A Characterization of Single-Link Search in Learning Belief Networks

One alternative to manual acquisition of belief networks from domain experts is automatic learning of these networks from data. Common algorithms for learning belief networks employ a single-link lookahead search. It is unclear, however, what types of domain models are learnable by such algorithms and what types of models will escape. We conjecture that these learning algorithms that use a single-link search are specializations of a simple algorithm which we call LIM. We put forward arguments that support such a conjecture, and then provide an axiomatic characterization of models learnable by LIM. The characterization coupled with the conjecture identifies models that are definitely learnable and definitely unlearnable by a class of learning algorithms. It also identifies models that are highly likely to escape these algorithms. Research to formally prove the conjecture is ongoing.

[1]  Yang Xiang,et al.  Learning Belief Networks in Domains with Recursively Embedded Pseudo Independent Submodels , 1997, UAI.

[2]  David Poole,et al.  MULTIPLY SECTIONED BAYESIAN NETWORKS AND JUNCTION FORESTS FOR LARGE KNOWLEDGE‐BASED SYSTEMS , 1993, Comput. Intell..

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

[4]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[5]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .

[6]  Gregory F. Cooper,et al.  An Entropy-driven System for Construction of Probabilistic Expert Systems from Databases , 1990, UAI.

[7]  Judea Pearl,et al.  The recovery of causal poly-trees from statistical data , 1987, Int. J. Approx. Reason..

[8]  Gregory F. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 1992 .

[9]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[10]  Yang Xiang,et al.  A “Microscopic” Study of Minimum Entropy Search in Learning Decomposable Markov Networks , 2004, Machine Learning.

[11]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .

[12]  Yang Xiang,et al.  Towards Understanding of Pseudo-independent Domains , 1997 .

[13]  Wai Lam,et al.  LEARNING BAYESIAN BELIEF NETWORKS: AN APPROACH BASED ON THE MDL PRINCIPLE , 1994, Comput. Intell..

[14]  Yang Xiang,et al.  CONSTRUCTION OF A MARKOV NETWORK FROM DATA FOR PROBABILISTIC INFERENCE , 1994 .