Research And Application Of Bayesian Gaussian Process Latent Variable Model

Latent Variable Models(LVM)can model the latent low dimensional representation by supposing a corresponding mapping from latent variables to observed outputs.Gaussian process latent variable model(GPLVM)stands out by the flexible of Gaussian process mapping.We focus on the study of Bayesian Gaussian process latent variable models from depth and width.On one hand,deep Gaussian process model,the deeper model of Gaussian process latent variable model,has been put forward in recent years,and the researches on the reasoning and learning of the model is relatively mature.Therefore,this paper explores the extension of its depth model in specific applications.Our first task is to solve the educational and non-educational classification problems based on Deep Gaussian processes.Specifically,we crawled the educational text data from the Internet and represented it by word2 vec method after data preprocessing.Then,we conduct experiments on the data and record the average accuracy,the time spent and the log likelihood results.We also do the experiment on levels like the number of the layer,the number of the inducing points,etc.Results validate our framework proposed on the text data classification.On the other hand,we study Bayesian Gaussian process latent variable model from the perspective of width.GPLVM supposes the mapping from the latent variables to the outputs to be Gaussian,which is not applicable when the data is in 'multi-modality' or 'multi-peaks' distributions.To solve this problem,we come up with a novel model named mixtures of shared Gaussian process latent variable model(MsGPLVM).In MsGPLVM,there is a group of base Gaussian processes shared between all the outputs.Meanwhile,we introduce indicator variables used to indicate how the Gaussian processes are mixed.We can get the low dimensional representation by finding the corresponding latent variables.We can also fill out the missing data like in the pictures.Experimental results show the effectiveness of our model...