Estimating Dependency Structure as a Hidden Variable

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors.

[1]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[2]  Jeffrey W. Roberts,et al.  遺伝子の分子生物学 = Molecular biology of the gene , 1970 .

[3]  Donald B. Rubin,et al.  Max-imum Likelihood from Incomplete Data , 1972 .

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

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

[6]  Jude W. Shavlik,et al.  Training Knowledge-Based Neural Networks to Recognize Genes , 1990, NIPS.

[7]  Jude W. Shavlik,et al.  Interpretation of Artificial Neural Networks: Mapping Knowledge-Based Neural Networks into Rules , 1991, NIPS.

[8]  Dan Geiger,et al.  An Entropy-based Learning Algorithm of Bayesian Conditional Trees , 1992, UAI.

[9]  Hermann Ney,et al.  On structuring probabilistic dependences in stochastic language modelling , 1994, Comput. Speech Lang..

[10]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[11]  Brendan J. Frey,et al.  Does the Wake-sleep Algorithm Produce Good Density Estimators? , 1995, NIPS.

[12]  David Heckerman,et al.  Knowledge Representation and Inference in Similarity Networks and Bayesian Multinets , 1996, Artif. Intell..

[13]  Geoffrey E. Hinton,et al.  The delve manual , 1996 .

[14]  Nir Friedman,et al.  Building Classifiers Using Bayesian Networks , 1996, AAAI/IAAI, Vol. 2.