Sparse Linear Identifiable Multivariate Modeling

TL;DR

This paper introduces SLIM, a Bayesian framework for sparse, identifiable multivariate models that efficiently infer latent structures and outperform existing methods like LiNGAM in biological data analysis.

Contribution

It proposes a novel Bayesian hierarchical approach with stochastic search for sparse, identifiable linear models, extending to non-linear and correlated latent variable models.

Findings

SLIM performs as well or better than LiNGAM in experiments.

The method is computationally efficient and scalable.

Extensions include non-linear and correlated latent variable models.

Abstract

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for sparse models using slab and spike priors (two-component delta-function and continuous mixtures), non-Gaussian latent factors and a stochastic search over the ordering of the variables. The framework, which we call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable computational complexity. We attribute this mainly to the stochastic search strategy used, and to parsimony (sparsity and identifiability), which is an explicit part of the model. We propose two extensions to the basic i.i.d. linear framework: non-linear dependence on observed variables, called SNIM (Sparse Non-linear Identifiable Multivariate modeling) and allowing for correlations between latent variables, called CSLIM (Correlated SLIM), for the temporal and/or spatial data. The source code and scripts are available from http://cogsys.imm.dtu.dk/slim/.