VAE-KRnet and its Applications to Variational Bayes

In this work,we have proposed a generative model,called VAE-KRnet,for density estimation or approximation,which combines the canonical variational autoencoder(VAE)with our recently developed flow-based generativemodel,called KRnet.VAE is used as a dimension reduction technique to capture the latent space,and KRnet is used to model the distribution of the latent variable.Using a linear model between the data and the latent variable,we show that VAE-KRnet can be more effective and robust than the canonical VAE.VAE-KRnet can be used as a density model to approximate either data distribution or an arbitrary probability density function(PDF)known up to a constant.VAE-KRnet is flexible in terms of dimensionality.When the number of dimensions is relatively small,KRnet can effectively approximate the distribution in terms of the original random variable.For high-dimensional cases,we may use VAE-KRnet to incorporate dimension reduction.One important application of VAE-KRnet is the variational Bayes for the approximation of the posterior distribution.The variational Bayes approaches are usually based on the minimization of the Kullback-Leibler(KL)divergence between the model and the posterior.For highdimensional distributions,it is very challenging to construct an accurate densitymodel due to the curse of dimensionality,where extra assumptions are often introduced for efficiency.For instance,the classical mean-field approach assumes mutual independence between dimensions,which often yields an underestimated variance due to oversimplification.To alleviate this issue,we include into the loss the maximization of the mutual information between the latent random variable and the original random variable,which helps keep more information from the region of low density such that the estimation of variance is improved.Numerical experiments have been presented to demonstrate the effectiveness of our model.

Effective Frameworks Based on Infinite Mixture Model for Real-World Applications

Interest in automated data classification and identification systems has increased over the past years in conjunction with the high demand for artificial intelligence and security applications.In particular,recognizing human activities with accurate results have become a topic of high interest.Although the current tools have reached remarkable successes,it is still a challenging problem due to various uncontrolled environments and conditions.In this paper two statistical frameworks based on nonparametric hierarchical Bayesian models and Gamma distribution are proposed to solve some realworld applications.In particular,two nonparametric hierarchical Bayesian models based on Dirichlet process and Pitman-Yor process are developed.These models are then applied to address the problem of modelling grouped data where observations are organized into groups and these groups are statistically linked by sharing mixture components.The choice of the Gamma mixtures is motivated by its flexibility for modelling heavy-tailed distributions.In addition,deploying the Dirichlet process prior is justified by its advantage of automatically finding the right number of components and providing nice properties.Moreover,a learning step via variational Bayesian setting is presented in a flexible way.The priors over the parameters are selected appropriately and the posteriors are approximated effectively in a closed form.Experimental results based on a real-life applications that concerns texture classification and human actions recognition show the capabilities and effectiveness of the proposed framework.

Effects of PHC on Water Quality of Jiaozhou BayⅢ.Land Transfer Process

Based on investigation data of PHC content in Jiaozhou Bay,China from 1979 to 1983,the seasonal variations of PHC content and monthly changes of precipitation in Jiaozhou Bay were analyzed. The results showed that seen from the spatial and temporal distribution,the seasonal variation of PHC content in the surface water of Jiaozhou Bay was based on the flow of the rivers as well as human activity,so PHC content in the rivers depended on the flow of the rivers and human activity,and the peaks and valleys of PHC content appeared in various seasons. The seasonal variation of PHC content in the surface water of Jiaozhou Bay depended on its land transfer process. The land transfer process was composed of use of PHC by mankind,deposition of PHC in soil and on the earth＇s surface,and transportation of PHC to offshore waters of sea by rivers and surface runoff. PHC content depended on mankind during the process from being used to entering soil and on precipitation during the process of being transported from soil to ocean.

Phase noise correction for OFDM signal based on DCT approach and variational inference

A novel scheme to joint phase noise （PHN） correcting and channel noise variance estimating for orthogonal frequency division multiplexing （OFDM） signal was proposed, The new scheme was based on the variational Bayes （VB） method and discrete cosine transform （DCT） approximation. Compared with the least squares （LS） based scheme, the proposed scheme could overcome the over-fitting phenomenon and thus lead to an improved performance. Computer simulations showed that the proposed VB based scheme outperforms the existing LS based scheme