step S14, the determination unit 12 calculates the Kolmogorov-Smirnov statistic D by the following equation based on the cumulative probability distributions P (x) and Q (x).
D = max _x | P (x) -Q (x) |

In step S15, the determination unit 12 calculates D [mm'/ (m + m')] ^1/2 as an index for determining malignant data from the number of regular users m, the number of malignant users m', and the statistic D. do.

In step S16, the determination unit 12 determines whether or not the value of D [mm'/ (m + m')] ^1/2 is larger than K _α with respect to the significance level α. However, K _α is a number that satisfies Pr [D [mm'/ (m + m')] ^1/2 ≤ K _α ] = 1-α. If this determination is YES, the process proceeds to step S17, and if the determination is NO, the process proceeds to step S18.

In step S17, the determination unit 12 rejects the null hypothesis, determines that the populations of X _j and X _j'are not the same, and counts up the number of determination items k (k = k + 1).

In step S18, the determination unit 12 determines whether or not the number of determination items k is equal to or greater than the threshold value t. If this determination is YES, the process proceeds to step S19, and if the determination is NO, the process proceeds to step S20.

In step S19, the determination unit 12 determines that the evaluation matrix M'is malignant data mixed by a malignant user, and ends the process.

In step S20, the determination unit 12 determines whether the index j is equal to the number of items n, that is, whether or not the test has been performed for all the items. If this determination is YES, the process proceeds to step S21, and if the determination is NO, the process returns to step S12.

In step S21, the determination unit 12 determines that the evaluation matrix M'is regular data given by a regular user.

According to the present embodiment, the determination device 1 uses the Kolmogorov-Smirnov test, which is one of the nonparametric test methods, and is based on the cumulative probability distribution of the sample of the evaluation values stored in the two evaluation matrices. Determine if two evaluation matrices are from the same population. Thereby, the determination device 1 can determine whether or not the added evaluation matrix is malignant data without assuming the shape of the distribution of the evaluation values of the regular user and the malignant user.
Therefore, the determination device 1 can suppress the influence of the data poisoning attack even in the collaborative filtering system that handles evaluation data that does not follow a specific distribution shape such as a normal distribution.

The determination device 1 uses a set of evaluation values stored in the evaluation matrix as a sample, calculates a cumulative probability distribution representing a histogram for each observed evaluation value, and is malignant based on the similarity of the distribution of the evaluation values. Data can be judged appropriately.

The determination device 1 uses a sample corresponding to each other in two evaluation matrices, and calculates a cumulative probability distribution representing a histogram of the presence or absence of evaluation values in the sample to obtain a specific part (for example, a group of items) in the evaluation matrix. Malignant data can be appropriately determined based on the similarity of the specimens focusing on.

The determination device 1 can apply the Kolmogorov-Smirnov test not only to the distribution of the entire evaluation data but also to the distribution of the evaluation values for each item by using the submatrix of the unit of the item in the evaluation matrix as a sample. As a result, even if the determination device 1 determines the malicious evaluation value so that the attacker has the same or similar distribution as the distribution of the evaluation value of the legitimate user, for example, the malicious user selects only a specific item. It can detect data poisoning attacks that are evaluated and eliminate malicious data.
At this time, the determination device 1 determines that the populations of the two evaluation matrices are not the same and the evaluation data of the malicious user is added when the number of items determined to be not the same population is equal to or more than a predetermined number. You may. As a result, the determination device 1 can suppress erroneous detection by determining only a specific item, and can appropriately determine malignant data.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments. Moreover, the effects described in the above-described embodiments are merely a list of the most suitable effects resulting from the present invention, and the effects according to the present invention are not limited to those described in the embodiments.

The determination method by the determination device 1 is realized by software. When realized by software, the programs that make up this software are installed in the information processing device (computer). Further, these programs may be recorded on a removable medium such as a CD-ROM and distributed to the user, or may be distributed by being downloaded to the user's computer via a network. Further, these programs may be provided to the user's computer as a Web service via a network without being downloaded.

1 Judgment device 10 Control unit 11 Calculation unit 12 Judgment unit 20 Storage unit

Claims (5)

In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation unit for calculating a cumulative probability distribution for a sample of the evaluation values, and a calculation unit.
If the difference in the cumulative probability distribution of each of the two different evaluation matrices and the index based on the number of users in each of the two evaluation matrices satisfy the condition based on a predetermined significance level, the population of the two evaluation matrices becomes It is equipped with a determination unit that determines that they are not the same.
The calculation unit uses a submatrix corresponding to one or more specific item groups in the evaluation matrix as the sample, and determines that the cumulative probability distribution is calculated from a histogram using the presence or absence of the evaluation value in the sample as a variable. Device. The determination device according to claim 1 , wherein the calculation unit uses a submatrix of units of the item in the evaluation matrix as the sample. The determination device according to claim 2 , wherein the determination unit determines that the populations of the two evaluation matrices are not the same when the number of the items satisfying the above conditions is a predetermined number or more in the two evaluation matrices. In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step for calculating a cumulative probability distribution for a sample of the evaluation values, and a calculation step.
If the difference between the cumulative probability distributions of two different evaluation matrices and the index based on the number of users in each of the two evaluation matrices satisfy the conditions based on a predetermined significance level, the population of the two evaluation matrices becomes The computer executes the determination step of determining that they are not the same,
In the calculation step, a determination method in which a submatrix corresponding to one or more specific item groups in the evaluation matrix is used as the sample, and the cumulative probability distribution is calculated from a histogram using the presence or absence of the evaluation value in the sample as a variable. .. In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step for calculating a cumulative probability distribution for a sample of the evaluation values, and a calculation step.
If the difference between the cumulative probability distributions of two different evaluation matrices and the index based on the number of users in each of the two evaluation matrices satisfy the conditions based on a predetermined significance level, the population of the two evaluation matrices becomes Have the computer execute the determination step to determine that they are not the same ,
In the calculation step, the partial matrix corresponding to one or more specific item groups in the evaluation matrix is used as the sample, and the cumulative probability distribution is calculated from the histogram with the presence or absence of the evaluation value in the sample as a variable. Judgment program.

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