Information processing device, information processing method, and program

Abstract

This information processing device comprising: a data generation unit that, on the basis of a data set and a graph structure of a Bayesian network learned from the data set, determines parameters of the Bayesian network by maximum posteriori probability estimation that assumes a predetermined distribution as the prior distribution of the parameters, and generates data from the Bayesian network having the parameters; and a security evaluation unit that evaluates differential privacy properties satisfied by the data generated by the data generation unit.

Description

Information processing device, information processing method, and program

[0001] The present invention relates to a technique for concealing personal data in a database using a probabilistic method.

[0002] The utilization of personal data is expected in various fields, but the use of privacy protection techniques is essential for handling this data. In particular, privacy protection using synthetic data generation techniques has attracted attention for tabular data. Furthermore, differential privacy is commonly used to guarantee theoretical security for such privacy protection.

[0003] A synthetic data generation technique using a Bayesian network for privacy protection based on differential privacy is known (Non-Patent Document 1). This synthetic data generation technique protects privacy by introducing random noise during parameter learning.

[0004] Jun Zhang, Graham Cormode, Cecilia M. Procopiuc, Divesh Srivastava, and Xiaokui Xiao. Privbayes: Private data release via bayesian networks. ACM Trans. Database Syst., 42(4), October 2017.

[0005] However, as with the synthetic data generation techniques described above, there is a problem in that the quality of the resulting synthetic data is degraded by introducing random noise during the parameter learning process.

[0006] The present invention has been made in consideration of the above points, and aims to provide a technology that enables synthetic data to be generated using a Bayesian network for privacy protection based on differential privacy without introducing random noise during the parameter learning process.

[0007] According to the disclosed technology, an information processing device is provided that includes: a data generation unit that determines parameters of a Bayesian network by maximum posterior probability estimation when a predetermined distribution is assumed as a prior distribution of the parameters based on a dataset and a graph structure of the Bayesian network learned from the dataset, and generates data from the Bayesian network having the parameters; and a safety evaluation unit that evaluates the differential privacy satisfied by the data generated by the data generation unit.

[0008] The disclosed technology provides a technology that enables synthetic data generation using a Bayesian network for privacy protection based on differential privacy without introducing random noise during the parameter learning process.

[0009] 1 is a diagram illustrating a configuration of an information processing device 100. FIG. 2 is a flowchart illustrating the operation of the information processing device 100. FIG. 3 is a diagram illustrating Algorithm 1. FIG. 4 is a diagram illustrating Algorithm 2. FIG. 5 is a diagram illustrating Algorithm 3. FIG. 6 is a diagram illustrating an example of a hardware configuration of an apparatus.

[0010] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0011] In the text of the specification, for convenience of description, characters in normal font are used to represent sets. It is clear from the context that the characters represent sets. In addition, in the text of the specification, subscripts of superscripts are represented using "_". Ｋ＿１ " is an example.

[0012] In this embodiment, an information processing device 100 (described later) generates synthetic data using a Bayesian network for privacy protection based on differential privacy. The information processing device 100 generates synthetic data without introducing random noise during parameter learning.

[0013] As described above, the quality of the data can be maintained because random noise is not introduced. Furthermore, when random noise is not introduced, it is generally not possible to properly evaluate security, but the information processing device 100 can output, in addition to the data, a security index for the differential privacy that the generated data satisfies.

[0014] The device configuration and operation according to this embodiment will be described below, but before that, differential privacy and Bayesian network structural learning, which are basic configuration technologies in this embodiment, will be described. Differential privacy itself and Bayesian network structural learning itself are both existing technologies, so only an overview will be described below.

[0015] (Differential Privacy) Differential privacy is a privacy-preserving index that quantitatively represents the degree to which inferences about original data can be made from the output of a random process.

[0016] Let DD be the set of all possible datasets, and YY be the set of all output values ​​of the query under consideration. Furthermore, if dataset D and dataset D'∈D differ by only one record, they are said to be adjacent datasets.

[0017] A randomization function M:DD→YY satisfies (ε, δ)-differential privacy if the following equation holds for any adjacent data sets D, D′ and any output range S⊂YY.

[0018] Pr[M(D)∈S]≦e εPr[M(D')∈S]+δ (Regarding Bayesian Network Structure Learning) In this embodiment, table data of categorical attributes is used as the data set. The table data has multiple attributes, and each attribute corresponds to a node in the Bayesian network. The data of a certain record takes one of multiple attribute values ​​for each attribute. The root node (parent node) has a probability distribution for the attribute value. A child node having a parent has a conditional probability distribution for the attribute value.

[0019] Learning of a Bayesian network consists of structural learning, which learns the graph structure of the Bayesian network, and parameter learning, which learns parameters corresponding to the probability distribution of each node from the frequency of data, etc.

[0020] In structural learning, relationships between attributes of table data are learned, and the relationships are output as an acyclic directed graph G. In this embodiment, structural learning is performed using Greedy Bayes (Non-Patent Document 1), which is an existing technology.

[0021] (Device Configuration Example) Fig. 1 shows a configuration example of an information processing device 100 according to this embodiment. As shown in Fig. 1, the information processing device 100 includes an input unit 110, a data synthesis unit 120, a safety evaluation unit 130, an output unit 140, and a data storage unit 150. The data synthesis unit 120 also includes a structure learning unit 121 and a data generation unit 122.

[0022] (Operation of Information Processing Apparatus 100) The operation of the information processing apparatus 100 having the above-described configuration will be described in accordance with the procedure of the flowchart shown in FIG.

[0023] <S101 (Step 101)> Data required for subsequent calculations is input from the input unit 110 to the information processing device 100. The input data is stored in the data storage unit 150. In this embodiment, the following data (1) to (6) are input to the information processing device 100.

[0024] (1) Dataset D∈DD The data set D is a table-format data set with d attributes and N records. Let K be the number of attribute values ​​of the i-th attribute.ｉ Let's say.

[0025] (2) Maximum number of parent nodes k (3) Number of output records n ｏｕｔ ∈Z ＞０ (4) Prior distribution parameter η １ ∈R Ｋ＿１ , ..., η ｄ ∈R Ｋ＿ｄ (5) Privacy-preserving budget ε for structural learning ｇ ∈R ≧０ (6) Allowable Error δε[0, 1] <S102: Structure Learning> In S102, the structure learning unit 121 in the data synthesis unit 120 performs structure learning of the Bayesian network.

[0026] The structure learning unit 121 receives a data set D, a maximum number k of parent nodes, and a privacy-preserving budget ε for structure learning. ｇ is read from the data storage unit 150 and used as an input.

[0027] Next, the structure learning unit 121 executes the procedure of Algorithm 1 shown in FIG. 3 to learn a differentially private graph structure and output the graph structure G.

[0028] As mentioned above, the structural learning method in this embodiment is an existing technology, and uses Greedy Bayes disclosed in Non-Patent Document 1. Only an outline will be explained here.

[0029] As shown in Figure 3, Greedy Bayes performs structural learning by determining the next node and its parent node using an exponential mechanism that uses the magnitude of mutual information as a score function. The "exponential mechanism" is disclosed, for example, in the reference "Frank McSherry and Kunal Talwar. Mechanism design via differential privacy. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), pages 94-103. IEEE, 2007."

[0030] It should be noted that the information processing device 100 may not include the structure learning unit 121. In this case, the learned graph structure G is input to the information processing device 100 and used in the data generation process.

[0031] <S103: Data Generation> In S103 of the flow in FIG. 2, the data generation unit 122 in the data synthesis unit 120 generates data.

[0032] The data generation unit 122 combines the trained graph structure G obtained in S102 with the data set D, the number of outputs n ｏｕｔ , the prior distribution parameter η １ , ..., η ｄ " is the input.

[0033] Next, the data generation unit 122 executes the procedure of Algorithm 2 shown in FIG. 4 to obtain n ｏｕｔ The output is privacy-preserving synthetic data consisting of records.

[0034] That is, the data generating unit 122 learns the parameters using Equations 1 and 2 described later, and generates a specified number n based on the learned parameters. ｏｕｔ records are output. Formula 1 and Formula 2 will be explained.

[0035] Let N be the number of records in the input data set. For node X (here, a certain attribute), let Y be the set of its parent attributes, and let y be one realization value. Let us write it as follows:

[0036] N ｙ :=#{x∈D|x| Ｙ = y} The above description corresponds to counting the number of records in dataset D where the value of attribute set Y is y. In addition, when the realization value of X is i, it will be written as follows.

[0037] N ｉ，ｙ :=#{x∈D|x| Ｘ = i, x | Ｙ= y} The above description corresponds to counting the number of records in the data set D where the value of attribute X is i and the value of attribute set Y is y.

[0038] In this embodiment, parameter learning of the Bayesian network is performed using an appropriate Dirichlet distribution (hyperparameters are η∈R Ｋ＿Ｘ The probability distribution is calculated by maximum a posteriori probability estimation (MAP estimation) assuming that the prior distribution is the probability distribution shown in the following equation 1.

[0039] The above θ Ｘ ｉ，ｙ is θ Ｘ The probability of X maximizing the posterior probability that X = i and Y = y when the prior distribution of follows a Dirichlet distribution with η as a parameter. Ｘ ｉ，ｙ The probability distribution is calculated by calculating

[0040] Similar processing can also be performed on the root node (a node with no parent), and the probability shown in the following equation 2 can be obtained.

[0041] The above θ Ｘ ｉ is θ Ｘ is the probability in X that maximizes the posterior probability that X = i when the prior distribution of follows a Dirichlet distribution with η as a parameter. Ｘ ｉ The probability distribution is calculated by calculating

[0042] The data generation unit 122 learns parameters (probability distribution) from the data set by performing calculations using Equations 1 and 2, and samples data based on the learned probability distribution to generate synthetic data D ｓｙｎ Generate.

[0043] A more specific process will be described with reference to Fig. 4. Here, the description will be made assuming that the line numbers in Fig. 4 are step numbers.

[0044] In S1 (step 1), the data generator 122 assigns η to the prior distribution using Equation 2. １ MAP estimation using the Dirichlet distribution of the parameter θ １ Ask for.

[0045] In S2 to S6, the data generating unit 122 executes S3 to S5 for each of t=2 to 1.

[0046] In steps S3 to S5, the data generation unit 122 assigns η to the prior distribution for each combination of the attributes of the parents of t. ｔ MAP estimation using the Dirichlet distribution of the parameter θ ｔ，ｙ Ask for.

[0047] In S7, the data generation unit 122 generates the probability distribution θ １ , θ ２，ｙ１ ,..., based on n ｏｕｔ pieces of data are sampled and this data is designated as D'. The process of sampling data from the probability distribution is the same as the process of generating data using a normal Bayesian network.

[0048] In S8, the data generating unit 122 converts D' into composite data D ｓｙｎ At this time, the composite data D ｓｙｎ may be output from the output unit 140.

[0049] In this embodiment, the Dirichlet distribution is used as the prior distribution, but the distribution used as the prior distribution is not limited to the Dirichlet distribution.

[0050] 2, the safety evaluation unit 130 performs safety evaluation. The safety evaluation unit 130 evaluates the safety of the dataset D, the privacy budget for structural learning ε ｇ , number of outputs n ｏｕｔ , the prior distribution parameter η １ , ..., η ｄ , and the allowable error δ are read from the data storage unit 150 and used as input. Next, the safety evaluation unit 130 outputs the safety index ε by executing the procedure of Algorithm 3 shown in FIG.

[0051] More specifically, the safety evaluation unit 130 evaluates the composite data D output from the data generation unit 122. ｓｙｎ It is known that the data generated by the data generation unit 122 executing Algorithm 2 satisfies (ε, δ)-differential privacy for the following ε. The safety evaluation unit 130 uses Algorithm 3 to calculate ε using the following calculation:

[0052] In Algorithm 3 shown in FIG. 5, the safety evaluation unit 130 calculates ε ０ In S2 to S6, the safety evaluation unit 130 calculates S3 to S5 for each of i=1 to d. In S3, the safety evaluation unit 130 calculates η ｉ The minimum value of η ｉ，ｍｉｎ In S4, η ｉ，ｓｕｍ =Σ ｊ η ｉ，ｊ -1, and in S5, ε ０ is updated. ε is found in S7.

[0053] The upper equation in the above "Equation 3" is "the probability distribution of the nodes in the original data D (assumed to be P) and the synthetic data D ｓｙｎ It is the logarithm of the total product of the "maximum value of the ratio (Q / P) of the probability distribution of the node (Q) in the node (1 to d)".

[0054] The lower equation in "Mathematical Expression 3" is based on the proposition that "if a mechanism m satisfies ε-differential privacy, then for δ>0, a mechanism that adaptively uses m k times satisfies (2ε√(2klog(1 / δ)), δ)-differential privacy." Note that "√(2klog(1 / δ))" intends that "2klog(1 / δ)" is in the root.

[0055] <S105> In S105 of the flow of FIG. 2, the output unit 140 outputs the composite data D ｓｙｎ (The number of attributes is d, and the number of records is n. ｏｕｔ ), and the privacy protection index ε (a positive real number). ｓｙｎ satisfies (ε, δ)-differential privacy.

[0056] (Example) The processing procedure summarizing the above-mentioned processes is shown as Algorithm 4 in Fig. 6. The input data has already been described. Fig. 6 mainly describes the Algorithm. The operation of the information processing device 100 will be described below with reference to Fig. 6.

[0057] In S1, the structure learning unit 121 calculates D, k, ε ｇ In S2, the data generator 122 receives D, G, and η １ , ..., η ｄ , n ｏｕｔ is input, and D ｓｙｎ In S3, the safety evaluation unit 130 outputs D, ε ｇ , n ｏｕｔ , η １ , ..., η ｄ In S4, the output unit 141 receives D ｓｙｎ and output ε.

[0058] (Hardware Configuration Example) The information processing device 100 described in this embodiment can be realized, for example, by causing a computer to execute a program. This computer may be a physical computer or a virtual machine on the cloud.

[0059] That is, the information processing device 100 can be realized by using hardware resources such as a CPU and memory built into a computer to execute a program corresponding to the processing performed by the information processing device 100. The program can be recorded on a computer-readable recording medium (such as a portable memory) and can be saved or distributed. The program can also be provided via a network such as the Internet or email.

[0060] Fig. 7 is a diagram showing an example of the hardware configuration of the computer. The computer in Fig. 7 includes a drive device 1000, an auxiliary storage device 1002, a memory device 1003, a CPU 1004, an interface device 1005, a display device 1006, an input device 1007, an output device 1008, and the like, all of which are interconnected via a bus B. The computer may further include a GPU.

[0061] The program that realizes the processing on the computer is provided by a recording medium 1001, such as a CD-ROM or a memory card. When the recording medium 1001 storing the program is set in the drive device 1000, the program is installed from the recording medium 1001 to the auxiliary storage device 1002 via the drive device 1000. However, the program does not necessarily have to be installed from the recording medium 1001, but may be downloaded from another computer via a network. The auxiliary storage device 1002 stores the installed program as well as necessary files, data, etc.

[0062] The memory device 1003 reads and stores a program from the auxiliary storage device 1002 when an instruction to start the program is received. The CPU 1004 realizes functions related to the information processing device 100 in accordance with the program stored in the memory device 1003. The interface device 1005 is used as an interface for connecting to a network, etc. The display device 1006 displays a GUI (Graphical User Interface) or the like according to the program. The input device 1007 is composed of a keyboard, mouse, buttons, a touch panel, etc., and is used to input various operation instructions. The output device 1008 outputs the results of calculations.

[0063] (Summary, Effects, etc. of the Embodiments) As described above, the technology described in the present embodiment makes it possible to generate data without intentionally adding random noise by replacing parameter learning, which conventionally requires adding noise to ensure privacy protection, with maximum a posteriori probability estimation (Algorithm 2). Furthermore, security can be evaluated using Algorithm 3 without adding random noise.

[0064] That is, the technology described in this embodiment makes it possible to generate synthetic data that is guaranteed to be secure in the sense of differential privacy for datasets related to individuals in the form of individual records. Since it is not necessary to add random noise during parameter learning, the quality of the synthetic data is maintained. Furthermore, while conventional evaluation methods could not evaluate security without adding random noise, this embodiment makes it possible to evaluate security (differential privacy). Therefore, it becomes possible to evaluate security within the same framework as existing methods while maintaining quality.

[0065] The following additional notes are provided regarding the above-described embodiments.

[0066] <Additional Notes> (Additional Item 1) An information processing device comprising: a data generation unit that determines parameters of a Bayesian network by maximum a posteriori estimation when a predetermined distribution is assumed as a prior distribution of the parameters, based on a dataset and a graph structure of a Bayesian network learned from the dataset, and generates data from the Bayesian network having the parameters; and a safety evaluation unit that evaluates differential privacy satisfied by the data generated by the data generation unit. (Additional Item 2) The information processing device according to Additional Item 1, wherein the predetermined distribution is a Dirichlet distribution. (Additional Item 3) An information processing method executed by an information processing device, comprising: a data generation step that determines the parameters by maximum a posteriori estimation when a predetermined distribution is assumed as a prior distribution of the parameters of the Bayesian network, based on a dataset and a graph structure of a Bayesian network learned from the dataset, and generates data from the Bayesian network having the parameters; and a safety evaluation step that evaluates differential privacy satisfied by the data generated by the data generation step. (Supplementary Item 4) A non-transitory storage medium storing a program for causing a computer to function as each unit in the information processing device according to Supplementary Item 1 or 2.

[0067] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims.

[0068] REFERENCE SIGNS LIST 100 Information processing device 110 Input unit 120 Data synthesis unit 121 Structure learning unit 122 Data generation unit 130 Safety evaluation unit 140 Output unit 150 Data storage unit 1000 Drive device 1001 Recording medium 1002 Auxiliary storage device 1003 Memory device 1004 CPU 1005 Interface device 1006 Display device 1007 Input device 1008 Output device

Claims

1. An information processing device comprising: a data generation unit that determines parameters of a Bayesian network by maximum posterior probability estimation assuming a predetermined distribution as a prior distribution of the parameters based on a dataset and the graph structure of the Bayesian network learned from the dataset, and generates data from the Bayesian network having the parameters; and a security evaluation unit that evaluates the differential privacy satisfied by the data generated by the data generation unit.

2. The information processing device according to claim 1, wherein the predetermined distribution is a Dirichlet distribution.

3. An information processing method executed by an information processing device, comprising: a data generation step of determining parameters of a Bayesian network by maximum posterior probability estimation assuming a predetermined distribution as a prior distribution of the parameters based on a dataset and the graph structure of the Bayesian network learned from the dataset, and generating data from the Bayesian network having the parameters; and a security evaluation step of evaluating the differential privacy satisfied by the data generated by the data generation step.

4. A program for causing a computer to function as each unit in the information processing device according to claim 1 or 2.

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