For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two low-dimensional features, which distribute in the row-wise and column-wise latent subspaces respectively. In consequence, PCSA captures the dependencies among entries intricately, and is able to handle non-Gaussian and heteroscedastic densities. By formulating the posterior updating into the task of solving Sylvester equations, we propose an efficient variational inference algorithm. Furthermore, PCSA is extended to tackling and filling missing values, to adapting model sparseness, and to modelling tensor data. In comparison with several state-of-art methods, experiments demonstrate the effectiveness and efficiency of Bayesian (sparse) PCSA on modeling matrix (tensor) data and filling missing values.

For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two features, which distribute in the row-wise and column-wise latent subspaces. Consequently, it captures the dependencies among entries intricately, and is able to model the non-Gaussian and heteroscedastic density. Variational inference is proposed on PCSA for approximate Bayesian learning, where the updating for posteriors is formulated into the problem of solving Sylvester equations. Furthermore, PCSA is extended to tackling and filling missing values, to adapting its sparseness, and to modelling tensor data.

For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two features, which distribute in the row-wise and column-wise latent subspaces. Consequently, it captures the dependencies among entries intricately, and is able to model the non-Gaussian and heteroscedastic density. Variational inference is proposed on PCSA for approximate Bayesian learning, where the updating for posteriors is formulated into the problem of solving Sylvester equations. Furthermore, PCSA is extended to tackling and filling missing values, to adapting its sparseness, and to modelling tensor data. In comparison with several state-of-art approaches, experiments demonstrate the effectiveness and efficiency of Bayesian (sparse) PCSA on modeling matrix (tensor) data and filling missing values.

For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two features, which distribute in the row-wise and column-wise latent subspaces. Consequently, it captures the dependencies among entries intricately, and is able to model the non-Gaussian and heteroscedastic density. Variational inference is proposed on PCSA for approximate Bayesian learning, where the updating for posteriors is formulated into the problem of solving Sylvester equations. Furthermore, PCSA is extended to tackling and filling missing values, to adapting its sparseness, and to modelling tensor data. In comparison with several state-of-art approaches, experiments demonstrate the effectiveness and efficiency of Bayesian (sparse) PCSA on modeling matrix (tensor) data and filling missing values.