Evolving dynamic Bayesian networks with Multi-objective genetic algorithms

Abstract

A dynamic Bayesian network (DBN) is a probabilistic network that models interdependent entities that change over time. Given example sequences of multivariate data, we use a genetic algorithm to synthesize a network structure that models the causal relationships that explain the sequence. We use a multi-objective evaluation strategy with a genetic algorithm. The multi-objective criteria are a network's probabilistic score and structural complexity score. Our use of Pareto ranking is ideal for this application, because it naturally balances the effect of the likelihood and structural simplicity terms used in the BIC network evaluation heuristic. We use a basic structural scoring formula, which tries to keep the number of links in the network approximately equivalent to the number of variables. We also use a simple representation that favors sparsely connected networks similar in structure to those modeling biological phenomenon. Our experiments show promising results when evolving networks ranging from 10 to 30 variables, using a maximal connectivity of between 3 and 4 parents per node. The results from the multi-objective GA were superior to those obtained with a single objective GA.

A Matrix-Based Genetic Algorithm for Structure Learning of Bayesian Networks

“…Each element is defined as 1 if a variable is a parent of a variable , 0 otherwise. Unlike the previous works [12,13,15,18,19], our matrix does not go through the process of the sequence-based manipulation for a chromosome representation.…”

“…To show the effectiveness of the proposed method, we compared the performance of the proposed method with the method of Larranaga et al [12] and the method of Ross et al [15] based on 10 repeated experiments. Three wellknown data sets are employed.…”

“…Additionally they extended a GA method to search for better variable ordering [13]. Ross et al presented a dynamic BN structure learning method to optimize the multiple objectives through a GA [15].…”

Cooperative Coevolution for Agrifood Process Modeling

“…Various strategies were used, based on evolutionary programming [3], immune algorithms [34], multi-objective strategies [58], lamarkian evolution [64] or hybrid evolution [67].…”

A learning method for dynamic Bayesian network structures using a multi-objective particle swarm optimizer

“…We evaluate both the likelihood and complexity of the DBN structures obtained, and compare these with the conventional learning method based on a MOGA. 3 In numerical simulations, the proposed method found more effective DBN structures and obtained them faster than the conventional method. Generally, there exist trade-off relations between the likelihood and complexity…”