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Approximating discrete probability distributions with dependence trees
Abstract
A method is presented to approximate optimally ann-dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set ofn - 1first order dependence relationship among thenvariables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution.
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“In particular, the Chow-Liu algorithm (Chow & Liu, 1968) can efficiently learn tree graphs (i.e.G is the set of trees).”
From A Theory of Usable Information Under Computational Constraints (2020) · cites this paper as Chow & Liu, 1968
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“k-d forests [397], [398], Chow Liu trees [399], decision trees [400].”
BackgroundA Theory of Usable Information Under Computational Constraints
Xu, Y., Zhao, S., Song, J., Stewart, R., & Ermon, S. (2020) · arXiv · doi:10.48550/arxiv.2002.10689 · Cited by 142
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Metadata
- Authors
- Chow, C., & Liu, C.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1968-05
- Volume
- 14
- Issue
- 3
- Pages
- 462-467
- ISSN
- 0018-9448
- 1557-9654
- Cited by
- 1,720
- References
- 0
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