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Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks

Author

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  • Kun-Lin Kuo

    (National University of Kaohsiung)

  • Yuchung J. Wang

    (Rutgers University)

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.

Suggested Citation

  • Kun-Lin Kuo & Yuchung J. Wang, 2023. "Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10016-3
    DOI: 10.1007/s11009-023-10016-3
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    References listed on IDEAS

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    1. Kuo, Kun-Lin & Song, Chwan-Chin & Jiang, Thomas J., 2017. "Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 115-123.
    2. Ip, Edward H. & Wang, Yuchung J., 2009. "Canonical representation of conditionally specified multivariate discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1282-1290, July.
    3. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2002. "Exact and near compatibility of discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 231-252, August.
    4. Wang, Yuchung J. & Kuo, Kun-Lin, 2010. "Compatibility of discrete conditional distributions with structural zeros," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 191-199, January.
    5. Kun-Lin Kuo & Yuchung J. Wang, 2019. "Pseudo-Gibbs sampler for discrete conditional distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 93-105, February.
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