Generative probabilistic matrix model of data with different low-dimensional linear latent structures

We construct a generative probabilistic matrix model of large data based on mixing of linear latent features distributed following Gaussian and Dirichlet distributions. Key ingredient of our model is that we allow for statistical dependence between the mixing coefficients, as well as latent features with a statistically dependent structure. Latent dimensionality and correlation patterns of the data are controlled by two model parameters. The model’s data patterns include (overlapping) clusters, sparse mixing, and constrained (non-negative) mixing. We describe the correlation and the eigenvalue distributions of these patterns. As a possible application of our model, we discuss how it can be used to generate structured training data for supervised learning.