Markov chain Monte Carlo for Structural Inference with Prior Information

This paper addresses the question of making inferences rega rdin features of conditional independence graphs in settings chara terized by the availability of rich prior information regarding such feat ures. We focus on Bayesian networks, and use Markov chain Monte Carlo to draw s mples from the relevant posterior over graphs. We introduce a clas s of “locallyinformative priors” which are highly flexible and capable of taking account of specific information regarding graph features, and are, i n addition, informative at a scale appropriate to local sampling moves. We pre sent examples of such priors for beliefs regarding edges, groups and class es of edges, degree distributions and sparsity, applying our methods to ch allenging synthetic data as well as data obtained from a biological network in can cer.

[1]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[2]  Wray L. Buntine.  Theory Refinement on Bayesian Networks , 1991, UAI.

[3]  Paolo Giudici,et al.  Improving Markov Chain Monte Carlo Model Search for Data Mining , 2004, Machine Learning.

[4]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

[5]  J. York,et al.  Bayesian Graphical Models for Discrete Data , 1995 .

[6]  Trey Ideker,et al.  Building with a scaffold: emerging strategies for high- to low-level cellular modeling. , 2003, Trends in biotechnology.

[7]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[8]  Petros Dellaportas,et al.  Model determination for categorical data with factor level merging , 2005 .

[9]  Michael A. West,et al.  Archival Version including Appendicies : Experiments in Stochastic Computation for High-Dimensional Graphical Models , 2005 .

[10]  H. Kitano.  Systems Biology: A Brief Overview , 2002, Science.

[11]  P. Dellaportas,et al.  Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models , 1999 .

[12]  Nir Friedman,et al.  Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks , 2004, Machine Learning.

[13]  Michael I. Jordan.  Graphical Models , 1998 .

[14]  C. Tarantola.  MCMC model determination for discrete graphical models , 2004 .

[15]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[16]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[17]  P. Green,et al.  Decomposable graphical Gaussian model determination , 1999 .

[18]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[19]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .