Conditional Matrix Flows for Gaussian Graphical Models

• URL: http://arxiv.org/abs/2306.07255v2
• Date: Thu, 16 Nov 2023 13:54:59 GMT
• Title: Conditional Matrix Flows for Gaussian Graphical Models
• Authors: Marcello Massimo Negri, F. Arend Torres and Volker Roth
• Abstract summary: We propose a general framework for variation inference matrix GG-Flow in which the benefits of frequent keyization and Bayesian inference are studied. As a train of the sparse for any $lambda$ and any $l_q$ (pse-) and for any $l_q$ (pse-) we have to (i) train the limit for any $lambda$ and any $l_q$ (pse-) and (like for the selection) the frequent solution.
• Score: 1.6435014180036467
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $q\leq1$. However, most GMMs rely on the $l_1$ norm because the objective is highly non-convex for sub-$l_1$ pseudo-norms. In the frequentist formulation, the $l_1$ norm relaxation provides the solution path as a function of the shrinkage parameter $\lambda$. In the Bayesian formulation, sparsity is instead encouraged through a Laplace prior, but posterior inference for different $\lambda$ 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 $\lambda$ and all $l_q$ norms, including non-convex sub-$l_1$ pseudo-norms. Within one model we thus have access to (i) the evolution of the posterior for any $\lambda$ 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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