Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach

• URL: http://arxiv.org/abs/2503.13899v1
• Date: Tue, 18 Mar 2025 04:53:22 GMT
• Title: Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach
• Authors: Sarah Liaw, Rebecca Morrison, Youssef Marzouk, Ricardo Baptista,
• Abstract summary: We propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property.<n>The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps.
• Score: 0.3749861135832072
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical model, which encodes these dependencies, by assuming that the variables follow a distribution with a simple parametric form. Moreover, the computational cost of many algorithms scales poorly for high-dimensional distributions, as they need to estimate all the edges in the graph simultaneously. In this work, we propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property. The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps to represent the conditional distribution for each variable. We show that L-SING includes existing approaches, such as neighborhood selection with Lasso, as a special case. We demonstrate the effectiveness of our algorithm in both Gaussian and non-Gaussian settings by comparing it to existing methods. Lastly, we show the scalability of the proposed approach by applying it to high-dimensional non-Gaussian examples, including a biological dataset with more than 150 variables.

Related papers

• Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data [2.6499018693213316]
  We introduce a novel generative model for the representation of joint probability distributions of discrete random variables.<n>The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions.
  arXiv  Detail & Related papers  (2024-06-06T21:58:33Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Delta-AI: Local objectives for amortized inference in sparse graphical models [64.5938437823851]
  We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs) Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. We illustrate $Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.
  arXiv  Detail & Related papers  (2023-10-03T20:37:03Z)
• A Heavy-Tailed Algebra for Probabilistic Programming [53.32246823168763]
  We propose a systematic approach for analyzing the tails of random variables. We show how this approach can be used during the static analysis (before drawing samples) pass of a probabilistic programming language compiler. Our empirical results confirm that inference algorithms that leverage our heavy-tailed algebra attain superior performance across a number of density modeling and variational inference tasks.
  arXiv  Detail & Related papers  (2023-06-15T16:37:36Z)
• Characteristic Function of the Tsallis $q$-Gaussian and Its Applications in Measurement and Metrology [0.0]
  The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution. This paper presents the characteristic function of a linear combination of independent $q$-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis.
  arXiv  Detail & Related papers  (2023-03-15T13:42:35Z)
• Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees [57.67528738886731]
  We study the numerical stability of scalable sparse approximations based on inducing points. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
  arXiv  Detail & Related papers  (2022-10-14T15:20:17Z)
• Wrapped Distributions on homogeneous Riemannian manifolds [58.720142291102135]
  Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions. We empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model.
  arXiv  Detail & Related papers  (2022-04-20T21:25:21Z)
• Learning non-Gaussian graphical models via Hessian scores and triangular transport [6.308539010172309]
  We propose an algorithm for learning the Markov structure of continuous and non-Gaussian distributions. Our algorithm SING estimates the density using a deterministic coupling, induced by a triangular transport map, and iteratively exploits sparse structure in the map to reveal sparsity in the graph.
  arXiv  Detail & Related papers  (2021-01-08T16:42:42Z)
• An Embedded Model Estimator for Non-Stationary Random Functions using Multiple Secondary Variables [0.0]
  This paper introduces the method and shows that it has consistency results that are similar in nature to those applying to geostatistical modelling and to Quantile Random Forests. The algorithm works by estimating a conditional distribution for the target variable at each target location.
  arXiv  Detail & Related papers  (2020-11-09T00:14:24Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Variational Filtering with Copula Models for SLAM [5.242618356321224]
  We show how it is possible to perform simultaneous localization and mapping (SLAM) with a larger class of distributions. We integrate the distribution model with copulas into a Sequential Monte Carlo estimator and show how unknown model parameters can be learned through gradient-based optimization.
  arXiv  Detail & Related papers  (2020-08-02T15:38:23Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.