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.
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Funding
The work of Kun-Lin Kuo was supported in part by the Ministry of Science and Technology, Taiwan (MOST 107-2118-M-390-003 and MOST 108-2118-M-390-004-MY2).
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Kuo, KL., Wang, Y.J. Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks. Methodol Comput Appl Probab 25, 29 (2023). https://doi.org/10.1007/s11009-023-10016-3
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DOI: https://doi.org/10.1007/s11009-023-10016-3
Keywords
- Compatibility check
- Non-standard dependency network
- Ordered pseudo-Gibbs sampling
- Reducible Markov chain
- Stationary distribution
- Structure zero