Exploiting compositionality to explore a large space of model structures

TL;DR

This paper introduces a grammar-based approach for automatic model structure selection in probabilistic models, efficiently exploring a large space of models to identify suitable decompositions for diverse datasets.

Contribution

It proposes a compositional grammar to generate and evaluate a vast space of models, enabling automatic structure inference with a small set of algorithms.

Findings

Successfully identifies correct structures in synthetic data

Gracefully simplifies models under heavy noise

Learns meaningful structures across diverse datasets

Abstract

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.