{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/conditional-matrix-flows-for-gaussian-1","title":"Conditional Matrix Flows for Gaussian Graphical Models","arxiv_id":"2306.07255","date":"2023-06-12","proceeding":"NeurIPS 2023 11","authors":["Marcello Massimo Negri","F. Arend Torres","Volker Roth"],"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.","url_abs":"https://arxiv.org/abs/2306.07255v2","url_pdf":"https://arxiv.org/pdf/2306.07255v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"conditional-matrix-flows-for-gaussian-1","repo_url":"https://github.com/fabricioarendtorres/flowconductor","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"conditional-matrix-flows-for-gaussian-1","repo_url":"https://github.com/marcello-negri/cmf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[{"method_slug":"variational-inference","method_name":"Variational Inference"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2306.07255","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.07255"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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