System and method for generating binary Laplace noise sequence with given correlation

Abstract

The present invention provides a binary Laplace noise sequence generation system and method with given correlation. The system is provided with a binary Gaussian white noise sequence generation module, comprising 4 groups of binary Gaussian white noise sequence generators, each group of binary Gaussian white noise sequence generators respectively generates a group of binary Gaussian white noise sequences; a binary correlated Gaussian noise sequence generation module, comprising 4 groups of binary filters, the 4 groups of binary filters input are respectively binary Gaussian white noise sequences, and the outputs are respectively correspondingly generated binary correlated Gaussian noise sequences; a binary correlated Laplace noise sequence generation module, using the 4 groups of binary correlated Gaussian noise sequences to generate a binary correlated Laplace noise sequence through calculation; by adjusting the parameters of the binary filters in the binary correlated Gaussian noise sequence generation module, the generated binary correlated Laplace noise sequence meets the given autocovariance function, and supports the differential privacy protection requirements of binary variable time series data.

Description

Technical Field

[0001] The present invention relates to the field of data mining and privacy protection, and more specifically, to a method for generating a binary Laplace noise sequence with a given correlation in a differential privacy protection mechanism, which is used to solve the technical problem of automatically generating a binary Laplace noise sequence with a given correlation. Background Art

[0002] With the rapid development of big data and artificial intelligence technology, the value of data has been widely recognized and has become an important resource in fields including commercial applications and scientific research. However, various types of data usually contain private information of relevant parties, including individuals. Concerns about privacy leakage will undoubtedly become a major obstacle to data collection, publishing and sharing. Therefore, the issue of data privacy protection is one of the important issues that need to be urgently addressed in the era of big data.

[0003] In the existing privacy protection theory, differential privacy borrows the concept of "computational indistinguishability" from traditional cryptography, defines privacy protection from the perspective of probability statistics, mathematically and rigorously quantifies and analyzes the strength of privacy protection, and in principle ensures that the actual privacy protection strength is not affected by the attacker's background knowledge. Therefore, it is regarded as the most promising privacy protection technology. For numerical data, the Laplace mechanism is one of the most commonly used differential privacy protection mechanisms. It achieves privacy protection by adding independent and identically distributed Laplace noise to the data. However, time series data obtained from continuous observations usually have correlation. Attackers can use this data correlation to filter out some perturbation noise, such as Wiener filtering, thereby offsetting some privacy protection effects. In order to resist this attack based on data correlation, the sequence indistinguishability theory requires that the sequence data before and after the differential privacy perturbation remain unchanged in terms of correlation, and proposes the Correlated Laplace Mechanism (CLM), which achieves sequence indistinguishability by adding a Laplace noise sequence with the same correlation to the original data, providing an effective solution for differential privacy protection of time series data.

[0004] The key to the correlated Laplace mechanism is to generate a Laplace noise sequence that satisfies the correlation characteristics of the target data. For a univariate data sequence, there are mature methods for generating a Laplace noise sequence corresponding to its correlation. For example, the authorized patent 201610597162.7 of the inventor team provides a technical solution for generating a univariate Laplace noise sequence. But in fact, the observation results of many applications are binary variable time series, such as position series data. In this regard, there is a simple sequence splitting scheme, which is to treat the binary variable time series as two univariate time series, so that CLM is applied to each of them independently for privacy protection. However, the correlation of binary variable time series is far more complicated than that of univariate time series. Not only are the data of the same dimension correlated, but there is also a certain degree of correlation between data of different dimensions. Attackers can use the data correlation of these two aspects to attack privacy protection at the same time. This is the so-called binary correlation attack. The privacy scheme based on sequence splitting completely ignores the correlation between different dimensions in the binary variable time series, which makes it difficult to achieve complete sequence indistinguishability and difficult to achieve the expected privacy protection effect under binary correlation attacks. In order to achieve differential privacy protection that satisfies sequence indistinguishability on binary variable time series, the privacy mechanism needs to add a binary Laplace noise sequence that satisfies the target data correlation (including data autocorrelation in the same dimension and data mutual correlation in different dimensions). However, so far, there is no method to generate a binary Laplace noise sequence with a given correlation.

[0005] Based on the above background, the present invention proposes a technical solution for generating a binary Laplace noise sequence with a given correlation, which provides a solution for differential privacy protection of binary variable time series data. Summary of the invention

[0006] In order to meet the differential privacy protection requirements of binary variable time series data, the present invention proposes a generation technology of binary Laplace noise sequence with given correlation.

[0007] The present invention provides a binary Laplace noise sequence generation system with a given correlation, comprising the following modules:

[0008] The binary Gaussian white noise sequence generation module includes 4 groups of binary Gaussian white noise sequence generators. Each group of binary Gaussian white noise sequence generators generates a group of binary Gaussian white noise sequences, generating a total of 4 groups of binary Gaussian white noise sequences. , and input to the binary correlated Gaussian noise sequence generation module;

[0009] Binary correlated Gaussian noise sequence generation module, including 4 sets of binary filters The four sets of binary filter inputs are binary Gaussian white noise sequences , the outputs are the corresponding binary correlated Gaussian noise sequences , and input to the binary correlated Laplace noise sequence generation module;

[0010] Binary correlated Laplace noise sequence generation module, using binary correlated Gaussian noise sequence After operation, a binary correlated Laplace noise sequence is generated ; By adjusting the binary filter in the binary correlated Gaussian noise sequence generation module The parameters of the generated binary correlated Laplace noise sequence Satisfies the given autocovariance function and supports the differential privacy protection requirements of binary variable time series data.

[0011] Moreover, the binary Gaussian white noise sequence generation module includes 4 sets of independently running binary Gaussian white noise sequence generators. , respectively generate the corresponding binary Gaussian white noise sequence output ;

[0012] The four groups of binary Gaussian white noise sequence generators have the same internal structure. Each group of binary Gaussian white noise sequence generators contains two Gaussian random number generators, corresponding to the first period, respectively, to generate Gaussian distribution random numbers , forming a binary Gaussian noise output , after continuous accumulation over time, a binary Gaussian white noise sequence is generated ,in represents a Gaussian distribution with zero mean and variance 1, Transpose the matrix.

[0013] Moreover, the four groups of binary filters in the binary correlated Gaussian noise sequence generation module , to realize the input of 4 sets of binary Gaussian white noise sequences Four sets of binary Gaussian noise sequences with autocorrelation are generated by independent processing ;

[0014] In each set of binary filters, set is the input branch parameter, expressed as matrix , is the output feedback branch parameter, variable index , expressed as Real Matrix , is the binary filter state variable, expressed as a vector , then the model of the binary filter is expressed as ,in:

[0015]

[0016]

[0017] in, is the binary filter order,

[0018] Binary Filters The processing includes filtering calculation and Status update, defined as follows:

[0019] The filtering calculation formula is:

[0020]

[0021] Corresponding to period, the binary filter takes the input sequence The corresponding vector in , the calculation produces the output sequence The corresponding vector in , is a random number that follows a Gaussian distribution;

[0022] The state update operation is implemented as follows, except for the last two elements, The remaining rows of elements in the . Element storage The first two lines of the filter are calculated after the filter calculation is completed in each time period. Perform status updates;

[0023] Generates binary correlated Gaussian noise sequences accumulated over time , its autocovariance function By the binary filter parameters Decide, is the time delay of the autocovariance function;

[0024] Binary Filter Give the same parameters , for binary filters Give the same parameters , so that The autocovariance function of Satisfy the conditions .

[0025] Moreover, the binary correlated Laplace noise sequence generation module includes two matrix multiplication operators and one matrix addition operator for implementing the operation , the binary correlated Gaussian noise sequence Processing to generate binary correlated Laplace noise sequences ,in is the binary Laplace noise, is a random number following a Laplace distribution, and The autocovariance function of satisfy , Represents the matrix element-wise multiplication operation.

[0026] Moreover, the binary filter parameters in the binary correlated Gaussian noise sequence generation module are set as follows: , according to the corresponding given autocovariance function , design binary filter banks Parameters and , so that The autocovariance function of satisfy .

[0027] Moreover, when setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, according to the given autocovariance function Constructing the autocovariance function of two sets of binary Gaussian noise sequences , and satisfies , The calculation parameters are and Provide a basis for the goal.

[0028] and, The following construction scheme is adopted:

[0029]

[0030] in, They are The autocorrelation function of the sequence data in different dimensions, express The cross-correlation function between sequence data of different dimensions in .

[0031] Moreover, when setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, the binary filter group is designed Parameters , so that The autocovariance function of satisfy .

[0032] Moreover, when setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, the binary filter group is designed Parameters , so that The autocovariance function of satisfy .

[0033] On the other hand, the present invention also provides a binary Laplace noise sequence generation method implemented according to the above binary Laplace noise sequence generation system with given correlation, and performs a binary correlated Laplace noise sequence dynamic generation process, comprising the following steps:

[0034] Step 10-1, initialization, including setting the time period index , let the binary Laplace noise number ; Set the binary filter order , set the initial stage window size ; is a binary filter Assign the parameters of , and set all elements in the binary filter state vector to 0;

[0035] Step 10-2, using the binary Gaussian white noise sequence generation module, generate 4 sets of binary Gaussian white noise ;

[0036] Step 10-3, using the binary correlated Gaussian noise sequence generation module, Input to the binary filter , output 4 sets of binary Gaussian noise , and update the binary filter state vector; calculate ;

[0037] Step 10-4, determine whether If yes, then go to step 10-5 to generate binary Laplace noise; otherwise, return to step 10-2 so that the binary filter Continue to iterate and update;

[0038] Step 10-5, using the binary correlated Laplace noise sequence generation module, according to Computes binary Laplace noise ;calculate , record the number of binary Laplace noises generated;

[0039] Step 10-6, determine whether to end, if so, end the generation process; otherwise, return to step 10-2 and enter the next cycle of generation operation.

[0040] Based on the transformation relationship between Laplace distribution and Gaussian distribution, the present invention transforms the generation problem of binary Laplace noise sequence satisfying a given correlation into the generation problem of binary Gaussian noise sequence satisfying a specific correlation, and the latter is realized by a binary Gaussian white noise sequence through a specific binary filter. The beneficial effect of the present invention is that the autocovariance function of the binary Laplace noise sequence generated by the present invention is consistent with the autocovariance function of the target data, including the data autocorrelation function of the same dimension and the data cross-correlation function of different dimensions, which can meet the differential privacy protection requirements of binary variable time series data. In order to achieve this goal, it is necessary to construct two groups of autocovariance functions of binary Gaussian noise sequences according to the target autocovariance function. To this end, the present invention further proposes a reasonable construction scheme, so that one group of autocovariance functions approximates a constant matrix, and the other group of autocovariance functions is consistent with the target autocovariance function, thereby avoiding complex calculation processes, and is suitable for dynamic adjustment of parameters for tracking time-varying correlations. In practical applications, the binary filter design part of the present invention can adopt a low-order binary filter, further reducing the computational complexity, facilitating efficient implementation, and having practical application value.

[0041] The solution of the present invention is simple and convenient to implement, has strong practicality, solves the problems of low practicality and inconvenience in actual application existing in related technologies, can improve user experience, and has important market value. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is an overall flow chart of an embodiment of the present invention;

[0043] Figure 2 It is a structural block diagram of a binary correlated Laplace noise sequence generation system according to an embodiment of the present invention;

[0044] Figure 3 is a block diagram of a binary filter structure in an embodiment of the present invention;

[0045] Figure 4 is a flow chart of binary filter parameter design in an embodiment of the present invention;

[0046] Figure 5 is an amplitude-frequency characteristic diagram of a triangular pulse distribution in an embodiment of the present invention;

[0047] Figure 6 is a flow chart of dynamic generation of a binary correlated Laplace noise sequence in an embodiment of the present invention;

[0048] Figure 7 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention;

[0049] Figure 8 is a schematic diagram of observation values ​​of different dimensions in target binary time series data in an embodiment of the present invention;

[0050] Fig. 9 2 is a schematic diagram of the distribution estimation result of the element corresponding to the period index 200 in the binary Laplace noise sequence in an embodiment of the present invention;

[0051] Fig.10 is a schematic diagram of the autocorrelation function estimation result of the same-dimensional data in the binary Laplace noise sequence in an embodiment of the present invention;

[0052] Fig.11 4 is a schematic diagram of the cross-correlation function estimation result of data of different dimensions in a binary Laplace noise sequence according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, characteristics and effects of the present invention.

[0054] According to the transformation relationship between Laplace distribution and Gaussian distribution, and the property that the linear combination of Gaussian noise still obeys Gaussian distribution, two sets of specific binary input binary output filters (referred to as binary filters) are designed firstly, so that the binary Gaussian white noise sequence passes through the binary filter to generate a binary Gaussian noise sequence with a specific autocovariance function. Then, according to the principle of generating Laplace noise from Gaussian noise, a binary Laplace noise sequence that meets the target autocovariance function is generated.

[0055] Suppose there is a binary variable time series data , and its autocovariance function is , then, the goal of the present invention is to generate a binary Laplace noise sequence ,in is the time period index, is the binary Laplace noise, are all random numbers that obey the Laplace distribution, so that The autocovariance function of satisfy , is the time delay of the autocovariance function. The present invention notes that there is an important mathematical relationship between Gaussian noise and Laplace noise, namely: ,in are independent Gaussian noises, Reason The present invention is based on this basic principle and reasonably generalizes it to the binary variable time series scenario, that is, using the binary correlated Gaussian noise sequence Generates a binary correlated Laplace noise sequence , its mathematical expression is: ,here Represents the multiplication operation of corresponding elements in the matrix.

[0056] Although the relevant concepts and definitions involved in the embodiments of the present invention can be understood and accepted by relevant professionals without any problem, in order to express the technical content of the present invention more standardized and clear, and to facilitate clearer and more accurate understanding, before introducing the content of the invention, the relevant binary variables and key concepts and definitions are first specifically and standardizedly explained.

[0057] 1) The so-called binary variable refers to a vector composed of two univariate variables. It is expressed in the form of is the matrix transpose, are univariate variables respectively. In particular, if are all random numbers that obey Gaussian distribution, then is a binary Gaussian noise. Correspondingly, if are all random numbers that obey the Laplace distribution, then is the binary Laplace noise;

[0058] 2) The so-called binary variable time series refers to the observation value sequence obtained by continuously observing the binary variable over a period of time, which is recorded as ,in is the time period index, the corresponding observation value , are univariate variables respectively. In particular, if is a binary Gaussian noise, then is a binary Gaussian noise sequence. Correspondingly, if is a binary Laplace noise, then is a binary Laplace noise sequence;

[0059] 3) The embodiment of the present invention uses the autocovariance function to describe the correlation of the binary variable time series. For the binary variable time series with zero mean , its autocovariance function The definition of is as follows,

[0060]

[0061] In the formula yes Real matrix, is the time delay of the autocovariance function, is the expectation operation, They are The autocorrelation function of the sequence data in different dimensions, express The cross-correlation function between sequence data of different dimensions in .

[0062] 4) The so-called binary input and binary output filter (abbreviated as binary filter) refers to a filter whose input and output are both binary variables. Figure 3 The binary filter structure block diagram shown in the embodiment of the present invention allows the binary Gaussian white noise sequence After binary filter Generates a binary Gaussian noise sequence that satisfies a certain correlation , corresponding to the time period The input is , the output is , All are random numbers that obey Gaussian distribution. The filtering operation formula is as follows:

[0063]

[0064] In the formula is the order of the binary filter, is the parameter index, Real Matrix is the parameter matrix of the input branch, Real Matrix is the parameter matrix of the feedback branch, which is defined as follows:

[0065]

[0066] Among them, the parameter matrix Elements in , , , is the input branch coefficient, parameter matrix Elements in , , , is the output feedback branch coefficient.

[0067] here For binary filters state, and when hour, ;

[0068] The above filtering operation can be expressed in matrix form:

[0069]

[0070] In the formula Real Matrix is the matrix composed of the feedback branch parameters, Real vector is the binary filter state vector.

[0071] Take the location series data (binary variable time series) of a certain user over a period of time as an example. The binary variable time series data is known to be , and its autocovariance function is The present invention defaults to is physically achievable, that is, it satisfies the autocovariance function The binary Gaussian noise sequence can be generated by passing the binary Gaussian white noise sequence through a stable binary filter.

[0072] The method provided by the technical solution of the present invention can use computer software technology to realize automatic operation and generation process, combined with Figure 1 The overall method flow chart of the embodiment of the present invention is shown in FIG. Figure 4 and Figure 6 The flowchart of step S2 and step S3 shown in the figure, in one embodiment of the present invention, provides a method for generating a binary Laplace noise sequence with a given correlation, and the specific steps include:

[0073] Step S1, define the composition of the binary correlated Laplace noise sequence generation system. The overall structure of the system is shown in the attached Figure 2 , mainly includes 3 modules: Binary Gaussian white noise sequence generation module, which consists of 4 groups of binary Gaussian white noise sequence generators, and its function is to generate 4 groups of binary Gaussian white noise sequences ; The binary correlated Gaussian noise sequence generation module consists of 4 sets of binary filters, whose inputs are , the outputs generate binary correlated Gaussian noise sequences The binary correlated Laplace noise sequence generation module consists of two matrix multiplication operators and one matrix addition operator. Its function is to use the binary correlated Gaussian noise sequence ,according to Generates a binary correlated Laplace noise sequence ;

[0074] The specific implementation of the optimization suggestion includes the following steps:

[0075] Step S1-1, define a binary Gaussian white noise sequence generation module, which includes 4 sets of independently running binary Gaussian white noise sequence generators, used to generate 4 sets of independent binary Gaussian white noise sequence outputs ;

[0076] The four sets of binary Gaussian white noise sequence generators have the same internal structure, each containing two Gaussian random number generators, corresponding to each time period such as period, respectively, to generate Gaussian distribution random numbers , forming a binary Gaussian noise output , It is a Gaussian distribution with zero mean and variance 1, which accumulates over time to generate a binary Gaussian white noise sequence ,and The autocovariance function of satisfy,

[0077]

[0078] In the formula is the autocovariance function delay, for The identity matrix, for Zero matrix.

[0079] correspond The four sets of binary Gaussian white noise sequences generated are ,in , , Gaussian distributed random numbers , Identify different Gaussian processes;

[0080] In the embodiment, a binary Gaussian white noise generating function is defined as , the implementation steps of this function are: generate 8 Gaussian distributed random numbers , and then combine them into 4 groups of binary Gaussian noise ;

[0081] Step S1-2, define a binary correlated Gaussian noise sequence generation module, which consists of 4 groups of binary filters Composition, to achieve the input of 4 sets of binary Gaussian white noise sequences Processing generates 4 sets of binary correlated Gaussian noise sequences with specific autocovariance functions , that is, each binary filter is processed independently to generate 4 sets of binary Gaussian noise sequences with autocorrelation;

[0082] The binary filter structure is shown in the attached Figure 3 As shown, is the input branch coefficient, expressed as matrix , is the output feedback branch coefficient (variable index ), expressed as Real Matrix , is the binary filter state variable, expressed as a vector , then the model of the binary filter is expressed as ,in:

[0083]

[0084] here is the order of the binary filter. In specific implementation, the user can set it according to the needs. The preferred recommended value is {2,3,4};

[0085] Binary Filters The processing includes filtering calculation and Status update, defined as follows:

[0086] The filtering calculation formula is:

[0087]

[0088] Its function is to correspond to each time period such as period, the binary filter takes the input sequence The corresponding vector in , the calculation produces the output sequence The corresponding vector in , All are random numbers that obey Gaussian distribution;

[0089] The status update calculation formula is:

[0090]

[0091] In the formula is the element index. The specific steps of the update operation are as follows: except for the last two elements, The remaining rows of elements in the . Element storage The first two lines of the filter calculation are required after each time period. Status updates;

[0092] Generates binary correlated Gaussian noise sequences accumulated over time , its autocovariance function By the binary filter parameters Decide;

[0093] 4 sets of binary filters Respectively Perform independent processing to generate binary correlated Gaussian noise sequences ,in , , , are all random numbers that obey Gaussian distribution. The autocovariance function of , defined as follows:

[0094]

[0095] in, They are The autocorrelation function of the sequence data in different dimensions, for The cross-correlation function between sequence data in different dimensions;

[0096] right Give the same parameters ,right Give the same parameters , to meet the condition ;

[0097] In this example, a binary filter object is created , whose properties include real numbers , Real Matrix , Real Matrix , Real vector ; Object methods include filtering operations , status update ;

[0098] Among them, the filtering operation is defined as follows:

[0099]

[0100] In the formula Both Real vectors, representing the input and output of the binary filter respectively;

[0101] Furthermore, the state update function The definition of is as follows,

[0102]

[0103] here is the element index, They are and Middle elements;

[0104] Step S1-3, define a binary correlated Laplace noise sequence generation module, which includes two matrix multiplication operators and one matrix addition operator, and its function is to realize the operation: , that is, two matrix multiplication operators are implemented separately , , and then input the matrix adder to achieve ; Transform the binary correlated Gaussian noise sequence Processing to generate binary correlated Laplace noise sequences ,in , Represents the matrix corresponding element multiplication operation, that is

[0105]

[0106] and The autocovariance function of satisfy,

[0107]

[0108] in, They are The autocorrelation function of the sequence data in different dimensions, They are The cross-correlation function between sequence data in different dimensions;

[0109] Therefore, the present invention adjusts the binary filter group in step S1-2 Parameters and , so that The autocovariance function of Meet the expected goals ;

[0110] In the embodiment, a binary Laplace noise generating function is defined as ,

[0111]

[0112] Here the function According to the vector Generate a diagonal matrix, that is

[0113]

[0114] Step S1 defines the binary correlated Laplace noise sequence generation system composition, and how to design appropriate binary filter parameters and , so that it outputs The autocovariance function of Meet the expected goals The problem will be solved through step S2.

[0115] Step S2, binary filter parameter design, including according to the given autocovariance function , design binary filter banks Parameters and , so that The autocovariance function of satisfy:

[0116]

[0117] Right now The elements satisfy the following conditions:

[0118]

[0119] Step S2-1, according to Constructing the autocovariance function of two sets of binary Gaussian noise sequences , and satisfies , is the calculation parameter and Provide a basis for the goal;

[0120] The present invention is based on the target, that is, a given autocovariance function Construct two sets of autocovariance functions , and as parameters and The design goal is to solve the parameters.

[0121] The construction method is not unique, but it is obvious that different construction schemes will have different effects. The embodiment of the present invention preferably provides a preferred construction scheme, as follows:

[0122]

[0123] besides, The construction methods also include but are not limited to

[0124]

[0125] In the formula is a symbolic function;

[0126] In the specific implementation, the structure It is necessary to ensure that the subsequent binary filter is stable;

[0127] It should be noted that any specific changes to the construction method on this basis cannot be considered as a substantial change to the present invention;

[0128] Step S2-2, designing a binary filter bank Parameters , so that The autocovariance function of satisfy ;

[0129] For step S2-1 Preferred structural scheme, preferred recommended parameters used in the embodiment of the present invention The design steps are as follows:

[0130] Step S2-2-1, follow the Figure 5 The amplitude-frequency characteristic shown is the pulse width And the amplitude is Design of all-pole filter parameters based on triangular pulse distribution ,here is the gain coefficient, To output the feedback branch parameters, the present invention recommends The value range is The calculation result is expressed as ;

[0131] In the specific implementation, according to the preferred construction scheme The present invention outputs Medium Element satisfy As the target, we only need to calculate the parameters Medium Element That simplifies the parameter solving process.

[0132] In a specific implementation, the amplitude-frequency characteristic of the full-pole filter is made to approximate a triangular pulse, so that the power spectrum of the output sequence is approximate to an impulse function, and according to the Fourier transform relationship, the autocorrelation function of the output sequence is made to approximate to a constant;

[0133] In the embodiment, the filter order is set , the pulse width of the triangular pulse , the specific parameter solution method can refer to the existing filter theory, which will not be elaborated here;

[0134] According to filter theory, it can be calculated They are: , -2.9633,2.9277, -0.9644.

[0135] Step S2-2-2, according to Constructing binary filter parameters ,

[0136]

[0137] In a specific implementation, this step makes the output Medium Element satisfy , thus ensuring the sequence The autocovariance function of The elements are the same;

[0138] In the embodiment, the binary filter parameters The calculation result is:

[0139]

[0140] Step S2-3, design a binary filter bank Parameters , so that The autocovariance function of satisfy ;

[0141] For step S2-1 Optimum structural scheme, the present invention recommends parameters The design steps are as follows:

[0142] Step S2-3-1, calculate according to the following formula Real Matrix and Real Matrix ,

[0143]

[0144]

[0145] Step S2-3-2, calculate according to the following formula Real Matrix ,

[0146]

[0147] In specific implementation, They are all defined as block matrices, so they need to be calculated according to the block matrix operation rules. The block matrix operations in the subsequent steps are the same;

[0148] Step S2-3-3, calculate , specifically including: calculating intermediate variables ;right Perform an orthogonal diagonalization operation and get ;calculate ;

[0149] In the formula for Real matrix, for The diagonal matrix of .

[0150] Step S3, dynamically generate a binary correlated Laplace noise sequence , specifically including the following steps:

[0151] Step S3-1, initialization, specifically includes: setting the time period index , let the binary Laplace noise number ; Set the binary filter order , set the initial stage window size According to the calculation result of step S2 (i.e. the binary filter parameter design result in the binary correlated Gaussian noise sequence generation module), the binary filter Assign the parameters of , and set all elements in the binary filter state vector to 0;

[0152] In the embodiment, let , ;set up , ,make for Zero matrix; create 4 sets of binary filter objects:

[0153]

[0154] Step S3-2, using the binary Gaussian white noise sequence generation module defined in step S1-1, generates 4 sets of binary Gaussian white noise ;

[0155] In the embodiment, the function defined in step S1-1 is called ;

[0156] Step S3-3, using the binary correlated Gaussian noise sequence generation module defined in step S1-2, Input to the binary filter , output 4 sets of binary Gaussian noise , and update the binary filter state vector. The definition of filtering operation and state update is shown in step S1-2; Calculate ;

[0157] In the embodiment, the calling object , respectively input , generate 4 sets of binary correlated Gaussian noise ,

[0158]

[0159] Afterwards, update the binary filter state ,

[0160]

[0161] The symbol "." in the formula indicates calling a method in an object; then, the calculation ;

[0162] Step S3-4, determine whether If yes, then go to step S3-5 to generate binary Laplace noise; otherwise, return to step S3-2 so that the binary filter Continue to iterate and update;

[0163] In the embodiment, it is determined whether , if yes, proceed to step S3-5; otherwise, return to step S3-2;

[0164] Step S3-5, using the binary correlated Laplace noise sequence generation module defined in step S1-3, according to Computes binary Laplace noise ;calculate , record the number of binary Laplace noises generated;

[0165] In the embodiment, calling function ,enter , generating binary correlated Laplace noise ,

[0166]

[0167] Afterwards, calculate ;

[0168] Step S3-6, determine whether to end, if so, end the generation process; otherwise, return to step S3-2 and enter the next cycle of generation operation.

[0169] In the embodiment, the known sequence The length is 200. According to the batch processing method, if , then the generation ends, otherwise, step S3-2, enters the generation operation of the next cycle.

[0170] The present invention does not limit the termination conditions. Whether to terminate the generation can be determined by setting the length of the binary Laplace noise sequence to be generated, that is, the batch processing mode, or the generation process can be terminated by an external instruction, that is, the streaming processing mode.

[0171] To facilitate understanding of the technical effect of the present invention, a specific application of an embodiment of the present invention is provided to demonstrate that the present invention can generate a binary Laplace noise sequence that satisfies a target autocovariance function. Figure 8 Given binary sequence data The observations of different dimensions in , and estimate their autocovariance function as follows,

[0172]

[0173] According to the preferred construction scheme provided in step S2-1 in the embodiment of the present invention, the autocovariance functions of two sets of binary Gaussian noise sequences are constructed in the embodiment: ,

[0174]

[0175] According to step S2-2 in the embodiment of the present invention, according to the preferred construction scheme , the binary filter can be calculated ,

[0176]

[0177] According to step S2-3 in the embodiment of the present invention, according to the preferred construction scheme , the binary filter can be calculated ,

[0178]

[0179] According to the binary correlated Laplace noise sequence generation system defined in step S1 in the embodiment of the present invention, and the binary correlated Laplace noise sequence dynamic generation process in step S3, the embodiment of the present invention generates a binary Laplace noise sequence The experiment was repeated 100,000 times, and the cycles in all experiments were summarized. The corresponding data is estimated The distribution of the Laplace distribution probability density function Fitting is performed, where are the mean and scale parameter of the Laplace distribution, Fig. 9 Shown The probability density function estimation results show that All of them conform to the Laplace distribution, and this result proves that the method provided by the embodiment of the present invention can generate a binary Laplace noise sequence.

[0180] In addition, the embodiment of the present invention estimates that The autocovariance function of as follows,

[0181]

[0182] Fig.10 They were shown and Autocorrelation function of data of the same dimension and , Fig.11 They were shown and The cross-correlation function between different dimensions in and It can be seen that the curves of the two are very close, and the relative change calculation results show that there is no significant difference between the two. This result further confirms that the method provided in the embodiment of the present invention can generate a binary Laplace noise sequence with a given autocovariance function.

[0183] In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the scope of protection of the present invention.

[0184] A possible embodiment is a binary Laplace noise sequence generation system with a given correlation, comprising the following modules:

[0185] The binary Gaussian white noise sequence generation module includes 4 groups of binary Gaussian white noise sequence generators. Each group of binary Gaussian white noise sequence generators generates a group of binary Gaussian white noise sequences, generating a total of 4 groups of binary Gaussian white noise sequences. , and input to the binary correlated Gaussian noise sequence generation module;

[0186] Binary correlated Gaussian noise sequence generation module, including 4 sets of binary filters The four sets of binary filter inputs are binary Gaussian white noise sequences , the outputs are the corresponding binary correlated Gaussian noise sequences , and input to the binary correlated Laplace noise sequence generation module;

[0187] Binary correlated Laplace noise sequence generation module, using binary correlated Gaussian noise sequence After operation, a binary correlated Laplace noise sequence is generated ; By adjusting the binary filter in the binary correlated Gaussian noise sequence generation module The parameters of the generated binary correlated Laplace noise sequence Satisfies the given autocovariance function and supports the differential privacy protection requirements of binary variable time series data.

[0188] In specific implementation, the above system can be realized in hardware and sold as a market product.

[0189] The following is a description of a binary Laplace noise sequence generating device with a given correlation provided by the present invention. The binary Laplace noise sequence generating device with a given correlation described below and the binary Laplace noise sequence generating method with a given correlation described above can be referenced to each other.

[0190] Figure 7 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 7 As shown, the electronic device may include: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus. The processor may call the logic instructions in the memory to execute a method for generating a binary Laplace noise sequence with a given correlation.

[0191] In addition, the logic instructions in the above-mentioned 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 technical solution of the present invention, in essence, 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, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each 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), disk or optical disk, etc., which can store program code.

[0192] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the method for generating a binary Laplace noise sequence with a given correlation provided by the above-mentioned methods.

[0193] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when the computer program is executed by a processor to execute the method for generating a binary Laplace noise sequence with a given correlation provided by the above methods.

[0194] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0195] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0196] 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 it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A system for generating a binary Laplace noise sequence with a given correlation, characterized in that: Includes the following modules, The binary Gaussian white noise sequence generation module includes 4 groups of binary Gaussian white noise sequence generators that run independently and have the same internal structure; each group of binary Gaussian white noise sequence generators contains two Gaussian random number generators, corresponding to the first period, respectively, to generate Gaussian distributed random numbers , forming a binary Gaussian noise output , after time accumulation, a binary Gaussian white noise sequence is generated ,in represents a Gaussian distribution with zero mean and variance 1, is the matrix transpose; this module generates a total of 4 sets of binary Gaussian white noise sequences , and input to the binary correlated Gaussian noise sequence generation module; Binary correlated Gaussian noise sequence generation module, including 4 sets of binary filters The four sets of binary filter inputs are binary Gaussian white noise sequences , the outputs are the corresponding binary correlated Gaussian noise sequences ; According to the given autocovariance function set up parameters to make The autocovariance function of satisfy , , ,in Represents the matrix corresponding element multiplication operation, is the time delay of the autocovariance function, and Input to the binary correlated Laplace noise sequence generation module; Binary Correlated Laplace Noise Sequence Generation Module, including 2 matrix multiplication operators and 1 matrix addition operator, used to implement the operation , the binary correlated Gaussian noise sequence Processing to generate binary correlated Laplace noise sequences ,in is the binary Laplace noise, is a random number following a Laplace distribution, and The autocovariance function of satisfy , so that With given data dependencies.

2. A system for generating a binary Laplace noise sequence with a given correlation according to claim 1, characterized in that: The four groups of binary filters in the binary correlated Gaussian noise sequence generation module , to realize the input of 4 sets of binary Gaussian white noise sequences Four sets of binary Gaussian noise sequences with autocorrelation are generated by independent processing ; In each set of binary filters, set is the input branch parameter, expressed as matrix , is the output feedback branch parameter, variable index , expressed as Real Matrix , is the binary filter state variable, expressed as a vector , then the model of the binary filter is expressed as ,in: in, is the binary filter order, Binary Filters The processing includes filtering calculation and Status update, defined as follows: The filtering calculation formula is: Corresponding to period, the binary filter takes the input sequence The corresponding vector in , the calculation produces the output sequence The corresponding vector in , is a random number that follows a Gaussian distribution; The state update operation is implemented as follows, except for the last two elements, The remaining rows of elements in the . Element storage The first two lines of the filter are calculated after the filter calculation is completed in each time period. Perform status updates; Generates binary correlated Gaussian noise sequences accumulated over time , its autocovariance function By the binary filter parameters Decide; Binary Filter Give the same parameters , for the binary filter Give the same parameters , so that The autocovariance function of Satisfy the conditions ; According to the given autocovariance function Setting parameters and , so that satisfy ; 3. A system for generating a binary Laplace noise sequence with a given correlation according to claim 2, characterized in that: When setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, according to the given autocovariance function Constructing the autocovariance function of two sets of binary Gaussian noise sequences , and satisfies , The calculation parameters are and Provide a basis for the goal.

4. A system for generating a binary Laplace noise sequence with a given correlation according to claim 3, characterized in that: The following construction scheme is adopted: in, They are The autocorrelation function of the sequence data in different dimensions, express The cross-correlation function between sequence data of different dimensions in .

5. A system for generating a binary Laplace noise sequence with a given correlation according to claim 4, characterized in that: When setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, design a binary filter bank Parameters , so that The autocovariance function of satisfy .

6. A system for generating a binary Laplace noise sequence with a given correlation according to claim 5, characterized in that: When setting the binary filter parameters in the binary correlated Gaussian noise sequence generation module, design a binary filter bank Parameters , so that The autocovariance function of satisfy .

7. A method for generating a binary Laplace noise sequence implemented by a binary Laplace noise sequence generation system with a given correlation according to any one of claims 1 to 6, characterized in that: The process of dynamically generating a binary correlated Laplace noise sequence includes the following steps: Step 7-1, initialization, including setting the time period index , let the binary Laplace noise number ; Set the binary filter order , set the initial stage window size ; is a binary filter Assign the parameters of , and set all elements in the binary filter state vector to 0; Step 7-2: Generate 4 sets of binary Gaussian white noise using the binary Gaussian white noise sequence generation module ; Step 7-3, using the binary correlated Gaussian noise sequence generation module, Input to the binary filter , output 4 sets of binary Gaussian noise , and update the binary filter state vector; calculate ; Step 7-4, determine whether If yes, then go to step 7-5 to generate binary Laplace noise; otherwise, return to step 7-2 so that the binary filter Continue to iterate and update; Step 7-5, using the binary correlated Laplace noise sequence generation module, according to Computes binary Laplace noise ;calculate , record the number of binary Laplace noises generated; Step 7-6, determine whether to end, if so, end the generation process; Otherwise, return to step 7-2 and enter the generation operation of the next cycle.

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