Table-type data publishing method based on local differential privacy

Abstract

This invention proposes a tabular data publishing method based on local differential privacy. The method includes: users locally perturbing the original data, encoding and adding noise to attribute values ​​before uploading to a server; the server estimating the first-order marginal distribution of single attributes and the joint distribution of attribute pairs, and using a marginal selection algorithm to select a set of two-dimensional attributes from all attributes that retain statistical characteristics and have low estimation errors; iteratively updating a randomly generated initial dataset based on the set, making its marginal statistical properties approximate the original data distribution, and generating a synthetic dataset. This invention completes perturbation, distribution estimation, and data synthesis under a local differential privacy architecture, avoiding the complete trust assumption of centralized methods on the server, ensuring user privacy while achieving data publishing, balancing privacy protection and data availability, and is applicable to various data analysis and mining tasks.

Description

Technical Field

[0001] This invention belongs to the field of electronic data processing technology, and further relates to a method for publishing tabular data based on local differential privacy. This invention is designed for data synthesis of structured tabular data and can be used for data anonymization and publishing in data sharing scenarios. Background Technology

[0002] With the widespread application of technologies such as artificial intelligence and data mining, structured tabular data, as an important data carrier, is widely collected and utilized in fields such as healthcare, finance, e-commerce, and government affairs. To promote data reuse and cross-organizational sharing, more and more data controllers hope to share and publish some data after anonymization, while ensuring privacy and security. However, traditional data anonymization methods, such as k-anonymity and l-diversity, are vulnerable to re-identification attacks when attackers possess supplementary information, failing to provide strict privacy protection. Therefore, differential privacy has been proposed as a mechanism that can provide strict mathematical privacy protection and is gradually becoming an important direction in privacy protection research and practical deployment.

[0003] In the practical application of differential privacy, a common practice is to directly add noise to the original data before publishing the query results or statistical indicators. While this method can provide theoretical privacy protection, it has several limitations: firstly, the noise in the query results accumulates rapidly with the increase in query dimensions or frequency, severely affecting the usability of the data; secondly, users can only perform predefined query operations (such as counting and summing), and if they need to perform new, undesigned queries (such as bucketing statistics or correlation analysis), they cannot directly use the published noise results, meaning this method lacks flexible access to the distribution of the original data. Therefore, in recent years, more and more research has turned to using differential privacy for data synthesis, that is, constructing a synthetic dataset that is statistically similar to the original dataset to replace the original data publication, allowing users to perform any type of data analysis task on the published data.

[0004] In centralized differential privacy frameworks, data synthesis methods typically assume the existence of a trusted server that directly accesses and processes the raw data, injecting noise during the modeling or sampling phase to meet differential privacy constraints. Such methods, such as PrivBayes, PGM, and PrivSyn, achieve high-quality data synthesis through probabilistic graphical models or marginal updates. However, centralized differential privacy methods have significant drawbacks: they rely heavily on the trustworthiness of the server. If the server is attacked or a data breach occurs, all raw data may be exposed, posing a serious risk to user privacy.

[0005] Fudan University disclosed a method for generating data for relational tables in its patent application, "Data Generation Method and Apparatus for Relational Tables" (Patent Application No.: 202410855453.6, Publication No.: CN 118734817 A). The specific steps of this method are: constructing a training dataset based on a specified table; constructing a discriminator and a generator; performing adversarial training on the discriminator and generator based on the training dataset to obtain a trained generator as a data synthesis model; concatenating randomly sampled noise vectors with conditional vectors to obtain an input vector; inputting the input vector into the data synthesis model to obtain a synthesized data vector; and transforming the synthesized data vector to obtain synthesized table data. This method can generate synthetic data that more closely resembles table data. However, this method still has two significant shortcomings: first, it requires direct access to and utilization of the original table data to construct the training dataset and model parameters; if malicious attacks occur during the training process, the user's sensitive data may be indirectly restored or reconstructed; second, some studies have shown that using deep learning methods to construct synthetic datasets has poor performance in terms of dataset usability. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technologies mentioned above by proposing a tabular data publishing method based on local differential privacy, which solves the following three problems: First, the insecurity of centralized differential privacy methods, where the entire original data may be exposed if the server is leaked; second, the problem of excessive noise accumulation due to blindly selecting too many margins, or severe information loss due to selecting too few margins; and third, the oscillation problem caused by the forced matching of the target distribution in traditional minimum cost flow methods.

[0007] The technical approach to achieving the objective of this invention is as follows: Users locally perturb the original data records and upload noisy data that satisfies local differential privacy constraints; the server collects the perturbed data, estimates the joint distribution between attribute pairs, and obtains approximate values ​​of two-dimensional margins; through a margin selection algorithm, a set of margins that satisfy specific conditions is obtained; based on this margin set, the randomly generated dataset is iteratively updated to generate synthetic tabular data that retains statistical structure under privacy protection. Because this invention uses local differential privacy perturbation technology, its essential characteristic is that users complete the noisy operation before uploading the data, thus ensuring privacy and security without trusting a centralized server. Leveraging this characteristic, this invention effectively solves the insecurity problem of centralized differential privacy methods, where a server leak could expose all original data. Because this invention introduces an attribute correlation measurement method, its essential characteristic is that it quantifies the similarity and correlation between attributes by calculating the joint distribution between attributes. Based on the margin selection algorithm, a set of margins that satisfy the conditions is dynamically selected, thereby achieving low-dimensional preservation of data statistical features. Building upon this foundation, the relationship between privacy protection and data availability is further modeled, transforming it into an optimization problem. This overcomes the issues of excessive noise accumulation due to blindly selecting too many boundaries, or severe information loss due to selecting too few boundaries, found in existing methods. Because this invention employs an iterative update approach, its essential characteristic is that it gradually approximates the target distribution during the synthetic data generation process, rather than forcibly matching each time, thereby reducing the oscillation problem inherent in traditional minimum cost flow methods. Relying on this gradual optimization mechanism, this invention can generate statistically more stable and realistic data while ensuring privacy.

[0008] To achieve the above objectives, the specific implementation steps of the present invention include the following:

[0009] Step 1: The user perturbs the individual data record to which they belong locally. Local differential privacy technology is used to encode and perturb the value of each attribute of the record, and the perturbed data is uploaded to the server.

[0010] Step 2: The server will compile all the perturbation records uploaded by users into a perturbation-based tabular dataset, and estimate the first-order marginal distribution of each attribute and the joint distribution between attribute pairs based on the dataset to obtain approximate values ​​of all two-dimensional marginal distributions.

[0011] Step 3: Using the marginal selection algorithm based on attribute correlation measurement, select a set of two-dimensional marginal sets that retain the statistical characteristics of the original data and have low estimation error from all approximations of the two-dimensional marginal distributions.

[0012] Step 4: Iteratively update the randomly generated dataset, adjust the data distribution of the randomly generated dataset to make it approximate the selected two-dimensional marginal set, and generate a synthetic dataset that meets privacy protection constraints.

[0013] Step 5: The server publishes the synthetic dataset to provide data analysts with subsequent queries and analysis.

[0014] Furthermore, the step of encoding the value of each attribute of the record using local differential privacy technology is as follows:

[0015] The first step is for each user to upload a message containing... Data records with one attribute:

[0016] ,

[0017] Each attribute corresponds to a set of hash functions:

[0018] ={ },

[0019] in, Represents the j-th attribute The value of , express A set of hash functions, express The number of elements in the corresponding hash function group , ;

[0020] The second step is to set the initial value of each attribute value encoded for each user to the length. A string of all zero bits, for each user Use hash function group Perform hashing, each hash function outputs An integer within the range, of The bits at the integer positions are set to 1, resulting in the final Bloom filter. At most One bit is 1, and the rest are 0.

[0021] Furthermore, the perturbation processing refers to the perturbation of each encoded value. Bit With probability Keep the original value, with probability The bit string is randomly permuted to 0 or 1; the perturbed bit string satisfies - Local differential privacy constraints no longer directly reflect the original attribute values, but under the aggregation of large-scale user data, they can still be used to recover the overall statistical characteristics. Their expression is:

[0022] ;

[0023] in, express The first in The value after bit perturbation , , where represents the perturbation parameter, the value of which is determined by the privacy budget. Decide.

[0024] Furthermore, uploading the perturbed data to the server means that each user concatenates all the perturbed bit strings according to their attribute order to obtain a vector: As a privacy protection measure, this data record is uploaded to the server. Indicates the first The bit string after perturbation of each attribute. This indicates a vector concatenation operation.

[0025] Furthermore, the step of estimating the first-order marginal distribution of each attribute is as follows:

[0026] The first step is for the server to receive all user records after perturbation, extract the bit string of each attribute after perturbation for each user, and count the total number of times each bit of each attribute bit string is 1 for all users.

[0027] The second step is to perform noise reduction on the total number of each bit that is 1, estimate the true sum of counts, and concatenate all the sums of counts with bits 1 into a binary string:

[0028] , ;

[0029] in, Attributes representing all users The first bit in the denoised bit string The sum of the counts where each bit is 1. Attributes representing all users The perturbed bit string The sum of the counts where each bit is 1. This represents the total number of all users. Attributes representing all users The count of all bits that are 1 in the denoised bit string and the concatenated binary string;

[0030] Step 3, Attributes have Each possible value is denoted as... For each value According to attributes Corresponding hash function group Generate Bloom Filter The first-order marginal distribution estimation problem is modeled as a regularized least squares problem: ,in, Indicates by attribute The candidate matrix formed by the Bloom filters for all possible values. Represents the coefficient vector. Represents the L1 regularization coefficient;

[0031] The fourth step is to solve the problem using the Lasso regression algorithm. Then the attribute The probability distribution estimate is 𝑝= .

[0032] Furthermore, the step of estimating the joint distribution among the attribute pairs is as follows:

[0033] The first step is to select two attributes that have not been combined from the attributes of the tabular dataset records;

[0034] The second step is to construct a vector from the sum of the counts of all bits of the Bloom filter for the two selected attributes:

[0035] ,

[0036] Combine Bloom filters that take all values ​​of the two selected attributes: Using the Lasso regression algorithm, the coefficient vector is solved. Then the joint distribution of the two attributes is:

[0037] ;

[0038] in, and This represents the sum of the counts of all bits in the Bloom filter for the two selected attributes; and A Bloom filter matrix representing all values ​​of the two selected attributes;

[0039] The third step is to set the initial estimates for the EM algorithm for the two selected attributes;

[0040] The fourth step is to execute the E-step of the EM algorithm; calculate the joint conditional probability of the two attributes selected by each user, and calculate the posterior probability of the two selected attributes according to Bayes' theorem:

[0041] ,

[0042] ,

[0043] ,

[0044] in, and These represent the Bloom filters after perturbing the two selected attributes, respectively. and This represents all possible combinations of values ​​corresponding to the non-zero coefficients of the two selected attributes. Indicates the value of the attribute Under the condition of disturbance, the Bloom filter is The probability, This indicates that the combination of attribute values ​​is Under the condition of disturbance, the Bloom filter is The joint probability, This indicates that the Bloom filter after perturbation is In the case of the selected two attribute values, the combination is as follows: The posterior probability, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate;

[0045] Fifth, execute the M-step of the EM algorithm; calculate the average posterior probability of all users and update the joint distribution estimate for the next iteration.

[0046] ,

[0047] in, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate;

[0048] Step 6: Repeat the E-step of the EM algorithm in step 4 and the M-step of the EM algorithm in step 5 until the estimated difference between two similar iterations no longer changes, and obtain the joint distribution of the two selected attributes.

[0049] Step 7: Repeat steps 1 through 6 to obtain the joint distribution of all pairwise attributes in the tabular dataset records.

[0050] Furthermore, the attribute correlation measure refers to generating a marginal distribution table for each attribute or two-dimensional attribute based on the first-order marginal distribution of each attribute in the tabular dataset and the joint distribution between attribute pairs, and calculating the correlation between attribute pairs:

[0051] ,

[0052] in, express and The correlation between them This indicates a modulo operation. Represents attributes With attributes The frequency of combined values ​​in the marginal distribution table Represents attributes Frequency of values, Represents attributes The frequency of the values.

[0053] Furthermore, the selection of a set of two-dimensional marginal sets that retains the original statistical characteristics of the data and has low estimation error refers to representing two attributes as attribute pairs, with the selection problem of each attribute pair representing an optimization problem. An iterative selection of attribute pairs is achieved using a greedy approach. In each round of selection, the change in overall error after adding the attribute pair is calculated, and the attribute pair that brings the greatest benefit is selected and added to the marginal set, until the overall error can no longer be further reduced, ultimately resulting in a set of two-dimensional attributes.

[0054] ,

[0055] in, This means selecting a set of two-dimensional attributes from all possible attribute pair selection schemes to minimize the overall estimation error; Represents attribute pairs Whether it is selected, the value can be 0 or 1. This indicates that the selection was not made. Indicates that you have been selected; This indicates estimating attribute pairs on the perturbed data. The estimation error introduced by the joint distribution, Indicates that no attribute pair was selected. The resulting dependency error;

[0056] Furthermore, the step of iteratively updating the randomly generated dataset based on the two-dimensional marginal set is as follows:

[0057] The first step is to generate a random dataset based on the attributes and record entries of the original dataset. ;

[0058] The second step is to select an attribute pair from the filtered set of two-dimensional attributes and calculate the current... The difference between the two-dimensional marginal distribution of the attribute pair and the target two-dimensional marginal distribution;

[0059] The third step is to select records from the combinations of attributes with insufficient frequency compared to the target distribution and replace their attribute values, thus making the result... The frequency distribution of this attribute pair is closer to the target two-dimensional marginal distribution;

[0060] Fourth step: When replacement is insufficient to meet the target distribution, copy. The existing data records are used to increase the frequency of corresponding attribute combination values, and redundant combination records are deleted to maintain the total number of records;

[0061] Fifth, repeat steps two through four for all attributes in the two-dimensional attribute set, continuously updating them. The distribution is optimized to approximate the selected two-dimensional marginal distribution, and the final output is a synthetic dataset that satisfies privacy protection constraints.

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] First, because this invention completes the data perturbation, distribution estimation, and data synthesis process under a local differential privacy architecture, it avoids the assumption of complete trust in the server and overcomes the risk that all original data may be exposed once the server is leaked in a centralized differential privacy method. This makes the invention more secure and particularly suitable for scenarios with extremely high data privacy requirements, such as medical and financial institutions.

[0064] Second, because this invention introduces an attribute correlation measurement method and models privacy protection and data availability as an optimization problem, it can select a set of low-dimensional marginal distributions that retain key statistical features of the data while satisfying privacy protection constraints. This overcomes the problems in existing methods where blindly selecting too many marginals leads to excessive noise accumulation, or selecting too few marginals leads to serious information loss. As a result, this invention achieves a better balance between privacy protection and data availability.

[0065] Third, because this invention adopts the idea of ​​iterative update, it gradually adjusts the distribution of the synthesized data to approach the target marginal set during the data synthesis stage, which effectively reduces the damage to the original distribution structure and overcomes the oscillation problem caused by the forced matching of the target distribution in the traditional minimum cost flow method. This makes the synthesized data of this invention more stable and has better global consistency. Without accessing the original data, it generates high-quality synthesized data for data analysis, thus protecting user privacy while supporting the publication and sharing of data. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the implementation of the present invention. Detailed Implementation

[0067] The following is in conjunction with the appendix Figure 1 The present invention will be further described in conjunction with the embodiments.

[0068] Step 1: The user performs data perturbation locally.

[0069] The local data perturbation process applies a random response mechanism to the encoded raw data records to ensure that each user output satisfies local differential privacy. Each data record has numerous attributes; specifically, this step converts each attribute value into a random bit string.

[0070] Step 1.1: Encode the original data records.

[0071] Assuming the final table data to be published contains For example, the user needs to upload a [item / file]. Data records with attributes , For attributes The value of each attribute. Each attribute has its own set of hash functions; specifically, the attribute... A corresponding set of hash functions ={ } , express Number of corresponding hash function groups . Used to encode each attribute value of the user Converted to a length of bit string This refers to a Bloom filter.

[0072] A Bloom filter is a space-efficient probabilistic data structure used to map an element to a fixed-length bit string. Specifically, for a given attribute value... They are then processed sequentially through a set of hash functions. ={ } Perform hashing, each hash function outputs a value in [1, ... For integers within the range [ ], set the bit at that position to 1. Ultimately, the attribute value is encoded into a string of length [ ]. Bloom filter bit string The most of them are One bit is 1, and the rest are 0. Due to the irreversibility and compressibility of the Bloom filter, it not only improves coding efficiency but also enhances the privacy of the original data to a certain extent, providing a basis for subsequent perturbation operations.

[0073] Step 1.2: Perturb the encoded data.

[0074] After completing the Bloom filter encoding, each user assigns a bit string to each attribute. Perturbation processing is performed. Specifically, each encoded value... Bit With probability Keep the original value, with probability The bit string is randomly permuted to 0 or 1; the perturbed bit string satisfies - Local differential privacy constraints no longer directly reflect the original attribute values, but under the aggregation of large-scale user data, they can still be used to recover the overall statistical characteristics. Their expression is:

[0075] ;

[0076] in, express The first in The value after bit perturbation , , where represents the perturbation parameter, the value of which is determined by the privacy budget. Decide.

[0077] Local differential privacy requires that, for any two possible inputs... and arbitrary output Disturbance mechanism satisfy:

[0078] .

[0079] This formula represents the perturbation mechanism. The probability difference between producing the same output under different inputs is strictly limited, not exceeding [a certain limit]. This ensures that the attacker's ability to distinguish the input is strictly limited, preventing the attacker from making high-confidence inferences about the original input by observing the perturbation results.

[0080] To provide a random response to a certain attribute value satisfies -Local differential privacy constraints, where

[0081] ,

[0082] h is the number of hash functions in the Bloom filter. According to the sequential composition theorem, the d-dimensional data record... .

[0083] Step 1.3: After perturbing all attributes, each user concatenates all perturbed bit strings according to attribute order to obtain a vector: As a privacy protection measure, this data record is uploaded to the server. This represents the bit string after the j-th attribute is perturbed. This indicates a vector concatenation operation.

[0084] Step 2: The server estimates the first-order marginal distribution and the joint distribution among the two-dimensional attributes.

[0085] Step 2.1, estimate the first-order marginal distribution of a single attribute.

[0086] The server receives all user-perturbed records, extracts the perturbed bit string for each attribute of each user, counts the total number of times each bit in the perturbed bit string for each attribute across all users is 1, performs noise reduction processing, estimates the true sum of the counts of each bit being 1, and concatenates all the sums of the counts of each bit being 1 into a binary string:

[0087] ,

[0088] ;

[0089] in, Attributes representing all users The first bit in the denoised bit string The sum of the counts where each bit is 1. Attributes representing all users The perturbed bit string The sum of the counts where each bit is 1. This represents the total number of all users. Attributes representing all users The count of all bits that are 1 in the denoised bit string and the concatenated binary string.

[0090] Specifically, attributes There are I possible values, denoted as For each value According to attributes Corresponding hash function group Generate Bloom Filter The first-order marginal distribution estimation problem is modeled as a regularized least squares problem:

[0091] ;

[0092] in, Indicates by attribute The candidate matrix formed by the Bloom filters for all possible values. Represents the coefficient vector. This represents the L1 regularization coefficient. It is calculated using the Lasso regression algorithm. Then the attribute The probability distribution estimate is 𝑝= .

[0093] Step 2.2, estimate the joint distribution among the two-dimensional attributes.

[0094] Based on the Lasso regression algorithm, the joint distribution of any two attributes can be initially obtained. Specifically, two uncombined attributes are selected, and the sum of the counts of all bits of the Bloom filter for the selected two attributes is used to construct a vector.

[0095] ,

[0096] Combine Bloom filters that take all values ​​of the two selected attributes: Using the Lasso regression algorithm, the coefficient vector is solved. Then the joint distribution of the two attributes is: ;in, and This represents the sum of the counts of all bits in the Bloom filter for the two selected attributes; and This represents a Bloom filter matrix containing all values ​​for the two selected attributes.

[0097] To further improve the accuracy of joint distribution estimation, irrelevant or low-frequency candidate attribute combinations are first ignored based on the Lasso regression fitting results. Then, the EM algorithm is used to further estimate the conditional probabilities of high-frequency attribute combinations. Furthermore, compared to using the EM algorithm alone, the Lasso regression algorithm can produce a better initial estimate of the joint distribution and further accelerate the convergence speed of the EM algorithm.

[0098] 1) E-step: Calculate the joint conditional probability of the two attributes selected by each user, and calculate the posterior probability of the two selected attributes according to Bayes' theorem:

[0099] ,

[0100] ,

[0101] ;

[0102] in, and These represent the Bloom filters after perturbing the two selected attributes, respectively. and This represents all possible combinations of values ​​corresponding to the non-zero coefficients of the two selected attributes. Indicates the value of the attribute Under the condition of disturbance, the Bloom filter is The probability, This indicates that the combination of attribute values ​​is Under the condition of disturbance, the Bloom filter is The joint probability, This indicates that the Bloom filter after perturbation is In the case of the selected two attribute values, the combination is as follows: The posterior probability, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate;

[0103] 2) M-step: Calculate the average posterior probability of all users and update the joint distribution estimate for the next iteration.

[0104] ,

[0105] in, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate.

[0106] Repeat the E-step and M-step of the EM algorithm until convergence occurs when the maximum difference between the estimates of two iterations is less than a specified threshold, thus obtaining the two selected attributes. The joint distribution of .

[0107] Repeat the above process to obtain the joint distribution of all pairwise attributes in the tabular dataset records.

[0108] Step 3: Select a suitable set of two-dimensional attributes according to the marginal selection algorithm.

[0109] Step 3.1: Calculate the correlation between the two-dimensional attributes.

[0110] Based on step 2, the first-order marginal distribution of a single attribute and the joint distribution among two-dimensional attributes are obtained. A marginal distribution table for each attribute or two-dimensional attribute is generated, and the correlation between attribute pairs is calculated.

[0111] ;

[0112] in, express and The correlation between them This indicates a modulo operation. Represents attributes With attributes The frequency of combined values ​​in the marginal distribution table Represents attributes Frequency of values, Represents attributes The frequency of the values. This formula reflects the difference between the actual joint distribution of paired attributes and the joint distribution under the independence assumption. The larger the value, the higher the attribute value. , The stronger the correlation.

[0113] Step 3.2: Select two-dimensional attributes with high relevance.

[0114] In this process, there are two main sources of error: one is the estimation error introduced by estimating the joint distribution among attributes, and the other is the dependency error caused by not selecting certain attribute pairs. If all two-dimensional attributes are selected for publication, the estimation error will be large, with no dependency error; when some attribute pairs are skipped, the error will come entirely from the dependency error.

[0115] Two attributes are represented as attribute pairs, and the selection problem for each attribute pair is an optimization problem. An iterative selection of attribute pairs is achieved using a greedy approach. In each round of selection, the change in overall error after adding the attribute pair is calculated, and the attribute pair that brings the greatest benefit is added to the marginal set. This process continues until the overall error can no longer be further reduced, ultimately resulting in a set of two-dimensional attributes.

[0116] ,

[0117] in, This means selecting a set of two-dimensional attributes from all possible attribute pair selection schemes to minimize the overall estimation error; Represents attribute pairs Whether it is selected, the value can be 0 or 1. This indicates that the selection was not made. Indicates that you have been selected; This indicates estimating attribute pairs on the perturbed data. The estimation error introduced by the joint distribution, Indicates that no attribute pair was selected. The resulting dependency error.

[0118] Step 4: Based on the idea of ​​stepwise updates, use a two-dimensional attribute set to obtain the synthetic data.

[0119] The first step is to generate a random dataset based on the attributes and record entries of the original dataset. ;

[0120] The second step is to select an attribute pair from the filtered set of two-dimensional attributes and calculate the current... The difference between the two-dimensional marginal distribution of the attribute pair and the target two-dimensional marginal distribution;

[0121] The third step is to select records from the combinations of attributes with insufficient frequency compared to the target distribution and replace their attribute values, thus making the result... The frequency distribution of this attribute pair is closer to the target two-dimensional marginal distribution;

[0122] Fourth step: When replacement is insufficient to meet the target distribution, copy. The existing data records are used to increase the frequency of corresponding attribute combination values, and redundant combination records are deleted to maintain the total number of records;

[0123] Fifth, repeat steps two through four for all attributes in the two-dimensional attribute set, continuously updating them. The distribution is optimized to approximate the selected two-dimensional marginal distribution, and the final output is a synthetic dataset that satisfies privacy protection constraints.

[0124] In each iteration, parameters φ (increment ratio) and φ (decrease ratio) are introduced to control the update magnitude. Instead of forcing immediate satisfaction of the current marginal constraint, the difference between the current distribution and the target marginal constraint is gradually reduced, ensuring that each adjustment produces minimal disturbance to the overall distribution. After the iteration stops, the final synthetic dataset is output, whose statistical distribution is highly consistent with the original dataset and conforms to... - Differential privacy definition. This synthetic dataset can be used for subsequent data mining, machine learning, and other analytical tasks without requiring an additional privacy budget.

[0125] Step 5: The server publishes the synthetic dataset to provide data analysts with subsequent queries and analysis.

Claims

1. A method for publishing tabular data based on local differential privacy, characterized in that, The method includes the following steps: Step 1: The user perturbs the individual data record to which they belong locally. Local differential privacy technology is used to encode and perturb the value of each attribute of the record, and the perturbed data is uploaded to the server. Step 2: The server will compile all the perturbation records uploaded by users into a perturbation-based tabular dataset, and estimate the first-order marginal distribution of each attribute and the joint distribution between attribute pairs based on the dataset to obtain approximate values ​​of all two-dimensional marginal distributions. Step 3: Using the marginal selection algorithm based on attribute correlation measurement, select a set of two-dimensional marginal sets that retain the statistical characteristics of the original data and have low estimation error from all approximations of the two-dimensional marginal distributions. Step 4: Iteratively update the randomly generated dataset, adjust the data distribution of the randomly generated dataset to make it approximate the selected two-dimensional marginal set, and generate a synthetic dataset that meets privacy protection constraints. Step 5: The server publishes the synthetic dataset to provide data analysts with subsequent queries and analysis.

2. The tabular data publishing method according to claim 1, characterized in that, The steps described in step 1 for encoding the value of each attribute of a record using local differential privacy technology are as follows: The first step is for each user to upload a record containing... Data records with one attribute: Each attribute corresponds to a set of hash functions: ={ },in, Represents the j-th attribute The value of , express A corresponding set of hash functions, express The number of elements in the corresponding hash function group , This indicates the number of attributes in the data record uploaded by the user; The second step is to set the initial value of each attribute value encoded for each user to the length. A string of all zero bits, for each user Use hash function group Perform hashing, each hash function outputs... An integer within the range, of The bits at the integer positions are set to 1, resulting in the final Bloom filter. At most One bit is 1, and the rest are 0.

3. The tabular data publishing method according to claim 2, characterized in that, The perturbation process described in step 1 refers to the perturbation of each encoded value. Bit With probability Keep the original value, with probability The bit string is randomly permuted to 0 or 1; the perturbed bit string satisfies - Local differential privacy constraints no longer directly reflect the original attribute values, but under the aggregation of large-scale user data, they can still be used to recover the overall statistical characteristics. Their expression is: ； in, express The first in The value after bit perturbation , , where represents the perturbation parameter, the value of which is determined by the privacy budget. Decide.

4. The tabular data publishing method according to claim 3, characterized in that, The step 1, uploading the perturbed data to the server, refers to each user concatenating all the perturbed bit strings according to their attribute order to obtain a vector: As a privacy protection measure, this data record is uploaded to the server. This represents the bit string after the j-th attribute is perturbed. This indicates a vector concatenation operation.

5. The tabular data publishing method according to claim 4, characterized in that, The steps for estimating the first-order marginal distribution of each attribute in step 2 are as follows: The first step is for the server to receive all user records after perturbation, extract the bit string of each attribute after perturbation for each user, and count the total number of times each bit of each attribute bit string is 1 for all users. The second step is to perform noise reduction on the total number of each bit that is 1, estimate the true sum of counts, and concatenate all the sums of counts with bits 1 into a binary string: , ;in, Attributes representing all users The first bit in the denoised bit string The sum of the counts where each bit is 1. Attributes representing all users The perturbed bit string The sum of the counts where each bit is 1. This represents the total number of all users. Attributes representing all users The count of all bits that are 1 in the denoised bit string and the concatenated binary string; Step 3, Attributes There are I possible values, denoted as For each value According to attributes Corresponding hash function group Generate Bloom Filter The first-order marginal distribution estimation problem is modeled as a regularized least squares problem: ,in, Indicates by attribute The candidate matrix formed by the Bloom filters for all possible values. Represents the coefficient vector. Represents the L1 regularization coefficient; The fourth step is to solve the problem using the Lasso regression algorithm. Then the attribute The probability distribution estimate is 𝑝= .

6. The tabular data publishing method according to claim 5, characterized in that, The steps for estimating the joint distribution between attribute pairs in step 2 are as follows: The first step is to select two attributes that have not been combined from the attributes of the tabular dataset records; The second step is to construct a vector from the sum of the counts of all bits of the Bloom filter for the two selected attributes: ， Combine Bloom filters that take all values ​​of the two selected attributes: Using the Lasso regression algorithm, the coefficient vector is solved. Then the joint distribution of the two attributes is: ； in, and This represents the sum of the counts of all bits in the Bloom filter for the two selected attributes; and These represent Bloom filter matrices that represent all values ​​of the two selected attributes, respectively. The third step is to set the initial estimates for the EM algorithm for the two selected attributes; The fourth step is to execute the E-step of the EM algorithm; calculate the joint conditional probability of the two attributes selected by each user, and calculate the posterior probability of the two selected attributes according to Bayes' theorem: ， ， ， in, and These represent the Bloom filters after perturbing the two selected attributes, respectively. and This represents all possible combinations of values ​​corresponding to the non-zero coefficients of the two selected attributes. Indicates the value of the attribute Under the condition of disturbance, the Bloom filter is The probability, This indicates that the combination of attribute values ​​is Under the condition of disturbance, the Bloom filter is The joint probability, This indicates that the Bloom filter after perturbation is In the case of the selected two attribute values, the combination is as follows: The posterior probability, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate; Fifth, execute the M-step of the EM algorithm; calculate the average posterior probability of all users and update the joint distribution estimate for the next iteration: ， in, Indicates the first The combination of the two attribute values ​​selected during round iteration The joint distribution estimate; Step 6: Repeat the E-step of the EM algorithm in step 4 and the M-step of the EM algorithm in step 5 until the estimated difference between two similar iterations no longer changes, and obtain the joint distribution of the two selected attributes. Step 7: Repeat steps 1 through 6 to obtain the joint distribution of all pairwise attributes in the tabular dataset records.

7. The tabular data publishing method according to claim 1, characterized in that, The attribute correlation measurement mentioned in step 3 refers to generating a marginal distribution table for each attribute or two-dimensional attribute based on the first-order marginal distribution of each attribute in the tabular dataset and the joint distribution between attribute pairs, and calculating the correlation between attribute pairs: ， in, Representing attributes With attributes The correlation between them This indicates a modulo operation. Representing attributes With attributes The frequency of combined values ​​in the marginal distribution table Representing attributes Frequency of values, Representing attributes The frequency of the values.

8. The tabular data publishing method according to claim 1, characterized in that, Step 3, which describes selecting a set of two-dimensional marginal sets that retains the statistical characteristics of the original data and has low estimation errors, refers to representing two attributes as attribute pairs. The selection problem for each attribute pair is an optimization problem. An iterative selection of attribute pairs is achieved using a greedy approach. In each round of selection, the change in overall error after adding the attribute pair is calculated, and the attribute pair that brings the greatest benefit is added to the marginal set. This process continues until the overall error can no longer be further reduced, ultimately resulting in a set of two-dimensional attributes. ， in, This means selecting a set of two-dimensional attributes from all possible attribute pair selection schemes to minimize the overall estimation error; Represents attribute pairs Whether it is selected, the value can be 0 or 1. This indicates that the selection was not made. Indicates that you have been selected; This indicates estimating attribute pairs on the perturbed data. The estimation error introduced by the joint distribution, Indicates that no attribute pair was selected. The resulting dependency error.

9. The tabular data publishing method according to claim 1, characterized in that, The steps in step 4 for iteratively updating the randomly generated dataset based on the two-dimensional marginal set are as follows: The first step is to generate a random dataset based on the attributes and record entries of the original dataset. ; The second step is to select an attribute pair from the filtered set of two-dimensional attributes and calculate the current... The difference between the two-dimensional marginal distribution of the attribute pair and the target two-dimensional marginal distribution; The third step is to select records from the combinations of attributes with insufficient frequency compared to the target distribution and replace their attribute values, thus making the result... The frequency distribution of this attribute pair is closer to the target two-dimensional marginal distribution; Fourth step: When replacement is insufficient to meet the target distribution, copy. The existing data records are used to increase the frequency of corresponding attribute combination values, and redundant combination records are deleted to maintain the total number of records; Fifth, repeat steps two through four for all attributes in the two-dimensional attribute set, continuously updating them. The distribution is optimized to approximate the selected two-dimensional marginal distribution, and the final output is a synthetic dataset that satisfies privacy protection constraints.

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