Research On Multi-view Collaborative Gaussian Process Dynamical Systems

Sequential data which are composed of the series of points with the temporal relationship are common in the real world.Sequential data are usually multi-dimensional.Different dimensions in sequential data that correspond to different outputs in the multi-output model are related to each other.The Gaussian process dynamical system(GPDS)is a probabilistic model for modeling sequential data.The GPDS employs the Gaussian process to model the relationship between data points and has achieved good performance in single-view tasks.With the rapid development of big data applications,more and more data present multi-view characteristics.Multi-view learning is often more efficient than single-view learning because multi-view learning makes full use of consistent and complementary information among different views.Therefore,this paper mainly studies the multi-view Gaussian process dynamical system.This paper proposes the collaborative Gaussian process dynamical system(CGPDS)with stronger modeling capability and the multi-view collaborative Gaussian process dynamical system(McGPDS)which is capable of processing multi-view sequential data.Firstly,in order to model the relevance among different dimensions in sequential data better and process the high-dimensional sequential data,this paper proposes the CGPDS.As a multi-output GPDS,the CGPDS assumes that each output is the sum of a global latent variable and a local latent variable,which enables to model common information and relevance among multiple outputs and depict unique characteristics of each output.The CGPDS adopts variational inference methods and introduces auxiliary variables to learn the model.On account of the conditional independence among multiple outputs,the variational lower bound can be decomposed regarding dimensions,which allows optimizing all parameters in a stochastic optimization framework.Therefore,the CGPDS can be applied to high-dimensional sequential data.We evaluate the CGPDS on three real-world datasets.The CGPDS achieves better performance than the state-of-the-art GPDS in the tasks of generating sequential data and recovering missing sequential data.Secondly,in order to enable the CGPDS to process multi-view sequential data,this paper further proposes the McGPDS.As a novel hierarchical multi-view model,the McGPDS makes full use of the characteristics of multi-view data and the advantages of the CGPDS.The McGPDS assumes that the private latent variable of each view is determined by its dynamical prior distribution and the shared latent variable.With the mapping from the shared latent variable to the private latent variable,on the one hand,the McGPDS achieves a deeper model structure that can model more flexible and complex mappings;On the other hand,the McGPDS explicitly models the relevance between the private latent variable and the shared latent variable,and the degree of relevance can be obtained by optimizing parameters.We evaluate the McGPDS on three multi-view datasets.The McGPDS outperforms the state-of-the-art multi-view GPDS in the tasks of learning an efficient representation of the latent space and generating novel data of one view given data of the other view.In conclusion,the McGPDS proposed in this paper can effectively process multi-view sequential data.In terms of modeling sequential data,the McGPDS is based on the newly proposed CGPDS.The validity and rationality of the CGPDS and McGPDS are verified by the experimental results on the single-view and multi-view sequential data.