CN-121980381-A - Method for establishing high-dimensional characteristic posterior probability estimator based on sparse Bayes method

CN121980381ACN 121980381 ACN121980381 ACN 121980381ACN-121980381-A

Abstract

The invention provides a method for establishing a high-dimensional characteristic posterior probability estimator based on a sparse Bayesian method, which comprises the following steps of (1) constructing a sparse Bayesian posterior probability estimation model, (2) representing model parameters based on Bayesian theorem, (3) solving model parameters by using sample data, and (4) realizing model sparsification based on automatic correlation confirmation. Aiming at the problems that the high-dimensional feature probability distribution estimation is difficult and the feature category attribution probability solving is difficult, the invention designs a high-dimensional feature posterior probability estimator by using a sparse Bayesian method.

Inventors

AN LIANG
CAI JIANING
FAN QING
ZHU CHUANQI
CAO HONGLI
CAI MENG

Assignees

东南大学

Dates

Publication Date: 20260505
Application Date: 20260113

Claims (5)

1. The method for establishing the high-dimensional characteristic posterior probability estimator based on the sparse Bayes method is characterized by comprising the following steps of: step 1, constructing a sparse Bayesian posterior probability estimator model based on a kernel method and a linear prediction model; Step 2, carrying out model parameter characterization based on a Bayesian theorem; step 3, solving model parameters based on Newton iteration method and Laplacian approximation by using characteristic sample data; And 4, model sparsification based on automatic correlation confirmation is performed, model parameter pruning is performed according to the model parameter prior distribution anisotropy hypothesis, and model sparsification is realized.
2. The method for establishing a sparse bayesian-based high-dimensional feature posterior probability estimator according to claim 1, wherein said step 1 comprises the steps of: step 1-1, aiming at a high-dimensional characteristic data set with characteristic dimension D and sample number N Each of the samples of (1) , Constructing basis function vectors based on Gaussian kernels : ; Wherein T represents the transpose, M represents the number of Gaussian kernel functions, The j-th basis function in (a) The method comprises the following steps: ; Wherein, the , In order to achieve a peripheral rate of the material, For the center of the j-th core, Expressed in natural constant The bandwidth matrix of the gaussian kernel is an exponential function of the base I is an identity matrix; step 1-2, for sample Basis function vector of (2) Introducing a linear prediction model: ; Wherein, the As a parameter of the model, it is possible to provide, , Expressed in a given parametric model Lower sample The posterior probability estimate of the belonging target class, Representing a Logistic Sigmoid function.
3. The method for establishing a sparse bayesian-based high-dimensional feature posterior probability estimator according to claim 1, wherein said step 2 comprises the steps of: step 2-1, known high-dimensional feature dataset Corresponding sample class label vector Wherein the sample is Corresponding class labels , The object class is represented by a representation of the object class, Representing non-target classes; model parameter characterization and construction according to Bayesian theorem ; Wherein, the Likelihood distribution for parameters: ; a priori distribution of parameters: ; Wherein, the To control model parameters The super-parameter vector of the distribution, , Representing a gaussian distribution.
4. The method for establishing a sparse bayesian-based high-dimensional feature posterior probability estimator according to claim 1, wherein said step 3 comprises the steps of: step 3-1, solving by Newton iteration method Maximum value, thereby obtaining model parameters Is an iterative update formula: ; Wherein, the 、 Respectively represent the first Secondary, the first The extreme point approximation solution obtained by the iteration, For the target class probability estimation vector of the current model, B is a vector calculated by the current model parameters Diagonal matrix: ; Matrix array The method comprises the following steps: ; repeatedly executing the above iterative process until the iterative times reach the upper limit Outputting the optimal parameters of the model ; Step 3-2, using Laplace approximation Approximating the Gaussian distribution form, and respectively obtaining the distribution mean value And variance of : ; Obtaining posterior distribution form of model parameters: 。
5. The method for establishing a sparse bayesian-based high-dimensional feature posterior probability estimator according to claim 1, wherein said step 4 comprises the steps of: step 4-1, relating the product of likelihood distribution and prior distribution to model parameters Integration yields the evidence function: ; step 4-2, let the evidence function relate to the super parameter Is zero, defines an effective degree of freedom factor Solving the super parameter at the best evidence: ; Wherein, the , Representing a covariance matrix The j-th element on the diagonal line, Representation of The j-th parameter of (a); step 4-3, setting an upper limit of the super parameter threshold If there is Model parameters are calculated Corresponding model parameters in (a) Pruning to obtain sparse model parameters Simultaneously, the model relates to related variables 、 Synchronous pruning is carried out according to the same index set; step 4-4, setting parameter convergence criteria And (3) circularly executing the steps 3-1 to 4-3 until the iterative variation of the model parameters meets the convergence condition: ; judging the convergence of the model and stopping iteration, and recording the sparse model parameters during convergence as , wherein, Representing the vector norm, the subscript representing the number of iterations, 、 Respectively representing the parameters of the sparse model obtained by the s-th iteration and the s+1st iteration, and calculating on an index set shared by the two ; So far, a high-dimensional feature posterior probability estimator based on a sparse Bayes method is realized, and any high-dimensional feature sample is realized The posterior probability estimate attributed to the target class is: ; Wherein, the Representing the basis function sub-vector selected from the set of indices remaining after pruning.

Description

Method for establishing high-dimensional characteristic posterior probability estimator based on sparse Bayes method Technical Field The invention belongs to the field of pattern recognition and intelligent information processing, and particularly relates to a method for establishing a high-dimensional characteristic posterior probability estimator based on a sparse Bayesian method. Background In a strong interference environment, it is often difficult for a single feature to adequately reflect the statistical difference between the target and the background. In order to improve the characteristic characterization capability, an effective measure is to extract multiple types of characteristics aiming at the same sample data and form a high-dimensional characteristic vector, and the posterior probability estimation of the high-dimensional characteristic vector under different category assumptions is taken as a target, so that the quantitative characterization of the attribute uncertainty of the sample category is realized. In classical detection theory, it is generally assumed that the sample class conditional probability density function (i.e. likelihood function) under each hypothesis is known, and based thereon an optimal detector based on the Neyman-Pearson criterion or the minimum bayesian risk criterion is constructed. However, in a high-dimensional feature scene, the probability density distribution is generally complex, and quantitative description is difficult to be performed through simple parameter distribution, so that the application of classical detection theory is limited. In the field of pattern recognition, the kernel density estimation method is a common method for estimating the posterior probability of a high-dimensional feature, however, the sample size required by the method increases exponentially with the feature dimension, resulting in a dimension disaster. Meanwhile, since the kernel density estimation belongs to non-parameter estimation, the computing resource overhead is usually large when facing large sample data. Therefore, a method for establishing a sparse Bayesian method-based high-dimensional feature posterior probability estimator is needed, a parameterized model can be learned from limited high-dimensional feature samples, and a high-precision high-dimensional feature posterior probability estimation result can be obtained while the calculation efficiency is considered. Disclosure of Invention The invention aims to overcome the defects of the prior art, provides a method for establishing a high-dimensional characteristic posterior probability estimator based on a sparse Bayesian method, introduces a sparse Bayesian modeling framework, constructs a high-dimensional characteristic posterior probability estimation model, solves model parameters through high-dimensional characteristic samples, performs model sparsification based on automatic correlation confirmation, and realizes posterior probability estimation of high-dimensional characteristics. In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the method for establishing the high-dimensional characteristic posterior probability estimator based on the sparse Bayes method comprises the following steps: step 1, constructing a sparse Bayesian posterior probability estimator model based on a kernel method and a linear prediction model; Step 2, carrying out model parameter characterization based on a Bayesian theorem; step 3, solving model parameters based on Newton iteration method and Laplacian approximation by using characteristic sample data; And 4, model sparsification based on automatic correlation confirmation is performed, model parameter pruning is performed according to the model parameter prior distribution anisotropy hypothesis, and model sparsification is realized. As a further improvement of the present invention, the step 1 comprises the steps of: step 1-1, aiming at a high-dimensional characteristic data set with characteristic dimension D and sample number N Each of the samples of (1),Constructing basis function vectors based on Gaussian kernels: ; Wherein T represents the transpose, M represents the number of Gaussian kernel functions,The j-th basis function in (a)The method comprises the following steps: ; Wherein, the ,In order to achieve a peripheral rate of the material,For the center of the j-th core,Expressed in natural constantThe bandwidth matrix of the gaussian kernel is an exponential function of the baseI is an identity matrix; step 1-2, for sample Basis function vector of (2)Introducing a linear prediction model: ; Wherein, the As a parameter of the model, it is possible to provide,,Expressed in a given parametric modelLower sampleThe posterior probability estimate of the belonging target class,Representing a Logistic Sigmoid function. As a further improvement of the present invention, the step 2 comprises the steps of: step 2-1, known high-dimensi