JP2020119201A - Determination device, determination method and determination program - Google Patents

Abstract

To provide a determination device, a determination method, and a determination program that can determine malignant data regardless of distribution of evaluation data.SOLUTION: A determination device 1 includes: a calculation unit 11 that calculates, in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a cumulative probability distribution for a sample of evaluation values; and a determination unit 12 that determines, when difference between cumulative probability distributions of two different evaluation matrices and index based on the number of users in each of the two evaluation matrices satisfy a condition based on a predetermined significance level, that populations of the two evaluation matrices are not same.SELECTED DRAWING: Figure 1

Description

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

In the collaborative filtering used in a recommendation system or the like, evaluation values for un-evaluated 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 improperly evaluates an item while pretending to be a legitimate user and mixes malicious data into the evaluation data. Data poisoning attacks are aimed at reducing predictive performance or increasing or decreasing the popularity of specific items.

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

B. Li, Y. Wang, A.; Singh, and Y. Vorobechik: Data Poisoning Attacks on Factorization-Based Collaborative Filtering, Proceedings of the 3rd Neural Information, IPS Systems 20. 1-13, 2016.

In the above method, it is assumed that the distributions of the evaluation values of the normal user and the malicious user are the normal distribution, but the distribution of the evaluation values does not always follow the normal distribution. Therefore, in many cases, the additional malicious data cannot be detected correctly.

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

The determination device according to the present invention is, in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation unit that calculates a cumulative probability distribution regarding a sample of the evaluation values, and two evaluation matrices for each of two different evaluation matrices. A difference between cumulative probability distributions, and a determination unit that determines that the populations of the two evaluation matrices are not the same when the index based on the number of users in each of the two evaluation matrices satisfies a condition based on a predetermined significance level, Equipped with.

The calculating unit may calculate the cumulative probability distribution that represents a histogram of the evaluation values, using the set of the evaluation values stored in the evaluation matrix as the sample.

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

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

The determination unit may determine that the populations of the two evaluation matrices are not the same when the number of items satisfying the condition in the two evaluation matrices is equal to or larger than a predetermined number.

A determination method according to the present invention is, in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step of calculating a cumulative probability distribution regarding a sample of the evaluation values, and two evaluation matrices for each of two different evaluation matrices. A difference between cumulative probability distributions, and a determination step of determining that the populations of the two evaluation matrices are not the same when the index based on the number of users in each of the two evaluation matrices satisfies a condition based on a predetermined significance level, Is executed by the computer.

A determination program according to the present invention, in an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step of calculating a cumulative probability distribution regarding a sample of the evaluation values, and two evaluation matrices different from each other. A difference between cumulative probability distributions, and a determination step of determining that the populations of the two evaluation matrices are not the same when the index based on the number of users in each of the two evaluation matrices satisfies a condition based on a predetermined significance level, To make a 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 device which concerns on embodiment. It is a flow chart which shows the procedure of the 1st judgment method concerning an embodiment. It is a flow chart which shows the procedure of the 2nd judgment method concerning an 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 using the Kolmogorov-Smirnov test that the evaluation matrix additionally provided is malignant data with respect to the regular evaluation matrix used for emphasis filtering.
The Kolmogorov-Smirnov test is one of the nonparametric test methods that does not rely on the distribution, unlike the t-test that assumes a normal distribution. This allows evaluation by a normal user without assuming the shape of the distribution for evaluation values. A matrix is distinguished from an evaluation matrix by a malicious user.

Here, let M be an evaluation matrix for n items by m regular users. M _i,j indicates 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 on collaborative filtering, the attacker becomes a legitimate user, illegally 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′ malicious users.
When the evaluation matrix M′ is additionally given to the evaluation matrix M of the normal user, the determination apparatus 1 of the present embodiment has the evaluation matrix M′ by the normal user or 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 an input/output device for various data, a communication device, and the like in addition to the control unit 10 and the storage unit 20.

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

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

The calculation unit 11 calculates a cumulative probability distribution regarding a sample of evaluation values in the evaluation matrices M and M′ in which evaluation values for a plurality of items for each user are stored.
The calculation unit 11 calculates, for example, a cumulative probability distribution representing a histogram of evaluation values, using a set of observed evaluation values stored in the evaluation matrices M and M′ as a sample.
In addition, for example, the calculation unit 11 uses, as samples, portions corresponding to each other in the two evaluation matrices M and M′, and calculates a cumulative probability distribution that represents a histogram of the presence or absence of evaluation values in these samples. Specifically, the calculation unit 11 may use the partial matrix of the unit of the items in the evaluation matrices M and M′ as a sample.

The determination unit 12 determines whether the difference between the cumulative probability distributions of the two different evaluation matrices M and M′ and the index based on the number of users m and m′ in each of the evaluation matrices M and M′ are based on a predetermined significance level. When it is satisfied, 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 determines that the populations of the two evaluation matrices M and M′ are not the same when the number of subsets (the number of items) satisfying the condition is equal to or larger than a predetermined value. May be determined.

Next, the procedure of the method of determining malicious data by the determination device 1 will be described in detail.
The determination device 1 employs, for example, the following first determination method or second determination method. In addition, 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 any of the methods, 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 apparatus 1 uses the Kolmogorov-Smirnov test to determine that M′ is malignant based on the difference between the cumulative probability distributions of the observed evaluation values included in each of the evaluation matrices M and M′. It is determined whether the evaluation matrix is for the user.

FIG. 2 is a flowchart showing the procedure of the first determination method according to this embodiment.
When using the Kolmogorov-Smirnov test, let X be a sample of the evaluation value of a normal user and X′ be a sample of the evaluation value of a malignant user. In addition, the null hypothesis is “the populations of X and X′ are 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 regular user. Further, the calculation unit 11 calculates the cumulative probability distribution Q(x) of the sample X′ using the evaluation matrix M′ of the malicious 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 coexist as elements of the evaluation matrices M and M′, the calculation unit 11 causes the calculation unit 11 to calculate the evaluation value x( =1-5), the cumulative probability distribution is calculated.

In step S2, the determination unit 12 calculates the Kolmogorov-Smirnov statistic D by the following formula 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 malicious data from the number m of regular users, the number m'of malicious users, and the statistic D. To 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 mixed by a malignant user.

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

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

FIG. 3 is a flowchart showing the procedure of the second determination method according to this embodiment.
When using the Kolmogorov-Smirnov test, let X _{j be} a sample of the evaluation value for the j-th item by the normal user and X _j ′ be a sample of the evaluation value for the j-th item by the malicious user. However, the evaluation value is a binary value of 0 or 1, that is, 1 if the user is evaluating the j-th item, regardless of the evaluation level, and 0 if not. In addition, the null hypothesis is “the populations of X _j and X _j ′ are the same”.

In step S11, the control unit 10 initializes the index j of n items and the number k of items 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 regular user. In addition, the calculation unit 11 obtains the cumulative probability distribution Q(x) of the sample X _j ′ using the evaluation matrix M′ of the malicious 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 the elements of the evaluation matrices M and M′, the calculation unit 11 evaluates that there is no evaluation (x=0). The cumulative probability distribution is calculated from the histogram of (x=1).

In step S14, the determination unit 12 calculates the Kolmogorov-Smirnov statistic D by the following formula 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 m of regular users, the number m'of malicious users, and the statistic D. To 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 the 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 the number k of items for determination is equal to or greater than the threshold value t. If the 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 the malicious data mixed by the malicious user, and ends the processing.

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 all items have been tested. 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 the regular data given by the regular user.

According to the present embodiment, the determination apparatus 1 uses the Kolmogorov-Smirnov test, which is one of the nonparametric test methods, based on the cumulative probability distribution regarding the samples 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 the added evaluation matrix is malicious data without assuming the shape of the distribution of the evaluation values of the normal user and the malicious user.
Therefore, the determination device 1 can suppress the influence of the data poisoning attack even in a 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, and calculates a cumulative probability distribution representing a histogram for each observed evaluation value, to determine whether the distribution of evaluation values is malignant. Data can be judged appropriately.

The determination device 1 uses a portion corresponding to each other in two evaluation matrices as a sample, and calculates a cumulative probability distribution that represents a histogram of the presence or absence of the evaluation value in the sample to determine a specific portion (for example, an item group) in the evaluation matrix. The malignant data can be appropriately determined based on the similarity of the samples focused 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 value for each item by using the submatrix of the item of the evaluation matrix as a sample. As a result, even if the determination device 1 determines a malicious evaluation value such that the attacker has the same or similar distribution as the distribution of the evaluation values of the legitimate users, for example, the malicious user only selects a specific item. Detect malicious data poisoning attacks 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 malignant user is added when the number of items for which the populations are not the same is equal to or larger than a predetermined number. May be. As a result, the determination device 1 can suppress erroneous detection due to determination using 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. Further, the effects described in the above-described embodiments are merely enumeration of the most suitable effects produced by 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 implemented by software, a program forming the software is installed in an information processing device (computer). In addition, these programs may be recorded on a removable medium such as a CD-ROM and distributed to users, or may be distributed by being downloaded to users' computers via a network. Further, these programs may be provided to the user's computer as a Web service via the network without being downloaded.

1 determination device 10 control unit 11 calculation unit 12 determination unit 20 storage unit

Claims (7)

In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation unit that calculates a cumulative probability distribution regarding a sample of the evaluation values,
When 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 a condition based on a predetermined significance level, the population of the two evaluation matrices is A determination device that determines that they are not the same. The determination device according to claim 1, wherein the calculation unit uses the set of evaluation values stored in the evaluation matrix as the sample and calculates the cumulative probability distribution representing a histogram of the evaluation values. The determination device according to claim 1, wherein the calculation unit calculates, as the sample, portions corresponding to each other in the two evaluation matrices, the cumulative probability distribution representing a histogram of the presence or absence of the evaluation value in the sample. The determination device according to claim 3, wherein the calculation unit uses the partial matrix of the unit of the item in the evaluation matrix as the sample. The determination device according to claim 4, wherein the determination unit determines that the populations of the two evaluation matrices are not the same when the number of items satisfying the condition in the two evaluation matrices is equal to or larger than a predetermined number. In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step of calculating a cumulative probability distribution regarding a sample of the evaluation values,
When 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 a condition based on a predetermined significance level, the population of the two evaluation matrices is And a determination step of determining that they are not the same. In an evaluation matrix in which evaluation values for a plurality of items for each user are stored, a calculation step of calculating a cumulative probability distribution regarding a sample of the evaluation values,
When 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 a condition based on a predetermined significance level, the population of the two evaluation matrices is A determination program for causing a computer to execute a determination step of determining that they are not the same.

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