Publications: Probability

· J. Kuipers, G. Moffa, and D. Heckerman. Addendum on the scoring of Gaussian directed acyclic graphical models. Annals of Statistics 42, 1689-1691, Aug 2014.

· D. Heckerman, C. Meek, and T. Richardson. Variations on undirected graphical models and their relationships. Kybernetika 50, 363–377, July 2014.

· D. Chickering, D. Heckerman, and C. Meek, Large-Sample Learning of Bayesian Networks is NP-Hard.  Journal of Machine Learning Research. 5: 1287-1330, 2004.

In comparison to Geiger and Heckerman, arXiv 1993, this paper starts with stronger preconditions (local distributions are binary-like lattice and binary-like totally strictly positive) and proves a stronger result (joint distribution is perfect with respect to the graph).

· D. Geiger and D. Heckerman. Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions. The Annals of Statistics, 30: 1412-1440, 2002.  UAI 1999 version (local copy).  Also appears as Technical Report MSR-TR-98-67, Microsoft Research, December, 1998 (Revised January, 2002).

A few errors regarding priors for Gaussian distributions are corrected in Kuipers et al., Annals of Statistics 2014.

· D. Geiger, D. Heckerman, H. King, C. Meek. Stratified Exponential Families: Graphical Models and Model Selection. The Annals of Statistics, 29:505-529, 2001. A preliminary version can be found in the Proceedings of Fifth Conference on Artificial Intelligence and Statistics, Ft. Lauderdale, FL. January 1999.  Microsoft copy.

· D. Geiger, D. Heckerman. A Characterization of the Dirichlet Distribution Through Global and Local Independence. The Annals of Statistics, 25:1344-1369, 1997.  Also appears as Technical Report MSR-TR-94-16, Microsoft Research, November, 1994 (revised February, 1994).

· D. Geiger and D. Heckerman.  Knowledge representation and inference in similarity networks and Bayesian multinets.  Artificial Intelligence, 82:45-74, 1996.

· D. Geiger and D. Heckerman. Dependence and Relevance: A probabilistic view. arXiv:1611.02126, Feb 1993.

In comparison to Chickering, Heckerman, and Meek, JMLR 2004, this paper starts with weaker preconditions (joint distribution is strictly positive binary) and proves a weaker result (total independence implies total disconnectedness).

· D. Heckerman.  Probabilistic Similarity Networks.  MIT Press, Cambridge, MA, 1991.  Review.

· D. Heckerman.  An axiomatic framework for belief updates.  In Proceedings of the Second Workshop on Uncertainty in Artificial Intelligence, Philadelphia, PA, pages 123-128. Association for Uncertainty in Artificial Intelligence, Mountain View, CA, August 1986.  Also in L. Kanal and J. Lemmer, editors, Uncertainty in Artificial Intelligence 2, pages 11-22. North-Holland, New York, 1988.  Local copy.

· D. Heckerman.  Probabilistic interpretations for MYCIN's certainty factors.  In Proceedings of the Workshop on Uncertainty and Probability in Artificial Intelligence, Los Angeles, CA, pages 9-20. Association for Uncertainty in Artificial Intelligence, Mountain View, CA, August 1985.  Also in L. Kanal. and J. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 167-196. North-Holland, New York, 1986.