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# Markov Random Fields

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  1. arXiv

    Skewed and heavy-tailed data can now pick an undirected graph: Student copula gives a zero-partial-correlation necessary condition

    Student copula Markov networks express the pairwise Markov property as a necessary condition of zero partial correlation and pair it with a penalized ECM graph-selection algorithm, letting undirected graphical models be fitted to skewed or heavy-tailed data.

    University of the Witwatersrand
    Salha Mamane（First author）
    Student Copula Markov NetworksExpectation-Conditional Maximization AlgorithmMarkov Random Fields
  2. arXiv

    Discrete diffusion for categorical MRFs: a pinning decomposition and weight-sharing score learner yield end-to-end sample complexity bounds

    For categorical distributions with local dependence modeled by low-order Markov random fields, the work introduces a pinning decomposition of the discrete score, builds a weight-sharing neural score learner combined with tau-leaping into an end-to-end sampling procedure, derives optimal sampling guarantees from finite data with explicit dependence on vocabulary size, MRF interaction order, and sample size, and reports numerical experiments on Potts, Ising, and tree-structured models where weight-sharing score networks outperform fully connected ones for sampling long sequences.

    University of Chicago
    Shivam Kumar（First author）
    Discrete DiffusionSample Complexity BoundsPinning DecompositionWeight-Sharing Neural Score LearnerMarkov Random Fields

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