CN115495778A - Differential privacy histogram publishing method and device based on grouping combination - Google Patents

Abstract

The invention provides a differential privacy histogram publishing method and equipment based on group merging. The method includes: step S1 to step S5. The present invention divides the data reasonably and accurately by adopting the method of grouping and merging the histogram, which effectively improves the accuracy of grouping division, further reduces the error of publishing data, improves the usability of data, and can realize the optimal histogram grouping. Optimal division greatly reduces the impact of noise on data accuracy, and effectively improves data availability and release efficiency while meeting differential privacy constraints.

Description

Method and device for publishing differentially private histograms based on group merging

technical field

Embodiments of the present invention relate to the technical field of histogram data privacy protection, and in particular to a method and device for publishing differentially private histograms based on packet merging.

Background technique

Histogram publishing is a widely used technology in the field of data publishing. The histogram can intuitively and clearly reflect the statistical characteristics of the data, and users can quickly obtain the information they need based on the histogram. However, it is easy for an attacker to launch an attack on the published histogram and steal user privacy. Therefore, in order to prevent data privacy leaks, data publishers usually use differential privacy technology to deprivate the histogram, but differential privacy also brings about a problem while protecting data privacy: reduced data availability; Problems plague researchers in the field of histogram data distribution. Therefore, developing a differentially private histogram distribution method and device based on group merging, which can effectively overcome the above-mentioned defects in related technologies, has become a technical problem to be solved urgently in the industry.

Contents of the invention

In view of the above-mentioned problems existing in the prior art, embodiments of the present invention provide a method and device for publishing a differentially private histogram based on group merging.

其中

表示求取均值后的均值分组集合；

表示第K个均值分组；S4：对

添加Laplace噪声得到

其中：

表示由均值分组集合添加噪音得到的噪音分组集合；

表示第K个添加噪音的分组；S5：对

恢复原始直方图顺序，得到发布的差分隐私直方图

其中：

表示由

恢复原始直方图顺序得到的差分隐私直方图；

表示直方图中添加噪音的桶；n表示差分隐私直方图桶的总数。In the first aspect, the embodiment of the present invention provides a differential privacy histogram publishing method based on group merging, including: S1: privacy budget division, privacy budget ε is divided into ε ₁ and ε ₂ ; S2: group merging, first Set the final combined grouping number K, and use each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate grouping to obtain the grouping set g(g ₁ ,g ₂ , ..., g _n ); Then, pairwise merge the groups in g, and traverse all the merged schemes, calculate the scheme distance of each merged scheme, select the merged scheme through the index mechanism for approximate merger, and merge The plan is regarded as a new group, replacing the original two groups, repeating the above merging process until the final grouping number K is reached, and the final merging plan is obtained to form a histogram grouping G(G ₁ ,G ₂ ,... ,G _k ); where: H={h ₁ ,h ₂ ,...,h _n } represents the original histogram sequence; h ₁ ,h ₂ ,...,h _n represent the buckets in the histogram, and n is The total number of original histogram buckets; g(g ₁ ,g ₂ ,...,g _n ) represents the initial grouping set before merging; g ₁ ,g ₂ ,...,g _n represents the grouping in the initial grouping set, Each group consists of a bucket, so the total number of initial groups is n; G(G ₁ ,G ₂ ,...,G _k ) represents the final grouping set obtained by merging, G ₁ ,G ₂ ,...,G _k Represents the grouping in the final grouping set, G _k represents the Kth grouping; S3: calculate the mean value for each grouping of G to get

in

Indicates the mean value grouping set after calculating the mean value;

Indicates the Kth mean grouping; S4: pair

Add Laplace noise to get

in:

Represents the noise grouping set obtained by adding noise to the mean grouping set;

Indicates the Kth noise-added grouping; S5: Yes

Restore the original histogram order and get the published differential privacy histogram

in:

Indicated by

The differentially private histogram obtained by restoring the original histogram order;

Indicates the buckets in which noise is added in the histogram; n indicates the total number of differentially private histogram buckets.

On the basis of the contents of the above-mentioned method embodiments, in the differential privacy histogram release method based on group merging provided in the embodiment of the present invention, the privacy budget ε in step S1 is a given positive value, and ε ₁ is used for group merging, ε ₂ is used to add noise in groups.

On the basis of the content of the above-mentioned method embodiment, the implementation of the differential privacy histogram publishing method based on group merging provided in the embodiment of the present invention specifically includes: S2.1 setting the final number of groups K, where K=1, 2,...,n. n is the grouping number of the histogram; S2.2 treats each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate grouping, and obtains the grouping set g(g ₁ ,g ₂ ,...,g _n ); S2.3 Merge the groups in the histogram in pairs, and traverse all possible merge schemes P(p ₁ ,p ₂ ,...,p _y ); where : P(p ₁ ,p ₂ ,...,p _y ) represents the set of merging schemes; p ₁ ,p ₂ ,...,p _y represents all possible merging schemes; y represents the total number of schemes; S2.4 Calculation Calculate the solution distance u(p,p _s ) of each combined solution, and set it as the utility function:

表示分组之间的最小距离，该距离用来衡量分组之间的相似性，效用函数设置应满足要求：分组之间的距离越小，被合并的概率也就越大；为后续概率计算满足此要求，采用分组距离的相反数

来构造效用函数；S2.5利用指数机制结合方案距离计算出每个合并方案的抽样概率Pr(p,p_s)：Among them: p _s (g _i , g _j ) is a merge plan in the plan set P, P _s contains two groups g _i and g _j , h is a certain bucket in g _i , _h ′ represents the a bucket of

Indicates the minimum distance between groups, which is used to measure the similarity between groups, and the utility function setting should meet the requirements: the smaller the distance between groups, the greater the probability of being merged; for subsequent probability calculations, this Requirements, using the opposite number of grouping distance

to construct a utility function; S2.5 calculates the sampling probability Pr(p, p _s ) of each merged scheme by using the exponential mechanism combined with the scheme distance:

为合并方案P_s的适应度函数；分子计算的是合并方案P_s的适应度值，分母计算的是所有合并方案的适应度值的总和；S2.6根据每个合并方案的抽样概率；利用轮盘对合并方案进行选取；S2.7将选取到的合并方案进行合并，并将其视为一个新的分组，替代原有的两个分组；S2.8重复S2.3-S2.7，直到合并为K个分组，循环结束；S2.9返回最终合并方案G(G₁,G₂,...,G_k)。Among them, the combination scheme probability Pr(p, p _s ) represents the probability of the combination scheme P _s being selected, ε ₁ is the privacy budget; Δu is the global sensitivity; u(p, p _s ) is the utility function of P _s ; The definition of degree shows that deleting any record in the data set has a maximum impact of 1 on the utility function, so Δu=1, y represents the total number of solutions;

is the fitness function of the merged scheme P _s ; the numerator calculates the fitness value of the merged scheme P _s , and the denominator calculates the sum of the fitness values of all merged schemes; S2.6 is based on the sampling probability of each merged scheme; using The roulette selects the merge plan; S2.7 merges the selected merge plan and treats it as a new group to replace the original two groups; S2.8 repeats S2.3-S2.7, Until K groups are merged, the loop ends; S2.9 returns the final merge solution G(G ₁ ,G ₂ ,...,G _k ).

On the basis of the content of the above-mentioned method embodiments, in the method for publishing differentially private histograms based on group merging provided in the embodiments of the present invention, in step S2, if the number of buckets in the histogram is n, then the number of groups is also n.

添加的Laplace噪声的大小为ε₂。On the basis of the contents of the above-mentioned method embodiments, in the method for issuing differentially private histograms based on group merging provided in the embodiments of the present invention, in step S4, the

The magnitude of the added Laplace noise is ε ₂ .

的维度为一维。On the basis of the content of the above-mentioned method embodiment, the differential privacy histogram release method based on group merging provided in the embodiment of the present invention, the differential privacy histogram in step S5

The dimension of is one-dimensional.

其中

表示求取均值后的均值分组集合；

表示第K个均值分组；第四主模块，用于实现S4：对

添加Laplace噪声得到

其中：

表示由均值分组集合添加噪音得到的噪音分组集合；

表示第K个添加噪音的分组；第五主模块，用于实现S5：对

恢复原始直方图顺序，得到发布的差分隐私直方图

其中：

表示由

恢复原始直方图顺序得到的差分隐私直方图；

表示直方图中添加噪音的桶；n表示差分隐私直方图桶的总数。In the second aspect, the embodiment of the present invention provides a differential privacy histogram distribution device based on group merging, including: a first main module, used to realize S1: divide the privacy budget, and divide the privacy budget ε into _ε1 and ε ₂ ; the second main module is used to realize S2: group merging, firstly set the final merging group number K, and convert each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } to A single grouping, get the grouping set g(g ₁ ,g ₂ ,...,g _n ); then merge the groups in g in pairs, traverse all the merging schemes, and calculate the scheme of each merging scheme Distance, select the merge plan through the index mechanism for approximate merge, and regard the merged plan as a new group, replace the original two groups, repeat the above merge process until the final number of groups K is reached, and the final merge plan is obtained , forming a histogram group G(G _1, G ₂ ,...,G _k ); where: H={h ₁ ,h ₂ ,...,h _n } represents the original histogram sequence; h ₁ ,h ₂ ,...,h _n represent the buckets in the histogram, n is the total number of buckets in the original histogram; g(g ₁ ,g ₂ ,...,g _n ) represents the initial grouping set before merging; g ₁ ,g ₂ ,...,g _n represent the groups in the initial grouping set, each group consists of a bucket, so the total number of initial groups is n; G(G ₁ ,G ₂ ,...,G _k ) represents the combined The final grouping set, G ₁ , G ₂ ,..., G _k represent the groups in the final grouping set, and G _k represents the Kth grouping; the third main module is used to realize S3: for each grouping of G mean get

in

Indicates the mean value grouping set after calculating the mean value;

Represents the Kth mean value grouping; the fourth main module is used to realize S4: pair

Add Laplace noise to get

in:

Represents the noise grouping set obtained by adding noise to the mean grouping set;

Represents the Kth noise-added grouping; the fifth main module is used to realize S5: right

Restore the original histogram order and get the published differential privacy histogram

in:

Indicated by

The differentially private histogram obtained by restoring the original histogram order;

Indicates the buckets in which noise is added in the histogram; n indicates the total number of differentially private histogram buckets.

In a third aspect, an embodiment of the present invention provides an electronic device, including:

at least one processor; and

at least one memory communicatively coupled to the processor, wherein:

The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the differential privacy histogram publishing method based on group merging provided by any one of the various implementations of the first aspect.

In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, where the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute any one of the various implementations of the first aspect. A differentially private histogram publishing method based on group merging provided by an implementation.

The differentially private histogram release method and device based on group merging provided by the embodiments of the present invention divide the data reasonably and accurately by adopting the method of group merging for the histogram, which effectively improves the accuracy of group division and further reduces the The error of published data improves the availability of data, can realize the optimal division of histogram grouping, greatly reduces the impact of noise on data accuracy, and effectively improves the availability and release of data while satisfying differential privacy constraints. efficiency.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will give a brief introduction to the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is the flow chart of the differential privacy histogram release method based on packet merging provided by the embodiment of the present invention;

FIG. 2 is a schematic structural diagram of a differentially private histogram distribution device based on packet merging provided by an embodiment of the present invention;

FIG. 3 is a schematic diagram of a physical structure of an electronic device provided by an embodiment of the present invention.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention. In addition, the technical features in each embodiment or a single embodiment provided by the present invention can be combined arbitrarily with each other to form a feasible technical solution. This combination is not restricted by the sequence of steps and/or structural composition mode, but it must be Based on the ability of those skilled in the art to realize, when the combination of technical solutions is contradictory or unrealizable, it should be considered that such combination of technical solutions does not exist and is not within the protection scope of the present invention.

其中

表示求取均值后的均值分组集合；

表示第K个均值分组；S4：对

添加Laplace噪声得到

其中：

表示由均值分组集合添加噪音得到的噪音分组集合；

表示第K个添加噪音的分组；S5：对

恢复原始直方图顺序，得到发布的差分隐私直方图

其中：

表示由

恢复原始直方图顺序得到的差分隐私直方图；

表示直方图中添加噪音的桶；n表示差分隐私直方图桶的总数。The present invention divides the privacy budget; sets the final number of groups K, regards each bucket in the histogram as a separate group, and uses group merging to traverse all possible merging schemes. By calculating the combination index mechanism of the scheme distance of each merging scheme, the merging scheme is approximately selected, and the selected merging scheme is merged to replace the original two groups; then the grouping and merging process is repeated until the final grouping scheme is formed. Finally, calculate the average value of the obtained histogram group, add Laplace noise and restore its original order, and obtain the published differential privacy histogram. Based on this idea, the embodiment of the present invention provides a differential privacy histogram publishing method based on group merging, see FIG. 1, the method includes: S1: privacy budget division, privacy budget ε is divided into ε ₁ and ε ₂ ; S2: Grouping and merging. First, set the final number of merged groups K, and use each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate group to obtain the grouping set g( g ₁ ,g ₂ ,...,g _n ); then merge the groups in g in pairs, and traverse all the merged schemes, calculate the scheme distance of each merged scheme, and select the merged scheme through the index mechanism for approximation Merge, and treat the merged plan as a new group, replace the original two groups, repeat the above merging process until the final number of groups K is reached, and obtain the final merged plan to form a histogram group G(G ₁ , G ₂ ,...,G _k ); where: H={h ₁ ,h ₂ ,...,h _n } represents the original histogram sequence; h ₁ ,h ₂ ,...,h _n represents the histogram In the bucket, n is the total number of buckets in the original histogram; g(g _1, g ₂ ,...,g _n ) represents the initial grouping set before merging; g ₁ , g ₂ ,..., g _n represents the initial Grouping in the grouping set, each grouping consists of a bucket, so the total number of initial groups is n; G(G ₁ ,G ₂ ,...,G _k ) represents the final grouping set obtained by merging, G ₁ ,G ₂ , ..., G _k represents the grouping in the final grouping set, G _k represents the Kth grouping; S3: calculate the mean value for each grouping of G to get

in

Indicates the mean value grouping set after calculating the mean value;

Indicates the Kth mean grouping; S4: pair

Add Laplace noise to get

in:

Represents the noise grouping set obtained by adding noise to the mean grouping set;

Indicates the Kth noise-added grouping; S5: Yes

Restore the original histogram order and get the published differential privacy histogram

in:

Indicated by

The differentially private histogram obtained by restoring the original histogram order;

Indicates the buckets in which noise is added in the histogram; n indicates the total number of differentially private histogram buckets.

Based on the content of the above-mentioned method embodiment, as an optional embodiment, in the differential privacy histogram distribution method based on group merging provided in the embodiment of the present invention, the privacy budget ε in step S1 is a given positive value, and ε ₁ is used for group merging, ε ₂ is used for group adding noise.

Based on the content of the above-mentioned method embodiment, as an optional embodiment, the implementation of step S2 of the differential privacy histogram release method based on group merging provided in the embodiment of the present invention specifically includes: S2.1 Setting the final number of groups K , where K=1,2,...,n. n is the grouping number of the histogram; S2.2 treats each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate grouping, and obtains the grouping set g(g ₁ ,g ₂ ,...,g _n ); S2.3 Merge the groups in the histogram in pairs, and traverse all possible merge schemes P(p ₁ ,p ₂ ,...,p _y ); where : P(p ₁ ,p ₂ ,...,p _y ) represents the set of merging schemes; p ₁ ,p ₂ ,...,p _y represents all possible merging schemes; y represents the total number of schemes; S2.4 Calculation Calculate the solution distance u(p,p _s ) of each combined solution, and set it as the utility function:

表示分组之间的最小距离，该距离用来衡量分组之间的相似性，效用函数设置应满足要求：分组之间的距离越小，被合并的概率也就越大；为后续概率计算满足此要求，采用分组距离的相反数

来构造效用函数；S2.5利用指数机制结合方案距离计算出每个合并方案的抽样概率Pr(p,p_s)：Among them: p _s (g _i , g _j ) is a merge plan in the plan set P, P _s contains two groups g _i and g _j , h is a certain bucket in g _i , _h ′ represents the a bucket of

Indicates the minimum distance between groups, which is used to measure the similarity between groups, and the utility function setting should meet the requirements: the smaller the distance between groups, the greater the probability of being merged; for subsequent probability calculations, this Requirements, using the opposite number of grouping distance

to construct a utility function; S2.5 calculates the sampling probability Pr(p, p _s ) of each merged scheme by using the exponential mechanism combined with the scheme distance:

为合并方案P_s的适应度函数；分子计算的是合并方案P_s的适应度值，分母计算的是所有合并方案的适应度值的总和；S2.6根据每个合并方案的抽样概率；利用轮盘对合并方案进行选取；S2.7将选取到的合并方案进行合并，并将其视为一个新的分组，替代原有的两个分组；S2.8重复S2.3-S2.7，直到合并为K个分组，循环结束；S2.9返回最终合并方案G(G₁,G₂,...,G_k)。Among them, the combination scheme probability Pr(p, p _s ) represents the probability of the combination scheme P _s being selected, ε ₁ is the privacy budget; Δu is the global sensitivity; u(p, p _s ) is the utility function of P _s ; The definition of degree shows that deleting any record in the data set has a maximum impact of 1 on the utility function, so Δu=1, y represents the total number of solutions;

is the fitness function of the merged scheme P _s ; the numerator calculates the fitness value of the merged scheme P _s , and the denominator calculates the sum of the fitness values of all merged schemes; S2.6 is based on the sampling probability of each merged scheme; using The roulette selects the merge plan; S2.7 merges the selected merge plan and treats it as a new group to replace the original two groups; S2.8 repeats S2.3-S2.7, Until K groups are merged, the loop ends; S2.9 returns the final merge solution G(G ₁ ,G ₂ ,...,G _k ).

Based on the content of the above-mentioned method embodiment, as an optional embodiment, in the method for publishing a differentially private histogram based on group merging provided in the embodiment of the present invention, in step S2, if the number of buckets in the histogram is n, then There are also n groups.

添加的Laplace噪声的大小为ε₂。Based on the content of the above-mentioned method embodiment, as an optional embodiment, the differential privacy histogram distribution method based on group merging provided in the embodiment of the present invention, in step S4

The magnitude of the added Laplace noise is ε ₂ .

的维度为一维。具体地，隐私性证明如下：设分组合并过程为M₁，求均值添加噪声过程为M₂。首先，合并过程中每次以正比于

的概率对合并方案进行选择，整个过程不会导致隐私泄露，因此合并过程满足ε₁-差分隐私。由于对均值分组添加的噪声为ε₂，因此过程M₂满足ε₂-差分隐私。又因为ε＝ε₁+ε₂，由差分隐私的组合性质可知，该方法整体满足ε-差分隐私。Based on the content of the above method embodiment, as an optional embodiment, the differential privacy histogram publishing method based on group merging provided in the embodiment of the present invention, the differential privacy histogram in step S5

The dimension of is one-dimensional. Specifically, the proof of privacy is as follows: Let the process of group merging be M ₁ , and the process of calculating the mean and adding noise is M ₂ . First, each time during the merge process is proportional to

The probability of is to choose the merging scheme, and the whole process will not lead to privacy leakage, so the merging process satisfies ε ₁ -differential privacy. Since the noise added to the mean grouping is ε ₂ , the process M ₂ satisfies ε ₂ -differential privacy. And because ε=ε ₁ +ε ₂ , it can be seen from the combination property of differential privacy that this method satisfies ε-differential privacy as a whole.

The differential privacy histogram publishing method based on group merging provided by the embodiment of the present invention divides the data reasonably and accurately by adopting the method of group merging for the histogram, which effectively improves the accuracy of group division and reduces the number of published data. The error improves the availability of data, realizes the optimal division of histogram grouping, greatly reduces the impact of noise on data accuracy, and effectively improves data availability and release efficiency while meeting differential privacy constraints.

其中

表示求取均值后的均值分组集合；

表示第K个均值分组；第四主模块，用于实现S4：对

添加Laplace噪声得到

其中：

表示由均值分组集合添加噪音得到的噪音分组集合；

表示第K个添加噪音的分组；第五主模块，用于实现S5：对

恢复原始直方图顺序，得到发布的差分隐私直方图

其中：

表示由

恢复原始直方图顺序得到的差分隐私直方图；

表示直方图中添加噪音的桶；n表示差分隐私直方图桶的总数。The implementation basis of each embodiment of the present invention is implemented by a device with a processor function performing programmed processing. Therefore, in engineering practice, the technical solutions and functions of the various embodiments of the present invention can be encapsulated into various modules. Based on this reality, on the basis of the above-mentioned embodiments, an embodiment of the present invention provides a differential privacy histogram publishing device based on packet merging, which is used to implement the packet merging-based Differentially private histogram publishing method. Referring to Fig. 2, the device includes: a first main module, used to realize S1: privacy budget division, divide the privacy budget ε into ε ₁ and ε ₂ ; a second main module, used to realize S2: group merging, first set the final Merge the number of groups K, and use each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate group to obtain a grouping set g(g ₁ ,g ₂ ,.. ., g _n ); then merge the groups in g in pairs, traverse all the merged schemes, calculate the scheme distance of each merged scheme, select the merged scheme through the index mechanism for approximate merger, and combine the merged scheme As a new group, replace the original two groups, repeat the above merging process until the final grouping number K is reached, and the final merging scheme is obtained to form a histogram grouping G(G ₁ ,G ₂ ,...,G _k ); where: H={h ₁ ,h ₂ ,...,h _n } represents the original histogram sequence; h ₁ ,h ₂ ,...,h _n represents the bucket in the histogram, and n is the original histogram The total number of graph buckets; g(g ₁ ,g ₂ ,...,g _n ) represents the initial grouping set before merging; g ₁ ,g ₂ ,...,g _n represent the groups in the initial grouping set, each Grouping consists of a bucket, so the total number of initial groups is n; G(G ₁ ,G ₂ ,...,G _k ) represents the final grouping set obtained by merging, and G ₁ ,G ₂ ,...,G _k represents the final Grouping in the grouping set, G _k represents the Kth grouping; the third main module is used to realize S3: calculate the mean value for each grouping of G to obtain

in

Indicates the mean value grouping set after calculating the mean value;

Represents the Kth mean value grouping; the fourth main module is used to realize S4: pair

Add Laplace noise to get

in:

Represents the noise grouping set obtained by adding noise to the mean grouping set;

Represents the Kth noise-added grouping; the fifth main module is used to realize S5: right

Restore the original histogram order and get the published differential privacy histogram

in:

Indicated by

The differentially private histogram obtained by restoring the original histogram order;

Indicates the buckets in which noise is added in the histogram; n indicates the total number of differentially private histogram buckets.

The differential privacy histogram release device based on group merging provided by the embodiment of the present invention adopts several modules in Fig. 2, and divides the data reasonably and accurately by adopting the method of group merging for the histogram, which effectively improves the efficiency of group division. Accuracy, which in turn reduces the error of published data, improves the availability of data, can realize the optimal division of histogram grouping, and greatly reduces the impact of noise on data accuracy. While meeting differential privacy constraints, it can effectively improve Improved data availability and release efficiency.

It should be noted that, in addition to implementing the methods in the above method embodiments, the devices in the device embodiments provided by the present invention can also be used to realize the methods in other method embodiments provided by the present invention. The only difference is that Corresponding functional modules are set, the principle of which is basically the same as that of the above-mentioned device embodiment provided by the present invention, as long as those skilled in the art refer to the specific technical solutions in other method embodiments on the basis of the above-mentioned device embodiment, through combination technology The corresponding technical means for obtaining the characteristics, and the technical solutions composed of these technical means, on the premise of ensuring the practicability of the technical solutions, the devices in the above device embodiments can be improved, so as to obtain corresponding device embodiments, Used to implement methods in other method class embodiments. E.g:

Based on the content of the above-mentioned device embodiment, as an optional embodiment, the device for issuing a differentially private histogram based on group merging provided in the embodiment of the present invention further includes: a first submodule, configured to implement the step S1 The privacy budget ε is a given positive value, and ε1 is used for group merging and _ε2 is used for group adding noise.

Based on the content of the above-mentioned device embodiment, as an optional embodiment, the device for issuing a differentially private histogram based on group merging provided in the embodiment of the present invention further includes: a second submodule, configured to implement step S2 Specifically include: S2.1 Set the final grouping number K, where K=1, 2,...,n. n is the grouping number of the histogram; S2.2 treats each bucket in the original histogram H={h ₁ ,h ₂ ,...,h _n } as a separate grouping, and obtains the grouping set g(g ₁ ,g ₂ ,...,g _n ); S2.3 Merge the groups in the histogram in pairs, and traverse all possible merge schemes P(p ₁ ,p ₂ ,...,p _y ); where : P(p ₁ ,p ₂ ,...,p _y ) represents the set of merging schemes; p ₁ ,p ₂ ,...,p _y represents all possible merging schemes; y represents the total number of schemes; S2.4 Calculation Calculate the solution distance u(p,p _s ) of each combined solution, and set it as the utility function:

表示分组之间的最小距离，该距离用来衡量分组之间的相似性，效用函数设置应满足要求：分组之间的距离越小，被合并的概率也就越大；为后续概率计算满足此要求，采用分组距离的相反数

来构造效用函数；S2.5利用指数机制结合方案距离计算出每个合并方案的抽样概率Pr(p,p_s)：Among them: p _s (g _i , g _j ) is a merge plan in the plan set P, P _s contains two groups g _i and g _j , h is a certain bucket in g _i , _h ′ represents the a bucket of

Indicates the minimum distance between groups, which is used to measure the similarity between groups, and the utility function setting should meet the requirements: the smaller the distance between groups, the greater the probability of being merged; for subsequent probability calculations, this Requirements, using the opposite number of grouping distance

to construct a utility function; S2.5 calculates the sampling probability Pr(p, p _s ) of each merged scheme by using the exponential mechanism combined with the scheme distance:

为合并方案P_s的适应度函数；分子计算的是合并方案P_s的适应度值，分母计算的是所有合并方案的适应度值的总和；S2.6根据每个合并方案的抽样概率；利用轮盘对合并方案进行选取；S2.7将选取到的合并方案进行合并，并将其视为一个新的分组，替代原有的两个分组；S2.8重复S2.3-S2.7，直到合并为K个分组，循环结束；S2.9返回最终合并方案G(G₁,G₂,...,G_k)。Among them, the combination scheme probability Pr(p, p _s ) represents the probability of the combination scheme P _s being selected, ε ₁ is the privacy budget; Δu is the global sensitivity; u(p, p _s ) is the utility function of P _s ; The definition of degree shows that deleting any record in the data set has a maximum impact of 1 on the utility function, so Δu=1, y represents the total number of solutions;

is the fitness function of the merged scheme P _s ; the numerator calculates the fitness value of the merged scheme P _s , and the denominator calculates the sum of the fitness values of all merged schemes; S2.6 is based on the sampling probability of each merged scheme; using The roulette selects the merge plan; S2.7 merges the selected merge plan and treats it as a new group to replace the original two groups; S2.8 repeats S2.3-S2.7, Until K groups are merged, the loop ends; S2.9 returns the final merge solution G(G ₁ ,G ₂ ,...,G _k ).

Based on the content of the above-mentioned device embodiment, as an optional embodiment, the device for issuing a differentially private histogram based on group merging provided in the embodiment of the present invention further includes: a third submodule, configured to implement step S2, If the number of buckets in the histogram is n, then the number of groups is also n.

添加的Laplace噪声的大小为ε₂。Based on the content of the above-mentioned device embodiment, as an optional embodiment, the device for issuing a differentially private histogram based on group merging provided in the embodiment of the present invention further includes: a fourth submodule, configured to realize the

The magnitude of the added Laplace noise is ε ₂ .

的维度为一维。Based on the content of the above-mentioned device embodiment, as an optional embodiment, the device for issuing a differentially private histogram based on group merging provided in the embodiment of the present invention further includes: a fifth submodule, configured to implement the step S5 Differential Privacy Histogram

The dimension of is one-dimensional.

The method in the embodiment of the present invention is realized by relying on electronic equipment, so it is necessary to introduce related electronic equipment. Based on this purpose, an embodiment of the present invention provides an electronic device. As shown in FIG. 3 , the electronic device includes: at least one processor, a communication interface, at least one memory and a communication A bus, wherein at least one processor, a communication interface, and at least one memory complete mutual communication through the communication bus. At least one processor can invoke logic instructions in at least one memory to execute all or part of the steps of the methods provided by the foregoing method embodiments.

In addition, the above logic instructions in the at least one memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the essence of the technical solution of the present invention or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including Several instructions are used to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in each method embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes. .

The device embodiments described above are only illustrative, and the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in One place, or it can be distributed to multiple network elements. Part or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. It can be understood and implemented by those skilled in the art without any creative efforts.

Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general-purpose hardware platform, and of course can also be implemented by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of software products, and the computer software products can be stored in computer-readable storage media, such as ROM/RAM, magnetic discs, optical discs, etc., including several instructions to make a computer device (which may be a personal computer, server, or network device, etc.) execute the methods described in various embodiments or some parts of the embodiments.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. Based on this understanding, each block in the flowchart or block diagram may represent a module, program segment or part of code, which contains one or more Executable instructions. It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks in succession may, in fact, be executed substantially concurrently, or may sometimes be executed in the reverse order, depending upon the functionality involved. It should also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by a dedicated hardware-based system that performs the specified function or action , or may be implemented by a combination of dedicated hardware and computer instructions.

In this patent, the terms "comprises," "comprises," or any other variation thereof are intended to cover a non-exclusive inclusion such that a process, method, article, or apparatus that includes a set of elements includes not only those elements, but also Include other elements not expressly listed, or also include elements inherent in the process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article or apparatus comprising said element.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (9)

1. A differential privacy histogram release method based on packet merging is characterized by comprising the following steps: s1: privacy budget partitioning, partitioning privacy budget ε into ε ₁ And epsilon ₂ (ii) a S2: grouping and merging, firstly setting the final merging grouping number K, and setting an original histogram H = { H = { (H) } ₁ ,h ₂ ,...,h _n Every bucket in the tree is a separate packet, resulting in a set of packets g (g) ₁ ,g ₂ ,...,g _n ) (ii) a Then, pairwise merging the groups in the group G, traversing all merging schemes, calculating the scheme distance of each merging scheme, selecting the merging schemes through an index mechanism for approximate merging, regarding the merged scheme as a new group to replace the original two groups, repeating the merging process until the final group number K is reached, obtaining the final merging scheme, and forming a histogram group G (G) ₁ ,G ₂ ,...,G _k ) (ii) a Wherein: h = { H = ₁ ,h ₂ ,...,h _n Denotes the original histogram sequence; h is a total of ₁ ,h ₂ ,...,h _n Representing the buckets in the histogram, n being the total number of original histogram buckets; g (g) ₁ ,g ₂ ,...,g _n ) Representing an initial packet set before merging; g ₁ ,g ₂ ,...,g _n Representing the packets in an initial set of packets, each packet consisting of one bucket, so the initial total number of packets is n; g (G) ₁ ,G ₂ ,...,G _k ) Representing the final set of packets resulting from the merging, G ₁ ,G ₂ ,...,G _k Representing packets in the final set of packets, G _k Represents the kth packet; s3: averaging each group of G to obtain

Wherein

Representing a mean grouping set after the mean value is solved;

represents the Kth mean grouping; s4: to pair

Adding Laplace noise to obtain

Wherein:

representing a noise packet set obtained by adding noise to the mean packet set;

a packet representing the kth added noise; s5: to pair

Recovering the original histogram order to obtain the issued differential privacy histogram

Wherein:

is represented by

Recovering the difference privacy histogram obtained by the original histogram sequence;

a bucket representing the added noise in the histogram; n denotes the total number of differential privacy histogram buckets.

2. The packet-based of claim 1Merged differential privacy histogram distribution method, characterized in that the privacy budget ε in step S1 is a given positive value, and ε 1 is used for packet merging ₂ For packet-added noise.

3. The method for distributing the differential privacy histogram based on the grouping combination according to claim 2, wherein the step S2 is implemented specifically by: s2.1 setting a final number of groups K, where K =1, 2.., n, n is the number of groups of the histogram; s2.2 original histogram H = { H = ₁ ,h ₂ ,...,h _n Every bucket in the tree is treated as a single packet, resulting in a set of packets g (g) ₁ ,g ₂ ,...,g _n ) (ii) a S2.3, pairwise merging is carried out on the groups in the histogram, and all possible merging schemes P (P) are traversed ₁ ,p ₂ ,...,p _y ) (ii) a Wherein: p (P) ₁ ,p ₂ ,...,p _y ) Representing a set of merging schemes; p is a radical of formula ₁ ,p ₂ ,...,p _y Indicating that there are all possible merging scenarios; y represents the total number of recipes; s2.4 calculate the solution distance u (p, p) for each merging solution _s ) And set it as utility function:

wherein: p is a radical of formula _s (g _i ,g _j ) For a merging scheme of a set of schemes P, P _s In which two packets g are included _i And g _j H is g _i A certain bucket in (1), h' represents g _j Is provided to the one of the buckets in the drum,

representing the minimum distance between the packets, which is used to measure the similarity between the packets, the utility function setting should satisfy the requirement: the smaller the distance between the packets, the greater the probability of being merged; for the subsequent probability calculation to meet the requirement, the inverse number of the grouping distance is adopted

To construct a utility function; s2.5 calculating the sampling probability Pr (p, p) of each merging scheme by using an exponential mechanism and combining scheme distances _s )：

Wherein, the probability Pr (p, p) of the merging scheme _s ) Represents a merging scheme P _s Probability of being selected, epsilon ₁ Is a privacy budget; Δ u is global sensitivity; u (p, p) _s ) Is P _s A utility function of (a); as can be seen from the definition of global sensitivity, deleting any record in the data set has a maximum influence on the utility function of 1, so Δ u =1, y represents the total number of solutions;

for merging scheme P _s A fitness function of (a); the numerator calculates the merging scheme P _s The denominator calculates the sum of the fitness values of all the merging schemes; s2.6, according to the sampling probability of each merging scheme; selecting a merging scheme by using a wheel disc; s2.7, merging the selected merging schemes, and regarding the merging schemes as a new group to replace the original two groups; s2.8, repeating S2.3-S2.7 until the groups are combined into K groups, and ending the cycle; s2.9 Return to the Final Merge scheme G (G) ₁ ,G ₂ ,...,G _k )。

4. The method according to claim 3, wherein in step S2, if the number of the histogram buckets is n, the number of the groups is n.

5. The method for distributing the differential privacy histogram based on the grouping combination as claimed in claim 4, wherein the step S4 is performed on

The magnitude of the added Laplace noise is epsilon ₂ 。

6. The method according to claim 5, wherein the differential privacy histogram distribution method in step S5 is characterized in that the differential privacy histogram distribution method in step S5 is implemented by using a plurality of different privacy histograms

Is one-dimensional.

7. A differential privacy histogram distribution apparatus based on packet merging, comprising: a first master module, configured to implement S1: privacy budget partitioning, partitioning privacy budget ε into ε ₁ And ε ₂ (ii) a A second master module, configured to implement S2: grouping and merging, firstly setting the final merging grouping number K, and setting an original histogram H = { H = { (H) } ₁ ,h ₂ ,...,h _n Each bucket in the set of buckets is a separate packet, resulting in a set of packets g (g) ₁ ,g ₂ ,...,g _n ) (ii) a Then merging the groups in the group G pairwise, traversing all merging schemes, calculating the scheme distance of each merging scheme, selecting the merging schemes through an exponential mechanism for approximate merging, regarding the merged scheme as a new group to replace the original two groups, repeating the merging process until the final group number K is reached, obtaining the final merging scheme, and forming a histogram group G (G) ₁ ,G ₂ ,...,G _k ) (ii) a Wherein: h = { H ₁ ,h ₂ ,...,h _n Denotes the original histogram sequence; h is ₁ ,h ₂ ,...,h _n Representing the buckets in the histogram, n being the total number of original histogram buckets; g (g) ₁ ,g ₂ ,...,g _n ) Representing an initial packet set before merging; g is a radical of formula ₁ ,g ₂ ,...,g _n Representing the packets in an initial set of packets, each packet consisting of one bucket, so the initial total number of packets is n; g (G) ₁ ,G ₂ ,...,G _k ) Representing the final set of packets resulting from the merging, G ₁ ,G ₂ ,...,G _k Representing packets in a final set of packets，G _k Represents the kth packet; a third main module, configured to implement S3: averaging each group of G to obtain

Wherein

Representing a mean grouping set after mean value calculation;

represents the Kth mean grouping; a fourth master module, configured to implement S4: to pair

Adding Laplace noise to obtain

Wherein:

representing a noise packet set obtained by adding noise to the mean packet set;

a packet representing the kth added noise; a fifth master module, configured to implement S5: to pair

Restoring the original histogram sequence to obtain the published differential privacy histogram

Wherein:

is represented by

Recovering the original histogram sequence to obtain a differential privacy histogram;

a bucket representing the added noise in the histogram; n represents the total number of differential privacy histogram buckets.

8. An electronic device, comprising:

at least one processor, at least one memory, and a communication interface; wherein,

the processor, the memory and the communication interface are communicated with each other;

the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1 to 6.

9. A non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method of any one of claims 1 to 6.

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