Sparse model selection in the highly under-sampled regime

TL;DR

This paper introduces a fast, closed-form method for sparse graphical model selection in low-sample regimes, outperforming existing algorithms in accuracy and efficiency, especially with hidden variables, demonstrated on financial and neural data.

Contribution

A novel, non-optimization-based approach for structure recovery in sparse graphical models using posterior probabilities with Jeffreys prior.

Findings

Comparable accuracy to state-of-the-art methods on sparse topologies

More accurate in the presence of hidden variables

Efficiently applied to real-world financial and neural data

Abstract

We propose a method for recovering the structure of a sparse undirected graphical model when very few samples are available. The method decides about the presence or absence of bonds between pairs of variable by considering one pair at a time and using a closed form formula, analytically derived by calculating the posterior probability for every possible model explaining a two body system using Jeffreys prior. The approach does not rely on the optimisation of any cost functions and consequently is much faster than existing algorithms. Despite this time and computational advantage, numerical results show that for several sparse topologies the algorithm is comparable to the best existing algorithms, and is more accurate in the presence of hidden variables. We apply this approach to the analysis of US stock market data and to neural data, in order to show its efficiency in recovering robust statistical dependencies in real data with non stationary correlations in time and space.