Papers › Conditional Matrix Flows for Gaussian Graphical Models

Conditional Matrix Flows for Gaussian Graphical Models

12 Jun 2023NeurIPS 2023 11arXiv:2306.07255archive 2025-07-28

Marcello Massimo Negri, F. Arend Torres, Volker Roth

Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through l_q regularization with q≤1. However, most GMMs rely on the l₁ norm because the objective is highly non-convex for sub-l₁ pseudo-norms. In the frequentist formulation, the l₁ norm relaxation provides the solution path as a function of the shrinkage parameter λ. In the Bayesian formulation, sparsity is instead encouraged through a Laplace prior, but posterior inference for different λ requires repeated runs of expensive Gibbs samplers. Here we propose a general framework for variational inference with matrix-variate Normalizing Flow in GGMs, which unifies the benefits of frequentist and Bayesian frameworks. As a key improvement on previous work, we train with one flow a continuum of sparse regression models jointly for all regularization parameters λ and all l_q norms, including non-convex sub-l₁ pseudo-norms. Within one model we thus have access to (i) the evolution of the posterior for any λ and any l_q (pseudo-) norm, (ii) the marginal log-likelihood for model selection, and (iii) the frequentist solution paths through simulated annealing in the MAP limit.

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