Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks

Kun-Lin Kuo () and Yuchung J. Wang ()
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Kun-Lin Kuo: National University of Kaohsiung
Yuchung J. Wang: Rutgers University

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-17

Abstract: Abstract Dependency network (DN) aims at using a collection of conditional distributions to identify a joint pdf. When the DN is compatible (self-consistent), the Gibbs sampler (GS) has been the algorithm to approximate the joint pdf. Without compatibility, GS will have multiple stationary distributions, named pseudo-Gibbs distributions (PGD), associated with different updating orders. To increase the computational efficiency and stability, we propose computing the marginal distributions. Closed-form marginal transition matrix is unearthed from DN. Thus, it becomes possible to compute the marginal distribution of PGD, which will be paired with a conditional distribution to obtain a PGD. We also show that multiple PGDs can be derived from one PGD. When the support is a union of disjoint regions, GS could not converge because the stationary pdf is a mixture of several joint distributions. Examples here show that our approach can obtain correct PGDs even for partitioned support. A new way to verify compatibility, under such circumstances, will also be proposed.

Keywords: Compatibility check; Non-standard dependency network; Ordered pseudo-Gibbs sampling; Reducible Markov chain; Stationary distribution; Structure zero; 65C60; 68T05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10016-3

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