Study On Constrained KSD Sampling Method

Research fields such as signal processing and machine learning are often faced with tasks that require sampling from an unknown distribution.However,extracting valid samples from complex or unknown probabilistic models can be difficult,and Stein Variational Gradient Descent(SVGD)is an effective method.It can start from the initial samples and particles of arbitrary distribution,and obtain the samples of complex target distribution through simple transformation and iteration.Its convergence speed is fast,and it is widely used in many fields.However,at present,SVGD can only deal with the target distribution which is log-concave and unconstrained.However,in most real cases,the samples are often constrained,that is,in real applications,the constraints of the samples limit the use of the traditional SVGD method.In this paper,we extend the SVGD method to the constrained target distribution sampling problem and propose the Constrained Stein Variational Gradient Descent(CSVGD)method.In addition,the CSVGD method is also based on Kernelized Stein Discrepancy(KSD),which makes the CSVGD method not only avoid the situation that the true probability density distribution of the data is unstandardized,but also avoid the problem that the real probability density distribution of the data is unstandardized.At the same time,it avoids the situation that the partition function in the prior distribution often has unknown relations and cannot be solved.Moreover,the CSVGD method can be more effectively applied to image,audio,signal and other fields with sample constraints in reality.In this paper,it is used for noise reduction of speech signals.In this paper,the proposed CSVGD method is used to extract multiple valid samples from the target distribution,and these samples are used to achieve the Minimum Mean Square Error(MMSE)estimation of the magnitude spectrum to be estimated based on the posterior distribution.At the same time,considering that the updated position of the particle may cross the feasible region,the projection method is used to project it back to the feasible region.In summary,this paper proposes a frequency domain denoising algorithm based on CSVGD and the proposed method is applied to speech signal denoising,at last,the effectiveness of the proposed method is proved by experiment.