Parameter estimation method based on data enhancement and related equipment

Abstract

The invention provides a parameter estimation method based on data enhancement and related equipment, and relates to the technical field of computers. The method comprises the following steps: acquiring low-frequency data, inserting auxiliary data points into the low-frequency data, and determining high-frequency data; determining a model function according to the target basis function; combining the model function with sparse prior to determine prior distribution of the model; the prior distribution is combined with the high-frequency data and the noise variance, joint posterior probability distribution of the model is determined, and the joint posterior probability distribution comprises each parameter of model training; and determining an estimated value of each parameter according to the joint posterior probability distribution. According to the method, the sampling frequency of the data is improved by inserting the auxiliary data points, the sparsity of the model is promoted in combination with sparse prior, the value of the model parameter is accurately estimated by sampling from posterior distribution, and the problem that the training model parameter is inaccurate in the diffusion process due to low-frequency data is solved.

Description

Technical Field

[0001] The present disclosure relates to the field of computer technology, and in particular to a parameter estimation method based on data enhancement and related equipment. Background Art

[0002] Diffusion processes are a class of stochastic differential equations perturbed by noise. They are widely used to mathematically model random phenomena, with applications in fields including financial systems, biological systems, physical systems, and neural networks. Established diffusion process models can characterize the evolution of state variables and, in turn, reveal the underlying mechanisms within the system.

[0003] In order to accurately model the system, data-driven modeling methods require a sufficiently high sampling frequency. However, in practical systems, high-frequency sampling data is difficult to obtain due to limitations in sampler deployment, labor costs, and other resources. During the training phase of the diffusion process, the low-frequency data collected has a large sampling interval and cannot reflect the system's dynamic behavior. The rate of change of the system state calculated from the low-frequency data differs significantly from the actual rate of change, making it impossible to accurately train the diffusion process model parameters.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0005] The present disclosure provides a parameter estimation method based on data enhancement and related equipment, which at least to some extent overcomes the problem of inaccurate parameters of diffusion process training models caused by low-frequency data in related technologies.

[0006] Other features and advantages of the present disclosure will become apparent from the following detailed description, or may be learned in part by practice of the present disclosure.

[0007] According to one aspect of the present disclosure, a parameter estimation method based on data enhancement is provided, including: acquiring low-frequency data, inserting auxiliary data points into the low-frequency data, and determining high-frequency data; determining a model function based on a target basis function; combining the model function with a sparse prior to determine a prior distribution of the model; combining the prior distribution with the high-frequency data and noise variance to determine a joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of model training; and determining an estimated value of each parameter based on the joint posterior probability distribution.

[0008] In some embodiments, before determining the model function based on the target basis function, the method further includes: determining the target basis function based on application object information of the model.

[0009] In some embodiments, combining the model function with a sparse prior to determine the prior distribution of the model includes: adding a Gaussian prior function or a t-distribution function with sparse promotion to the model parameters of the model function to determine the prior distribution of the model.

[0010] In some embodiments, determining the estimated value of each parameter based on the joint posterior probability distribution includes: collecting multiple samples of each parameter from the joint posterior probability distribution through a sampler; calculating the sample mean of each parameter to determine the estimated value of each parameter.

[0011] In some embodiments, combining the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model includes: combining the prior distribution with the likelihood distribution of the high-frequency data and the noise variance to determine the coupling relationship between the auxiliary data points, basis function coefficients, hyperparameters and noise of the model when combined with the high-frequency data.

[0012] In some embodiments, determining the estimated values ​​of each parameter based on the joint posterior probability distribution includes: collecting multiple samples of the auxiliary data points, multiple samples of the basis function coefficients, multiple samples of the hyperparameters, and multiple samples of the noise from the joint posterior probability distribution through a Markov chain Monte Carlo algorithm combined with a preprocessed conjugate gradient method sampler; discarding a preset number of the multiple samples of the auxiliary data points, the multiple samples of the basis function coefficients, the multiple samples of the hyperparameters, and the multiple samples of the noise to determine the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters, and the target samples of the noise; calculating the sample means of the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters, and the target samples of the noise to determine the estimated values ​​of the auxiliary data points, the estimated values ​​of the basis function coefficients, the estimated values ​​of the hyperparameters, and the estimated value of the noise.

[0013] According to another aspect of the present disclosure, a parameter estimation device based on data enhancement is also provided, including: a sampling frequency improvement module for acquiring low-frequency data, inserting auxiliary data points into the low-frequency data, and determining high-frequency data; a basis function module for determining a model function based on a target basis function; a sparse prior module for combining the model function with a sparse prior to determine a prior distribution of the model; a posterior probability distribution module for combining the prior distribution with the high-frequency data and the noise variance to determine a joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training; and an estimation module for determining an estimated value of each parameter based on the joint posterior probability distribution.

[0014] According to another aspect of the present disclosure, an electronic device is also provided, which includes: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute any one of the above-mentioned data enhancement-based parameter estimation methods by executing the executable instructions.

[0015] According to another aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, it implements any of the above-mentioned parameter estimation methods based on data enhancement.

[0016] According to another aspect of the present disclosure, a computer program product is further provided, including a computer program, wherein when the computer program is executed by a processor, the computer program implements any one of the above-mentioned parameter estimation methods based on data enhancement.

[0017] The parameter estimation method based on data enhancement provided in the embodiments of the present disclosure obtains low-frequency data, inserts auxiliary data points into the low-frequency data, and determines high-frequency data; determines a model function based on a target basis function; combines the model function with a sparse prior to determine a prior distribution of the model; combines the prior distribution with high-frequency data and noise variance to determine a joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training; and determines an estimated value of each parameter based on the joint posterior probability distribution. The present application increases the sampling frequency of the data by inserting auxiliary data points and promotes the sparsity of the model by combining a sparse prior, and accurately estimates the values ​​of the model parameters by sampling from the posterior distribution, thereby achieving accurate learning of the dynamic behavior of the diffusion process from low-frequency sampled data, and solving the problem of inaccurate parameters of the diffusion process training model caused by low-frequency data.

[0018] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, are used to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0020] Figure 1 A schematic diagram showing a parameter estimation system structure based on data enhancement in an embodiment of the present disclosure is shown;

[0021] Figure 2 A flow chart of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0022] Figure 3 A flowchart showing a specific example of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0023] Figure 4 A flowchart showing another specific example of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0024] Figure 5 A flowchart showing another specific example of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0025] Figure 6 A flowchart showing another specific example of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0026] Figure 7 A flowchart showing another specific example of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown;

[0027] Figure 8 A schematic diagram of a parameter estimation device based on data enhancement in an embodiment of the present disclosure is shown;

[0028] Figure 9 A structural block diagram of a computer device in an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0029] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0030] In addition, the accompanying drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0031] For ease of understanding, before introducing the embodiments of the present disclosure, several terms involved in the embodiments of the present disclosure are first explained as follows:

[0032] Diffusion Process: DP, Diffusion Process, is a type of random process in which the changes in state variables are gradual and continuous and are affected by random disturbances. Diffusion processes are widely used in statistical physics, data science, neural networks and other fields.

[0033] Markov Chain Monte Carlo Algorithm: MCMC, Markov Chain Monte Carlo, MCMC algorithm realizes Monte Carlo sampling of complex distributions by constructing a Markov chain. Specifically, MCMC algorithm uses a Markov chain to gradually approximate the target distribution, and generates a series of samples in the sample space through the state transition process in the chain. These samples will gradually follow the target distribution;

[0034] Preconditioned Conjugate Gradient method: PCG, Preconditioned Conjugate Gradient method;

[0035] Preconditioning time marching algorithm: pCN, Preconditioning Crank-Nicolson.

[0036] The specific implementation of the embodiment of the present disclosure is described in detail below with reference to the accompanying drawings.

[0037] Figure 1 FIG. 1 shows an exemplary application system architecture diagram to which the parameter estimation method based on data enhancement in the embodiment of the present disclosure can be applied. Figure 1 As shown, the system architecture may include a terminal device 101 , a network 102 and a server 103 .

[0038] The network 102 is a medium for providing a communication link between the terminal device 101 and the server 103 , and can be a wired network or a wireless network.

[0039] Optionally, the above-mentioned wireless network or wired network uses standard communication technologies and / or protocols. The network is typically the Internet, but it can also be any network, including but not limited to a local area network (LAN), a metropolitan area network (MAN), a wide area network (WAN), a mobile, wired or wireless network, a private network or any combination of a virtual private network). In some embodiments, technologies and / or formats including Hypertext Markup Language (HTML), Extensible Markup Language (XML), etc. are used to represent data exchanged over the network. In addition, conventional encryption technologies such as Secure Socket Layer (SSL), Transport Layer Security (TLS), Virtual Private Network (VPN), Internet Protocol Security (IPSec), etc. can be used to encrypt all or some links. In other embodiments, customized and / or dedicated data communication technologies can also be used to replace or supplement the above-mentioned data communication technologies.

[0040] The terminal device 101 can be various electronic devices, including but not limited to smart phones, tablet computers, laptop computers, desktop computers, smart speakers, smart watches, wearable devices, augmented reality devices, virtual reality devices, etc.

[0041] Optionally, the client of the application installed in different terminal devices 101 is the same, or the client of the same type of application based on different operating systems. Based on the different terminal platforms, the specific form of the client of the application can also be different, for example, the application client can be a mobile phone client, a PC client, etc.

[0042] In one example of the present disclosure, the above-mentioned terminal device obtains low-frequency data, inserts auxiliary data points into the low-frequency data, and determines high-frequency data; determines a model function based on the target basis function; combines the model function with a sparse prior to determine the prior distribution of the model; combines the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training; and determines the estimated value of each parameter based on the joint posterior probability distribution.

[0043] The server 103 may be a server that provides various services, such as a background management server that provides support for the devices operated by the user using the terminal device 101. The background management server may analyze and process the received request and other data, and feed back the processing results to the terminal device.

[0044] Optionally, the server can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms.

[0045] In one example of the present disclosure, the above-mentioned server is used to obtain low-frequency data, insert auxiliary data points into the low-frequency data, and determine high-frequency data; determine the model function based on the target basis function; combine the model function with the sparse prior to determine the prior distribution of the model; combine the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training; and determine the estimated value of each parameter based on the joint posterior probability distribution.

[0046] Those skilled in the art will know that Figure 1 The number of terminal devices, networks, and servers in the embodiment is merely illustrative, and any number of terminal devices, networks, and servers may be provided based on actual needs. This embodiment of the present disclosure does not limit this.

[0047] Figure 2 A flow chart of a parameter estimation method based on data enhancement in an embodiment of the present disclosure is shown as follows: Figure 1 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure includes the following steps:

[0048] S202: Acquire low-frequency data, insert auxiliary data points into the low-frequency data, and determine high-frequency data.

[0049] It should be noted that the above low-frequency data can be sparse observation data with large time or space sampling intervals. The above auxiliary data points can be artificially constructed virtual data, which can be constructed between low-frequency data points through mathematical interpolation, model generation or physical rules. The above high-frequency data is the data after the auxiliary data points are inserted into the low-frequency data. For example, the auxiliary data points It is mainly used to increase the sampling frequency of the original data X. By inserting M-1 auxiliary data points between adjacent data points (inserting auxiliary data points between adjacent data points of low-frequency data), the sampling frequency can be increased by M times.

[0050] In a specific example, an algorithm based on interpolation and completion, addressing the common problem of uneven sampling in real-world applications, can ensure the accuracy of model training by processing data with irregular time intervals. For example, for unevenly sampled data, varying numbers of auxiliary data points are inserted between adjacent data points to increase the sampling frequency and maintain consistency. This can effectively improve the accuracy of diffusion model training in industrial scenarios where uniform sampling is difficult to achieve.

[0051] S204: Determine a model function according to the target basis function.

[0052] It should be noted that the aforementioned basis functions can be a set of mathematical functions used to characterize the underlying dynamic behavior of the system, and the input-output relationship of the system (model) can be expressed as a linear combination of the basis functions. For example, the aforementioned basis functions can be polynomial basis functions, sinusoidal basis functions, and wavelet basis functions.

[0053] S206 , combining the model function with the sparse prior to determine the prior distribution of the model.

[0054] It should be noted that the aforementioned sparse prior can be a distribution function used to characterize the coefficients of the basis function model. Specifically, according to the principle of Occam's razor, real-world systems are often simple but highly interpretable mathematical models. Sparse prior distributions are added to the basis function coefficients to induce model sparsity. The aforementioned prior distribution can be an assumption about the probability distribution of model parameters or variables before observing data.

[0055] S208 , combining the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training.

[0056] It should be noted that the above-mentioned noise variance can be a statistic of random fluctuations or interference in the data, which is used to quantify the degree of deviation between the observed value and the true signal. The larger the noise variance, the smaller the influence of the observed data on the parameter update, the closer the posterior distribution is to the prior, and the data weight can be adjusted by the noise variance. The joint posterior probability distribution can be a probability distribution updated by Bayes' theorem (the posterior distribution is calculated by the prior distribution and data likelihood) after the data is collected, combining the prior distribution and the observed data, wherein the data likelihood represents the degree of support of the data for the parameter. The above-mentioned parameters include auxiliary data points, basis function coefficients, hyperparameters and noise.

[0057] S210 , determining estimated values ​​of various parameters according to the joint posterior probability distribution.

[0058] It should be noted that the above estimated values ​​may be the values ​​of model parameters.

[0059] This application increases the sampling frequency of the data by inserting auxiliary data points and combines sparse priors to promote the sparsity of the model. It samples from the posterior distribution to accurately estimate the values ​​of the model parameters, thereby accurately learning the dynamic behavior of the diffusion process from low-frequency sampled data and solving the problem of inaccurate parameters of the diffusion process training model caused by low-frequency data.

[0060] In one embodiment of the present disclosure, Figure 3 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure further includes the following steps before determining the model function according to the target basis function, which can match the data structure characteristics and improve the model performance and accuracy:

[0061] S302: Determine the target basis function according to the application object information of the model.

[0062] In a specific example, the form of the basis function is determined according to the application object information (the properties of the model system). For example, in the power system, since the voltage and current have a fixed industrial frequency periodicity, setting the basis function to a trigonometric function (for example, a sine function, a cosine function) can naturally match this periodicity; in the communication system, due to the variability of the channel signal, setting the basis function to a wavelet function can capture the instantaneous characteristics.

[0063] In one embodiment of the present disclosure, Figure 4 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure combines the model function with the sparse prior, and determines the prior distribution of the model, which specifically includes the following steps, which can enhance the sparsity of the model and simplify the model structure:

[0064] S402 : Add a Gaussian prior function or a t-distribution function with sparse promotion to the model parameters of the model function to determine the prior distribution of the model.

[0065] For example, the distribution function of the coefficients of the basis function model is characterized by the sparse prior p(θ|γ).

[0066] In one embodiment of the present disclosure, Figure 5 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure determines the estimated value of each parameter according to the joint posterior probability distribution, which specifically includes the following steps, which can improve the accuracy of the parameter estimation value:

[0067] S502, collecting multiple samples of each parameter from the joint posterior probability distribution through a sampler;

[0068] S504: Calculate the sample mean of each parameter and determine the estimated value of each parameter.

[0069] In one embodiment of the present disclosure, Figure 6 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure combines the prior distribution with high-frequency data and noise variance to determine the joint posterior probability distribution of the model, which specifically includes the following steps and can comprehensively quantify various parameters:

[0070] S602: Combine the prior distribution with the likelihood distribution and noise variance of the high-frequency data to determine the coupling relationship between the auxiliary data points, basis function coefficients, hyperparameters and noise when the model is combined with the high-frequency data.

[0071] For example, the posterior probability distribution is the likelihood distribution of the combined data The joint probability distribution of all unknown random variables derived from the sparse prior p(θ|γ)p(γ) of the coefficients and the noise variance p(σ) prior describes the probability distribution of the auxiliary data points given the observation data X (equivalent to the high-frequency data mentioned above). The coupling relationship between the basis function coefficients θ, hyperparameters γ, and noise σ.

[0072] In one embodiment of the present disclosure, Figure 7 As shown, the parameter estimation method based on data enhancement provided in the embodiment of the present disclosure includes the following steps of determining the estimated value of each parameter according to the joint posterior probability distribution:

[0073] S702, using a Markov chain Monte Carlo algorithm combined with a preconditioned conjugate gradient method sampler, collecting multiple samples of auxiliary data points, multiple samples of basis function coefficients, multiple samples of hyperparameters, and multiple samples of noise from the joint posterior probability distribution;

[0074] S704, discarding a preset number of the multiple samples of the auxiliary data points, the multiple samples of the basis function coefficients, the multiple samples of the hyperparameters, and the multiple samples of the noise, and determining target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters, and the target samples of the noise;

[0075] S706, calculate the sample means of the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of the noise, and determine the estimated values ​​of the auxiliary data points, the estimated values ​​of the basis function coefficients, the estimated values ​​of the hyperparameters and the estimated values ​​of the noise.

[0076] For example, from the pCN proposal distribution Mid-term collection If its acceptance probability is less than the uniform distribution p u ,but: otherwise, From the marginal posterior probability distribution of θ Collect samples θ k; From the marginal posterior probability distribution of γ Collect samples in γ k ; From the marginal posterior probability distribution of σ Collect samples σ k ; Using the Markov chain Monte Carlo algorithm designed above combined with the sampler of the preconditioned conjugate gradient method, the posterior distribution of the random variable can be obtained Collected about and σ are sufficient. According to the meticulous balance theorem, the first samples collected may not follow the target distribution, so the first half of the data (equivalent to the preset number) needs to be discarded to ensure the accuracy of the estimated value. Assuming that 2K data are collected and the first half of the data (equivalent to the target sample) is discarded, the mean of each random variable can be calculated using the following formula:

[0077]

[0078] Finally, consider the mean of the random variable as The estimated values ​​of σ and σ can realize the diffusion process training based on data enhancement.

[0079] The present invention integrates a Markov chain Monte Carlo algorithm with a preconditioned conjugate gradient method sampler to collect samples of random variables under high-dimensional or complex probability distributions, so that the collected samples converge to the target distribution more quickly, effectively improving computational efficiency while maintaining accuracy. In addition, the Markov chain Monte Carlo algorithm, which is robust to system dimensions, is combined with a preconditioned conjugate gradient method sampler. By utilizing the matrix inverse theorem and the matrix determinant theorem, the marginal posterior distribution of the auxiliary data points is split into a normal distribution term and a residual term, and the pCN proposal distribution is then used to sample the auxiliary data points, so that the acceptance probability of the sampling points does not decrease with the increase of the system dimension.

[0080] In a specific embodiment of the present disclosure, during specific implementation, with respect to the Langevin equation:

[0081] dx=-xdt+0.5dw;

[0082] Where dx represents the differential variable of the independent variable x, dt represents the deterministic damping term, and dw represents the Wiener process. The original sparse data was collected on the interval [0, 1500] with a sampling frequency of 0.3. In order to increase the sampling frequency of the data, an auxiliary data point is inserted between adjacent data points and the sampling frequency is increased to 0.15. In order to identify the dynamics of the system from the data, 1, x, x are selected. 2, exp(x), exp(2x) and exp(3x) are used as basis functions to construct the function space. In order to select the correct function term from the candidate basis functions, the Student's t distribution is added to the sparse prior coefficients to promote its sparsity. By combining the likelihood probability of the collected data and the prior distribution of the model parameters, the joint posterior distribution of the auxiliary data points and the model parameters can be derived. Finally, the Markov chain Monte Carlo algorithm combined with the preconditioned conjugate gradient method sampler collected 40,000 points from the posterior distribution and estimated the values ​​of the auxiliary data points and model parameters by calculating the average of the last 20,000 points. The trained Langevin equation is as follows:

[0083] dx=-0.96xdt+0.46dw;

[0084] According to the experimental results, the parameter estimation method based on data enhancement can accurately identify the model parameters.

[0085] Based on the same inventive concept, the present disclosure also provides a parameter estimation device based on data enhancement, as described in the following embodiments. Since the principle of solving the problem in the device embodiment is similar to that in the above method embodiment, the implementation of the device embodiment can refer to the implementation of the above method embodiment, and the repeated parts will not be repeated.

[0086] Figure 8 A schematic diagram of a parameter estimation device based on data enhancement in an embodiment of the present disclosure is shown. Figure 8 As shown, the device includes: a sampling frequency increasing module 81, a basis function module 82, a sparse priori module 83, a posterior probability distribution module 84 and an estimation module 85.

[0087] The sampling frequency increasing module 81 is used to obtain low-frequency data, insert auxiliary data points into the low-frequency data, and determine high-frequency data.

[0088] The basis function module 82 is used to determine the model function according to the target basis function.

[0089] The sparse prior module 83 is used to combine the model function with the sparse prior to determine the prior distribution of the model.

[0090] The posterior probability distribution module 84 is used to combine the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training.

[0091] The estimation module 85 is used to determine the estimated value of each parameter according to the joint posterior probability distribution.

[0092] In one example of the present disclosure, the above-mentioned parameter estimation device based on data enhancement further includes a target basis function determination module, which is used to determine the target basis function according to the application object information of the model.

[0093] In one example of the present disclosure, the sparse prior module is further used to add a Gaussian prior function or a t-distribution function with sparse promotion to the model parameters of the model function to determine the prior distribution of the model.

[0094] In one example of the present disclosure, the above-mentioned estimation module is further used to collect multiple samples of each parameter from the joint posterior probability distribution through a sampler; calculate the sample mean of each parameter, and determine the estimated value of each parameter.

[0095] In one example of the present disclosure, the above-mentioned posterior probability distribution module is also used to combine the prior distribution with the likelihood distribution and noise variance of the high-frequency data to determine the coupling relationship between the auxiliary data points, basis function coefficients, hyperparameters and noise when the model is combined with the high-frequency data.

[0096] In one example of the present disclosure, the above-mentioned valuation module is also used to collect multiple samples of auxiliary data points, multiple samples of basis function coefficients, multiple samples of hyperparameters and multiple samples of noise from the joint posterior probability distribution through a Markov chain Monte Carlo algorithm combined with a preprocessed conjugate gradient method sampler; discard a preset number of the multiple samples of auxiliary data points, multiple samples of basis function coefficients, multiple samples of hyperparameters and multiple samples of noise to determine the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of noise; calculate the sample mean of the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of noise to determine the estimated value of the auxiliary data point, the estimated value of the basis function coefficients, the estimated value of the hyperparameters and the estimated value of the noise.

[0097] It should be noted that the sampling frequency increasing module 81, basis function module 82, sparse prior module 83, posterior probability distribution module 84, and estimation module 85 described above correspond to S202 to S210 in the method embodiment. The examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the contents disclosed in the above method embodiment. It should be noted that the above modules, as part of the apparatus, can be executed in a computer system, such as a set of computer-executable instructions.

[0098] Those skilled in the art will appreciate that various aspects of the present disclosure may be implemented as systems, methods, or program products. Therefore, various aspects of the present disclosure may be implemented in the following forms: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which may be collectively referred to herein as "circuits," "modules," or "systems."

[0099] Refer to the following Figure 9 1 and 2 to describe the electronic device 900 according to this embodiment of the present disclosure. Figure 9 The electronic device 900 shown is merely an example and should not limit the functions and scope of use of the embodiments of the present disclosure.

[0100] like Figure 9 As shown, electronic device 900 is implemented as a general-purpose computing device. Components of electronic device 900 may include, but are not limited to, at least one processing unit 910, at least one storage unit 920, and a bus 930 connecting various system components (including storage unit 920 and processing unit 910).

[0101] The storage unit stores program codes, which can be executed by the processing unit 910, so that the processing unit 910 performs the steps described in the above “Exemplary Method” section of this specification according to various exemplary embodiments of the present disclosure.

[0102] For example, the processing unit 910 can perform the following steps of the above-mentioned method embodiment: obtain low-frequency data, insert auxiliary data points into the low-frequency data, and determine high-frequency data; determine the model function based on the target basis function; combine the model function with the sparse prior to determine the prior distribution of the model; combine the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter of the model training; and determine the estimated value of each parameter based on the joint posterior probability distribution.

[0103] For example, the processing unit 910 may execute the following steps of the above method embodiment: determining the target basis function according to the application object information of the model.

[0104] For example, the processing unit 910 may execute the following steps of the above method embodiment: adding a Gaussian prior function or a t-distribution function with sparse promotion to the model parameters of the model function to determine the prior distribution of the model.

[0105] For example, the processing unit 910 may perform the following steps of the above method embodiment: collecting multiple samples of each parameter from the joint posterior probability distribution through a sampler; calculating the sample mean of each parameter, and determining the estimated value of each parameter.

[0106] For example, the processing unit 910 can perform the following steps of the above method embodiment: combining the prior distribution with the likelihood distribution and noise variance of the high-frequency data, and determining the coupling relationship between the auxiliary data points, basis function coefficients, hyperparameters and noise of the model when combining the high-frequency data.

[0107] For example, the processing unit 910 can execute the following steps of the above-mentioned method embodiment: through the Markov chain Monte Carlo algorithm combined with the preprocessed conjugate gradient method sampler, multiple samples of auxiliary data points, multiple samples of basis function coefficients, multiple samples of hyperparameters and multiple samples of noise are collected from the joint posterior probability distribution; a preset number of the multiple samples of auxiliary data points, multiple samples of basis function coefficients, multiple samples of hyperparameters and multiple samples of noise are discarded to determine the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of noise; the sample mean of the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of noise are calculated to determine the estimated value of the auxiliary data point, the estimated value of the basis function coefficients, the estimated value of the hyperparameters and the estimated value of the noise.

[0108] The storage unit 920 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 9201 and / or a cache memory unit 9202 , and may further include a read-only memory unit (ROM) 9203 .

[0109] The storage unit 920 may also include a program / utility 9204 having a set (at least one) of program modules 9205, such program modules 9205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0110] Bus 930 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0111] The electronic device 900 can also communicate with one or more external devices 940 (e.g., a keyboard, a pointing device, a Bluetooth device, etc.), one or more devices that enable a user to interact with the electronic device 900, and / or any device that enables the electronic device 900 to communicate with one or more other computing devices (e.g., a router, a modem, etc.). Such communication can occur via an input / output (I / O) interface 950. Furthermore, the electronic device 900 can communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network such as the Internet) via a network adapter 960. As shown, the network adapter 960 communicates with other modules of the electronic device 900 via a bus 930. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with the electronic device 900, including but not limited to microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0112] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the example embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

[0113] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart may be implemented as a computer program product, which includes: a computer program, which implements the above-mentioned parameter estimation method based on data enhancement when executed by a processor.

[0114] In an exemplary embodiment of the present disclosure, a computer-readable storage medium is also provided. The computer-readable storage medium may be a readable signal medium or a readable storage medium. A program product capable of implementing the above-mentioned method of the present disclosure is stored thereon. In some possible implementations, various aspects of the present disclosure may also be implemented in the form of a program product, which includes program code. When the program product is run on a terminal device, the program code is used to cause the terminal device to execute the steps according to various exemplary embodiments of the present disclosure described in the "Exemplary Methods" section above of this specification.

[0115] More specific examples of computer-readable storage media in the present disclosure may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), optical fibers, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0116] In the present disclosure, a computer-readable storage medium may include a data signal propagated in baseband or as part of a carrier wave, which carries readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0117] Alternatively, the program code contained on the computer-readable storage medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof.

[0118] In a specific implementation, the program code for performing the operations of the present disclosure may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, and the like, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a standalone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0119] It should be noted that although several modules or units of the device for action execution are mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into multiple modules or units to be concretized.

[0120] Furthermore, although the steps of the method of the present disclosure are described in a particular order in the accompanying drawings, this does not require or imply that the steps must be performed in this particular order, or that all steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0121] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the example embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a mobile terminal, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

[0122] Other embodiments of the present disclosure will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the appended claims.

Claims

1. A parameter estimation method based on data enhancement, characterized in that: include: Obtaining low-frequency data, inserting auxiliary data points into the low-frequency data, and determining high-frequency data; Determine the model function according to the target basis function; Combining the model function with a sparse prior to determine a prior distribution of the model; Combining the prior distribution with the high-frequency data and the noise variance to determine a joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter trained on the model; According to the joint posterior probability distribution, estimated values ​​of various parameters are determined.

2. The parameter estimation method based on data enhancement according to claim 1, characterized in that Before determining the model function according to the target basis function, the method further includes: The target basis function is determined according to application object information of the model.

3. The parameter estimation method based on data enhancement according to claim 1, characterized in that Combining the model function with a sparse prior to determine the prior distribution of the model includes: A Gaussian prior function or a t-distribution function with sparse promotion is added to the model parameters of the model function to determine the prior distribution of the model.

4. The parameter estimation method based on data enhancement according to any one of claims 1 to 3, characterized in that Determining the estimated value of each parameter according to the joint posterior probability distribution includes: Collecting multiple samples of each parameter from the joint posterior probability distribution by a sampler; Calculate the sample mean of each parameter and determine the estimated value of each parameter.

5. The parameter estimation method based on data enhancement according to claim 1, characterized in that Combining the prior distribution with the high-frequency data and the noise variance to determine the joint posterior probability distribution of the model includes: The prior distribution is combined with the likelihood distribution of the high-frequency data and the noise variance to determine the coupling relationship between the auxiliary data points, basis function coefficients, hyperparameters and noise of the model when the high-frequency data is combined.

6. The parameter estimation method based on data enhancement according to claim 5, characterized in that Determining the estimated value of each parameter according to the joint posterior probability distribution includes: Collecting a plurality of samples of the auxiliary data points, a plurality of samples of the basis function coefficients, a plurality of samples of the hyperparameters, and a plurality of samples of the noise from the joint posterior probability distribution by using a Markov chain Monte Carlo algorithm combined with a preconditioned conjugate gradient method sampler; discarding a preset number of the plurality of samples of the auxiliary data points, the plurality of samples of the basis function coefficients, the plurality of samples of the hyperparameters, and the plurality of samples of the noise, and determining target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters, and the target samples of the noise; Calculate the sample means of the target samples of the auxiliary data points, the target samples of the basis function coefficients, the target samples of the hyperparameters and the target samples of the noise, and determine the estimated values ​​of the auxiliary data points, the estimated values ​​of the basis function coefficients, the estimated values ​​of the hyperparameters and the estimated value of the noise.

7. A parameter estimation device based on data enhancement, characterized in that: include: a sampling frequency increasing module for acquiring low-frequency data, inserting auxiliary data points into the low-frequency data, and determining high-frequency data; Basis function module, used to determine the model function according to the target basis function; A sparse prior module, configured to combine the model function with a sparse prior to determine a prior distribution of the model; a posterior probability distribution module, configured to combine the prior distribution with the high-frequency data and the noise variance to determine a joint posterior probability distribution of the model, wherein the joint posterior probability distribution includes each parameter trained on the model; The estimation module is used to determine the estimated value of each parameter according to the joint posterior probability distribution.

8. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the parameter estimation method based on data enhancement according to any one of claims 1 to 6 by executing the executable instructions.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the parameter estimation method based on data enhancement according to any one of claims 1 to 6 is implemented.

10. A computer program product comprising: A computer program or instruction, characterized in that when the computer program or instruction is executed by a processor, it implements the parameter estimation method based on data enhancement as described in any one of claims 1 to 6.

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