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, 363377, July 2014.


         D. Chickering, D. Heckerman, and C. Meek, Large-Sample Learning of Bayesian Networks is NP-HardJournal 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 multinetsArtificial 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.