Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood

• URL: http://arxiv.org/abs/2103.15540v1
• Date: Mon, 29 Mar 2021 12:13:15 GMT
• Title: Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood
• Authors: Johan Pensar and Henrik Nyman and Jukka Corander
• Abstract summary: We introduce the marginal pseudo-likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator.
• Score: 5.364120183147694
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov networks have been proposed. Here we consider the class of contextual Markov networks which takes into account possible context-specific independences among pairs of variables. Structure learning of contextual Markov networks is very challenging due to the extremely large number of possible structures. One of the main challenges has been to design a score, by which a structure can be assessed in terms of model fit related to complexity, without assuming chordality. Here we introduce the marginal pseudo-likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator. Experiments demonstrate the favorable properties of our method in terms of predictive accuracy of the inferred models.

Related papers

• Attention with Markov: A Framework for Principled Analysis of Transformers via Markov Chains [48.146073732531605]
  We study the sequential modeling capabilities of transformers through the lens of Markov chains. Inspired by the Markovianity of natural languages, we model the data as a Markovian source. We show the existence of global minima and bad local minima contingent upon the specific data characteristics and the transformer architecture.
  arXiv  Detail & Related papers  (2024-02-06T17:18:59Z)
• Cyclic Directed Probabilistic Graphical Model: A Proposal Based on Structured Outcomes [0.0]
  We describe a probabilistic graphical model - probabilistic relation network - that allows the direct capture of directional cyclic dependencies. This model does not violate the probability axioms, and it supports learning from observed data. Notably, it supports probabilistic inference, making it a prospective tool in data analysis and in expert and design-making applications.
  arXiv  Detail & Related papers  (2023-10-25T10:19:03Z)
• Flow Factorized Representation Learning [109.51947536586677]
  We introduce a generative model which specifies a distinct set of latent probability paths that define different input transformations. We show that our model achieves higher likelihoods on standard representation learning benchmarks while simultaneously being closer to approximately equivariant models.
  arXiv  Detail & Related papers  (2023-09-22T20:15:37Z)
• Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov Networks [11.77890309304632]
  A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. In this work, we characterize the conditional independence structure in general distributions for all data types. We also allow general functional relations among variables, thus giving rise to a Markov network structure learning algorithm.
  arXiv  Detail & Related papers  (2023-05-19T01:53:10Z)
• Equivariant Transduction through Invariant Alignment [71.45263447328374]
  We introduce a novel group-equivariant architecture that incorporates a group-in hard alignment mechanism. We find that our network's structure allows it to develop stronger equivariant properties than existing group-equivariant approaches. We additionally find that it outperforms previous group-equivariant networks empirically on the SCAN task.
  arXiv  Detail & Related papers  (2022-09-22T11:19:45Z)
• Bayesian Structure Learning with Generative Flow Networks [85.84396514570373]
  In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) from data. Recently, a class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling. We show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs.
  arXiv  Detail & Related papers  (2022-02-28T15:53:10Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Structural Causal Models Are (Solvable by) Credal Networks [70.45873402967297]
  Causal inferences can be obtained by standard algorithms for the updating of credal nets. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks. Experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
  arXiv  Detail & Related papers  (2020-08-02T11:19:36Z)
• Tractably Modelling Dependence in Networks Beyond Exchangeability [0.0]
  We study the estimation, clustering and degree behavior of the network in our setting. This explores why and under which general conditions non-exchangeable network data can be described by a block model.
  arXiv  Detail & Related papers  (2020-07-28T17:13:59Z)
• Consistency of Spectral Clustering on Hierarchical Stochastic Block Models [5.983753938303726]
  We study the hierarchy of communities in real-world networks under a generic block model. We prove the strong consistency of this method under a wide range of model parameters. Unlike most of existing work, our theory covers multiscale networks where the connection probabilities may differ by orders of magnitude.
  arXiv  Detail & Related papers  (2020-04-30T01:08:59Z)
• Struct-MMSB: Mixed Membership Stochastic Blockmodels with Interpretable Structured Priors [13.712395104755783]
  Mixed membership blockmodel (MMSB) is a popular framework for community detection and network generation. We present a flexible MMSB model, textitStruct-MMSB, that uses a recently developed statistical relational learning model, hinge-loss Markov random fields (HL-MRFs) Our model is capable of learning latent characteristics in real-world networks via meaningful latent variables encoded as a complex combination of observed features and membership distributions.
  arXiv  Detail & Related papers  (2020-02-21T19:32:32Z)

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.