Abstract

A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.

Citations

6236	Maximum likelihood from incomplete data via EM algorithm - Dempster, Laird, et al. - 1977
5662	Probabilistic reasoning in intelligent systems: networks of plausible inference - Pearl - 1988
2960	Artificial Intelligence: A Modern Approach. 2nd edn - Russell, Norvig - 2003
1583	Estimating the dimension of a model - Schwarz - 1978
1140	A new look at the statistical model identification - AKAIKE - 1974
1080	Local computations with probabilities on graphical structures and their application to expert systems (with discussion - Lauritzen, Spiegelhalter - 1988
886	Monte Carlo sampling methods using Markov chains and their applications. Biometrika - Hastings - 1970
876	A Bayesian method for the induction of probabilistic networks from data - Cooper, Herskovits - 1992
845	Graphical models - Lauritzen - 1996
786	Bayesian Theory - Bernardo, Smith - 1994
719	FV: An Introduction to Bayesian Networks - Jensen - 1996
718	Bayes factors - Kass, Raftery - 1995
711	A tutorial on learning with Bayesian networks - Heckerman - 1998
512	Optimal Statistical Decisions - DeGroot - 1970
512	Bayesian Learning for Neural Networks - Neal - 1994
510	Statistical Analysis of Finite Mixture Distributions - Titterington, Smith, et al. - 1985
448	Probabilistic inference using Markov chain Monte Carlo methods - Neal - 1993
383	Causation, prediction, and search - Spirtes, Glymour, et al. - 2000
357	Quasi-Experimentation: Design and Analysis Issues for Field Settings - Cook, Campbell - 1979
355	Probabilistic logic - Nilsson - 1986
345	Stochastic Simulation - Ripley - 1987
316	Gaussian influence diagrams - Shachter, Kenley - 1989
249	Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies - Rubin - 1974
247	A tutorial on learning Bayesian networks - Heckerman - 1995
213	Model selection and accounting for model uncertainty in graphical models using Occam’s window - Madigan, Raftery - 1994
212	Operations for learning with graphical models - Buntine - 1994
208	Learning Bayesian networks with local structure - Friedman, Goldszmidt - 1999
207	Identification of Causal Effects Using Instrumental Variables (with Discussion - Angrist, Imbens, et al. - 1996
197	Introduction to stochastic processes - Cinlar - 1975
197	Statistics and Causal Inference - Holland - 1986
178	The EM algorithm for graphical association models with missing data - Lauritzen - 1995
178	Equivalence and synthesis of causal models - Verma, Pearl - 1990
175	TS: A theory of inferred causation - Pearl, Verma
165	Bayesian graphical models for discrete data - Madigan, York - 1995
156	A guide to the literature on learning probabilistic networks from data - Buntine - 1996
154	Probabilistic independence networks for hidden markov probability models - Smyth - 1997
153	Theory refinement on bayesian networks - Buntine - 1991
147	Conditional independence in statistical theory - Dawid - 1979
132	Causal diagrams for empirical research - Pearl - 1994
131	Bayesian updating in recursive graphical models by local computations - Jensen, Lauritzen, et al. - 1989
128	Probabilistic similarity networks - Heckerman - 1990
122	Introduction to Graphical Modelling - Edwards - 1995
120	Mathematical Statistics - Wilks - 1943
114	An algebra of bayesian belief universes for knowledge based systems, Networks 20 - Jensen, Olesen, et al. - 1990
113	JM: A new approach to causal inference in mortality studies with sustained exposure periods – Application to control of the healthy worker survivor effect. Mathematical Modeling - Robins - 1986
110	Learning Equivalence Classes of Bayesian Network Structure - Chickering - 1996
102	Bayesian inference for causal effects: The role of randomization - Rubin - 1978
99	Hyper Markov laws in the statistical analysis of decomposable graphical models - Dawid, Lauritzen - 1993
72	M.: Building classifiers using bayesian networks. In - Friedman, Goldszmidt - 1996
69	Bayes factors and model uncertainty - Kass, Raftery - 1995