Model Selection in Compositional Spaces

We often build complex probabilistic models by composing simpler models—using one model to generate parameters or latent variables for another model. This allows us to express complex distributions over the observed data and to share statistical structure between different parts of a model. In this thesis, we present a space of matrix decomposition models defined by the composition of a small number of motifs of probabilistic modeling, including clustering, low rank factorizations, and binary latent factor models. This compositional structure can be represented by a context-free grammar whose production rules correspond to these motifs. By exploiting the structure of this grammar, we can generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 model structures using a small toolbox of reusable algorithms. Using a greedy search over this grammar, we au-tomatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct struc-ture for synthetic data and backs off gracefully to simpler models under heavy noise