Stochastic Local Algorithms for Learning Belief Networks: Searching in the Space of the Orderings

Campos, Luis M. de; Puerta, José M.

doi:10.1007/3-540-44652-4_21

Cited by 20 publications

(13 citation statements)

References 15 publications

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“…Stochastic search methods such as Markov Chain Monte Carlo and simulated annealing have also been applied to find a high-scoring structure (Heckerman, 1998;de Campos & Puerta, 2001;Myers, Laskey, & Levitt, 1999). These methods explore the solution space using non-deterministic transitions between neighboring network structures while favoring better solutions.…”

Section: Local Search Strategiesmentioning

confidence: 99%

Learning Optimal Bayesian Networks: A Shortest Path Perspective

Yuan¹,

Malone²

2013

jair

146

125

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In this paper, learning a Bayesian network structure that optimizes a scoring function for a given dataset is viewed as a shortest path problem in an implicit state-space search graph. This perspective highlights the importance of two research issues: the development of search strategies for solving the shortest path problem, and the design of heuristic functions for guiding the search. This paper introduces several techniques for addressing the issues. One is an A* search algorithm that learns an optimal Bayesian network structure by only searching the most promising part of the solution space. The others are mainly two heuristic functions. The first heuristic function represents a simple relaxation of the acyclicity constraint of a Bayesian network. Although admissible and consistent, the heuristic may introduce too much relaxation and result in a loose bound. The second heuristic function reduces the amount of relaxation by avoiding directed cycles within some groups of variables. Empirical results show that these methods constitute a promising approach to learning optimal Bayesian network structures.

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Section: Local Search Strategiesmentioning

confidence: 99%

Learning Optimal Bayesian Networks: A Shortest Path Perspective

Yuan¹,

Malone²

2013

jair

146

125

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“…Other authors 22,26,33,34 have proposed to perform the search in the space of orders of the n variables of the problem. The motivation for the birth of this approach is that several structure learning algorithms need the n variables ordered.…”

mentioning

confidence: 99%

Learning Bayesian networks in the space of structures by estimation of distribution algorithms

Blanco¹,

Inza²,

Larrañaga³

2003

Int. J. Intell. Syst.

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The induction of the optimal Bayesian network structure is NP-hard, justifying the use of search heuristics. Two novel population-based stochastic search approaches, univariate marginal distribution algorithm (UMDA) and population-based incremental learning (PBIL), are used to learn a Bayesian network structure from a database of cases in a score ϩ search framework. A comparison with a genetic algorithm (GA) approach is performed using three different scores: penalized maximum likelihood, marginal likelihood, and information-theory-based entropy. Experimental results show the interesting capabilities of both novel approaches with respect to the score value and the number of generations needed to converge.

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“…The initial solution of the search process is the empty network in all the cases. Experiments with other two forms of initialization (the networks obtained by the algorithms K2SN [11] and PC [21]) were also carried out, obtaining results similar to the ones displayed for the empty network. The GRASP-BN algorithm has also been implemented using the two neighborhood structures (GRASP-BNc and GRASP-BNm).…”

Section: Resultsmentioning

confidence: 75%

Local Search Methods for Learning Bayesian Networks Using a Modified Neighborhood in the Space of DAGs

Campos

Fernández‐Luna

Puerta

2002

Advances in Artificial Intelligence — IBERAMIA 2002

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Abstract.The dominant approach for learning Bayesian networks from data is based on the use of a scoring metric, that evaluates the fitness of any given candidate network to the data, and a search procedure, that explores the space of possible solutions. The most efficient methods used in this context are (Iterated) Local Search algorithms. These methods use a predefined neighborhood structure that defines the feasible elementary modifications (local changes) that can be applied to a given solution in order to get another, potentially better solution. If the search space is the set of directed acyclic graphs (dags), the usual choices for local changes are arc addition, arc deletion and arc reversal. In this paper we propose a new definition of neighborhood in the dag space, which uses a modified operator for arc reversal. The motivation for this new operator is the observation that local search algorithms experience problems when some arcs are wrongly oriented. We exemplify the general usefulness of our proposal by means of a set of experiments with different metrics and different local search methods, including Hill-Climbing and Greedy Randomized Adaptive Search Procedure (GRASP), as well as using several domain problems.

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Stochastic Local Algorithms for Learning Belief Networks: Searching in the Space of the Orderings

Cited by 20 publications

References 15 publications

Learning Optimal Bayesian Networks: A Shortest Path Perspective

Learning Optimal Bayesian Networks: A Shortest Path Perspective

Learning Bayesian networks in the space of structures by estimation of distribution algorithms

Local Search Methods for Learning Bayesian Networks Using a Modified Neighborhood in the Space of DAGs

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