A globally personalized local differentially private mean estimation method

Abstract

The application discloses a kind of global individualized local differential privacy mean estimation method, this method includes that personalized privacy utility optimization local differential privacy model is defined, then a new data disturbance mechanism is provided.Server calculates personalized privacy budget matrix according to the segment number and privacy budget function disclosed in advance by itself.Each user reports a single data value, and the user end disperses the true value to the segmented endpoint according to the segment number, and submits the secondary disturbed endpoint value after the first dispersed endpoint value according to the personalized privacy budget matrix.After the server end collects all the submitted values, the corresponding solution scheme is used to estimate the data mean.The application extends the single privacy budget local differential privacy to the personalized privacy field, which can be used for data mean estimation, further expanding the application range.

Description

Technical Field

[0001] This invention belongs to the field of information security technology, specifically relating to a local differential privacy mean estimation method that provides full-domain personalized features. Background Technology

[0002] In today's internet age, with the rapid development of science and technology, mobile devices such as smartphones, smartwatches, and fitness trackers have entered countless households. Cloud computing platforms like Tencent Cloud and Alibaba Cloud have made the collection of big data more convenient and efficient. In this environment of collective intelligence, the collection, processing, and analysis of users' personal and surrounding data can indeed bring convenience to users' lives. At the same time, information leakage is increasingly becoming a threat to user privacy.

[0003] Countries around the world have imposed increasingly stringent compliance requirements on data use. In April 2016, the European Union passed the General Data Protection Regulation (GDPR), which stipulates users' right to know and right to be forgotten regarding the use of their information. In January 2020, California in the United States also passed the Consumer Privacy Act (CCPA) to protect consumers' privacy data.

[0004] Traditional privacy protection strategies often require a third party to integrate, protect, and publish data. However, due to the lack of trustworthy third parties in real life, Local Differential Privacy (LDP) has emerged. With further refinement of privacy protection levels, Differentiable Input Local Differential Privacy (ID-LDP) and its more specific form (MinID-LDP) have been proposed to further protect user privacy.

[0005] Most existing LDP methods are based on a uniform privacy budget, which is based on the definition of LDP: the query result for any two different data sets should be less than or equal to the exp value of our privacy budget. Without improvement, a problem arises. For example, consider three diseases: cancer, AIDS, and influenza. General local differential privacy would assign a general privacy budget ε to these three diseases. However, in real life, the level of privacy required for these three diseases is obviously different. This necessitates designing a model that also incorporates personalized privacy budgets. If we further categorize data privacy protection levels, Gu et al. proposed the concept of Input-Discriminative Protection for Local Differential Privacy (ID-LDP), which allows users to customize the protection level of their privacy data, achieving more granular protection. Summary of the Invention

[0006] Purpose of the invention: This invention provides a local differential privacy mean estimation method with global personalization, which extends the frequency estimation under the existing ID-LDP to mean estimation, so as to facilitate wider application in the future.

[0007] To achieve the above-mentioned objectives, the technical solution provided by this invention is as follows.

[0008] A globally personalized local differential privacy mean estimation method includes the following steps:

[0009] S1. Set the values ​​on the server side based on the privacy budget function fun and the total number of segments l of the publicly disclosed scheme on the server side, and set the generated l+1 endpoints in ascending order as {t1, t2, ..., t3}. l+1};

[0010] S2. Each user will submit a number, denoted as d. i , where d i ∈[L,U], where L and U are the domains, and then the user will input the actual value d. i Discretize to the l+1 endpoints defined in step S1, taking into account any d values ​​that are not endpoints. i It must be in the interval (t) i ,t i+1 Within ) each true value d i They are all discretized to the two endpoints of the segment they are in. For d at the endpoint values i Then remain unchanged, and d i Mapped to X i , where d i The range of values ​​is (t) i ,t i+1 ), mapped to X i Two values ​​{t i ,t i+1 The probabilities are as follows:

[0011]

[0012] in E(X i ) is d i Unbiased estimation;

[0013] S3. The server generates a privacy budget for each endpoint based on the publicly available privacy budget function `fun` and the total number of segments `l`, thereby satisfying personalized privacy requirements. For any endpoint value `t`... i Its change may have occurred within the interval (t). i-1 ,t i+1 Any value in ) is selected to satisfy the definition of Minid-LDP.

[0014] The function f(x) is the privacy budget function disclosed in step S1, and it serves as the endpoint t. i The privacy budget value is used to generate a privacy budget set w, where the special values ​​w1 and w2 are... l+1 They are respectively,

[0015] S4. The server calculates the probability perturbation matrix P based on the set w and the number of segments l;

[0016] S5. The user, based on the matrix P calculated by the server, modifies the X generated in S2. i A second perturbation is performed to generate Y. i Then submit it to the server, and the server will determine the value based on the submitted Y. i Estimate the mean of the data.

[0017] Furthermore, step (S4) includes the following process:

[0018] MSE is defined as the metric in the method. The generated matrix P should minimize the MSE of the overall scheme. The definition of MSE is as follows:

[0019]

[0020] Where p ij Let be the probability value of the i-th endpoint being perturbed to the j-th endpoint according to GRR, taking endpoint t1 as an example:

[0021]

[0022] Based on the two equations above, the probability matrix P is obtained. This matrix is ​​then solved using optimization, and the optimization scheme is as follows:

[0023] min MSE

[0024]

[0025]

[0026] Where r(ε) i ,ε j ) is a function that satisfies the ID-LDP definition. When the r function is a min function, it satisfies the MinID-LDP definition.

[0027] Furthermore, in step (S5), the server receives the perturbed value and estimates the mean of the data as follows:

[0028] After statistical perturbation, the number of times each endpoint appears, c i , where c iIt consists of two parts: one part is the unchanging endpoint i, and the other part is the perturbation of endpoint i by the other endpoints. From this, we can obtain:

[0029]

[0030] The estimated value can be obtained after the change:

[0031]

[0032] estimated value The expression contains estimates for the remaining endpoints. The presence of the expression term necessitates solving a system of n equations to obtain an estimate. This system of n equations of degree n in n variables can then be solved using a linear non-homogeneous system of equations.

[0033]

[0034] After calculating the estimated value for each endpoint, multiply each value by the endpoint value to obtain the sum of the dataset. Divide this sum by the sample size of the dataset to obtain the estimated mean, as shown in the following formula:

[0035]

[0036] Beneficial effects: This invention discloses the overall privacy budget function and the total number of segments on the server side, and calculates the perturbation matrix P for each endpoint; this invention ensures that the level of personalized data privacy protection is not reduced in this model, and still satisfies ID-LDP and ε min -LDP. This invention extends frequency estimation under existing ID-LDP to mean estimation, which provides higher data protection and innovatively incorporates personalized differential privacy into mean estimation, making it more widely applicable. Attached Figure Description

[0037] Figure 1 This is a diagram of the privacy budget function disclosed on the server side of this invention;

[0038] Figure 2 This is a schematic diagram illustrating the privacy budget selection for this invention.

[0039] Figure 3 This is the overall flowchart of the present invention;

[0040] Figure 4 This is a schematic diagram illustrating the data changes of the present invention. Detailed Implementation

[0041] To illustrate the technical solutions disclosed in this invention in detail, further explanation will be provided below with reference to the accompanying drawings.

[0042] In summary, this invention addresses the problem that the uniform privacy budget setting in existing local differential privacy models (e.g., Duchi, PM) fails to meet users' personalized privacy protection needs due to its mean estimation model. Based on the Differentiable Input Local Partition Privacy (ID-LDP) model, this invention extends the definition of LDP using MinID-LDP, incorporating users' personalized privacy requirements into the protection model, and thereby establishing an optimization mathematical model and a perturbation recovery mechanism. By estimating the mean of data using the scheme described in this invention, it can be applied to multi-level and diverse privacy publishing, achieving more personalized protection of user privacy.

[0043] Combination Figure 1 The present invention provides a globally personalized local differential privacy mean estimation method, the implementation steps of which are summarized as follows:

[0044] (1) The privacy budget function and the number of segments in the domain publicly defined on the server side;

[0045] (2) The server calculates the personalized privacy budget matrix based on the number of segments and the privacy budget function;

[0046] (3) The user end uses the piecewise function to perturb the real value to the endpoints after segmentation;

[0047] (4) The user submits the perturbed endpoint values ​​to the server after a second perturbation based on the personalized privacy budget matrix.

[0048] (5) After the server collects all the submitted values, it uses the corresponding solution to estimate the mean of the data.

[0049] Based on the above overall implementation process, the present invention further proposes substantial improvements, which can be specifically reflected in the following implementation steps:

[0050] S1. Set the values ​​on the server side based on the privacy budget function fun and the total number of segments l of the publicly disclosed scheme on the server side, and set the generated l+1 endpoints in ascending order as {t1, t2, ..., t3}. l+1};

[0051] S2. Each user will submit a number, denoted as d. i , where d i ∈[L,U], where L and U are the domains, and then the user will input the actual value d. i Discretize to the l+1 endpoints defined in step S1, taking into account any d values ​​that are not endpoints. i It must be in the interval (t) i ,t i+1 Within ) each true value d iThey are all discretized to the two endpoints of the segment they are in. For d at the endpoint values i Then remain unchanged, and d i Mapped to X i , where d i The range of values ​​is (t) i ,t i+1 ), mapped to X i Two values ​​{t i ,t i+1 The probabilities are as follows:

[0052]

[0053] in E(X i ) is d i Unbiased estimation;

[0054] S3. The server generates a privacy budget for each endpoint based on the publicly available privacy budget function `fun` and the total number of segments `l`, thereby satisfying personalized privacy requirements. For any endpoint value `t`... i Its change may have occurred within the interval (t). i-1 ,t i+1 Any value in ) is selected to satisfy the definition of Minid-LDP.

[0055] The function f(x) is the privacy budget function disclosed in step S1, and it serves as the endpoint t. i The privacy budget value is used to generate a privacy budget set w, where the special values ​​w1 and w2 are... l+1 They are respectively,

[0056] S4. The server calculates the probability perturbation matrix P based on the set w and the number of segments l;

[0057] S5. The user, based on the matrix P calculated by the server, modifies the X generated in S2. i A second perturbation is performed to generate Y. i Then submit it to the server, and the server will determine the value based on the submitted Y. i Estimate the mean of the data.

[0058] In addition to the above technical solutions, the following operations are also required during the implementation of this invention.

[0059] (1) The steps required for the user side are as follows:

[0060] (1.1) Each user submits a number denoted as d. i , where d i∈[L,U], where L and U are the domains, and the user will submit the required d. i Discretize d across l+1 endpoints exposed by the server. For any d value that is not an endpoint value... i It must be within the interval (t) i ,t i+1 Within ) each d i Discretize to the two endpoints of the segment, for d at the endpoint value i Then it remains unchanged. d i Mapped to X i , where d i The range of values ​​is (t) i ,t i+1 ), mapped to X i Two values ​​{t i ,t i+1 The probabilities are as follows:

[0061]

[0062] in E(X i ) is d i An unbiased estimate.

[0063] (1.2) The present invention provides the following perturbation mechanism.

[0064] After disclosing the privacy budget function and the number of segments, the server can calculate and publish the probability perturbation matrix P through optimization model processing. The user terminal then applies the perturbation matrix to the transformed X. i A second perturbation is performed, with the following perturbation rules:

[0065] Where p ij Let be the probability value of the i-th endpoint being perturbed to the j-th endpoint according to GRR, taking endpoint t1 as an example:

[0066]

[0067] (1.3) Finally, a perturbed noise value Y is obtained. i This is then reported to the server.

[0068] (2) For the server side, the following steps are required:

[0069] (2.1) The server will expose a privacy budget function, such as Figure 2 And the number of segments, l. The server will calculate the privacy budget for each endpoint based on the segmented endpoint values ​​in the privacy budget function, such as... Figure 3 The y-value on the [the graph].

[0070] (2.2) After the server collects all the data reported by users, it performs statistical analysis on the data.

[0071] After statistical perturbation, the number of times each endpoint appears, c i , where c i It consists of two parts: one part is the unchanging endpoint i, and the other part is the perturbation of endpoint i by other endpoints (such as endpoint j). From this, we can obtain:

[0072]

[0073] The estimated value can be obtained after the change:

[0074]

[0075] estimated value The expression contains estimates for the remaining endpoints. The presence of the expression term necessitates solving a system of n equations to obtain an estimate. This system of n equations of degree n in n variables can then be solved using a non-homogeneous linear system of equations.

[0076]

[0077] To solve this non-homogeneous linear system of equations, its coefficient matrix needs to be expanded into an augmented matrix, as shown below:

[0078]

[0079] Therefore, the solution matrix is ​​obtained:

[0080]

[0081] After calculating the estimated value for each endpoint, multiply each value by the endpoint value to obtain the sum of the dataset. Divide this sum by the sample size of the dataset to obtain the estimated mean, as shown in the following formula:

[0082]

[0083] The data changes of this method are as follows Figure 4 As shown, the user's actual value d i Discretization transforms the value into endpoint t after a single perturbation. i , t i After the transformation, it becomes any endpoint value within the entire endpoint set.

[0084] Based on the above implementation process, the present invention provides the following specific embodiments.

[0085] The experiment used a synthetic dataset containing 50,011 data points. The dataset follows a normal distribution with a mean of 0 and a variance of 5 over the range [-100, 100]. The server-side configuration was set to 11 segments, providing 12 endpoint values ​​for users to apply a perturbation. The privacy budget function graph is shown below. Figure 2 As shown, this is the inverse function of the normal distribution function with a mean of 0 and a variance of 5. The privacy budgets for the 12 endpoints are shown in Table 1. The privacy function multipliers set in the experiment are 2, 2.2, 2.4, 2.8, 3.0, 3.2, 3.4, and 3.6, respectively. Multiplying by Table 1 gives the privacy budgets for multiple experiments.

[0086] Table 1 Basic Privacy Budget for Each Endpoint

[0087]

[0088] The probability perturbation matrix can be optimally constrained using the publicly available privacy budget function and the number of segments. Taking a multiple of 2 as an example, the probability matrix is ​​shown in Table 2.

[0089] Table 2 Probability perturbation matrix for ε = 2.0

[0090]

[0091]

[0092] As shown in Table 3 of the experimental results, the present invention maintains good estimation utility across all privacy budget values.

[0093] Table 3. Error between Personalized Mean Estimation Scheme and Actual Mean

[0094]

Claims

1. A globally personalized local differential privacy mean estimation method, characterized in that, Includes the following steps: S1. Set the values ​​on the server side, with the privacy budget function of the solution being publicly disclosed by the server. Total number of segments and will generate One endpoint is set in ascending order as follows: ; S2. Each user will submit a number, which will be recorded as the actual value. ,in , L and U Define the domain, and then the user will input the actual value. Discretize to the definition in step S1 At each endpoint, considering any true value at a non-endpoint value. It must be within the range Inside, each true value They are all discretized to the two endpoints of their respective segments, and for the true values ​​at the endpoints... Then remain unchanged, and keep the true value. Mapped to ,in The range of values ​​is Mapped to Two values The probabilities are as follows: in , ; S3, The server-side uses the publicly available privacy budget function. Total number of segments Generate privacy budgets for each endpoint to satisfy personalized privacy requirements for any endpoint value. Its change may have occurred within a range. Any value in the range is selected to satisfy the definition of Minid-LDP. ; function The privacy budget function disclosed in step S1 is used as an arbitrary endpoint value. Generate a privacy budget set based on the privacy budget value. Special values and They are respectively: S4, The server sets a privacy budget. Total number of segments Calculate the probability perturbation matrix ; S5, The matrix calculated by the user based on the server. For the product generated in step S2 Perform a secondary perturbation to generate Then submit it to the server, and the server will then process the submission. Estimate the mean of the data.

2. The method for estimating the local differential privacy mean value with full-domain personalization according to claim 1, characterized in that, Step S5: The server receives the perturbed value and estimates the mean of the data as follows: The number of occurrences of each endpoint after statistical perturbation ,in It consists of two parts, one of which is the unchanging endpoint. i Part of it is caused by disturbances from other endpoints to the endpoints. From this, we can conclude: The estimated value can be obtained after the change: estimated value The expression contains estimates for the remaining endpoints. The presence of the expression term necessitates solving for the estimated value by simultaneously establishing these terms. This formula yields a... Yuan The estimated value can be obtained by solving the system of equations of this order using a linear non-homogeneous system of equations: After calculating the estimated value for each endpoint, multiply each value by the endpoint value to obtain the sum of the dataset. Divide this sum by the sample size of the dataset to obtain the estimated mean, as shown in the following formula: 。

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