Critical Remarks on Single Link Search in Learning Belief Networks

TL;DR

This paper critically examines the limitations of single link lookahead search in learning belief networks, showing it can fail on certain models and suggesting multi-link search as a better alternative.

Contribution

It identifies specific probabilistic models where single link search fails and recommends more robust search strategies for accurate belief network learning.

Findings

Single link search can fail to learn certain models correctly.

Using multi-link lookahead improves learning accuracy.

Single link search may lead to inference errors in some domains.

Abstract

In learning belief networks, the single link lookahead search is widely adopted to reduce the search space. We show that there exists a class of probabilistic domain models which displays a special pattern of dependency. We analyze the behavior of several learning algorithms using different scoring metrics such as the entropy, conditional independence, minimal description length and Bayesian metrics. We demonstrate that single link lookahead search procedures (employed in these algorithms) cannot learn these models correctly. Thus, when the underlying domain model actually belongs to this class, the use of a single link search procedure will result in learning of an incorrect model. This may lead to inference errors when the model is used. Our analysis suggests that if the prior knowledge about a domain does not rule out the possible existence of these models, a multi-link lookahead search or other heuristics should be used for the learning process.