The DOI matches its Crossref record.
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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
Citations
Cites
No references could be resolved yet.
Cited by
Sorted by citations
Friedman, N., Geiger, D., & Goldszmidt, M. (1997) · Machine Learning · doi:10.1023/a:1007465528199 · Cited by 4,742
Margolin, A. A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Favera, R. D., & Califano, A. (2006) · BMC Bioinformatics · doi:10.1186/1471-2105-7-s1-s7 · Cited by 2,420
FAB-MAP: Probabilistic Localization and Mapping in the Space of Appearance
Cummins, M., & Newman, P. (2008) · The International Journal of Robotics Research · doi:10.1177/0278364908090961 · Cited by 1,472
Visual Place Recognition: A Survey
Lowry, S., Sünderhauf, N., Newman, P., Leonard, J. J., Cox, D., Corke, P., & Milford, M. J. (2016) · IEEE Transactions on Robotics · doi:10.1109/tro.2015.2496823 · Cited by 1,079
A model for reasoning about persistence and causation
Dean, T., & Kanazawa, K. (1989) · Computational Intelligence · doi:10.1111/j.1467-8640.1989.tb00324.x · Cited by 999
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Approximating discrete probability distributions with dependence trees. https://app.cochat.ai/papers/10.1109/tit.1968.1054142
- The paper
- Chow, C., & Liu, C. (1968). Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory. https://doi.org/10.1109/tit.1968.1054142
