Random Generation of Bayesian Networks
نویسندگان
چکیده
This paper presents new methods for generation of random Bayesian networks. Such methods can be used to test inference and learning algorithms for Bayesian networks, and to obtain insights on average properties of such networks. Any method that generates Bayesian networks must first generate directed acyclic graphs (the “structure” of the network) and then, for the generated graph, conditional probability distributions. No algorithm in the literature currently offers guarantees concerning the distribution of generated Bayesian networks. Using tools from the theory of Markov chains, we propose algorithms that can generate uniformly distributed samples of directed acyclic graphs. We introduce methods for the uniform generation of multi-connected and singly-connected networks for a given number of nodes; constraints on node degree and number of arcs can be easily imposed. After a directed acyclic graph is uniformly generated, the conditional distributions are produced by sampling Dirichlet distributions.
منابع مشابه
An Introduction to Inference and Learning in Bayesian Networks
Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure...
متن کاملBayesian Belief Network Simulation
A Bayesain belief network is a graphical representation of the underlying probabilistic relationships of a complex system. These networks are used for reasoning with uncertainty, such as in decision support systems. This requires probabilistic inference with Bayesian belief networks. Simulation schemes for probabilistic inference with Bayesian belief networks offer many advantages over exact in...
متن کاملTesting MCMC algorithms with randomly generated Bayesian networks
In this work we show how to generate random Bayesian networks and how to test inference algorithms using these samples. First, we present a new method to generate random networks through Markov chains. We then use random networks to investigate the performance of quasi-random numbers in Gibbs sampling algorithms for inference. We present experimental results and describe code that implements ou...
متن کاملGeneration of Random Bayesian Networks with Constraints on Induced Width, with Application to the Average Analysis of d-Connectivity, Quasi-random Sampling, and Loopy Propagation
We present algorithms for the generation of uniformly distributed Bayesian networks with constraints on induced width. The algorithms use ergodic Markov chains to generate samples, building upon previous algorithms by the authors. The introduction of constraints on induced width leads to more realistic results but requires new techniques. We discuss three applications of randomly generated netw...
متن کاملControlled generation of hard and easy Bayesian networks: Impact on maximal clique size in tree clustering
This article presents and analyzes algorithms that systematically generate random Bayesian networks of varying difficulty levels, with respect to inference using tree clustering. The results are relevant to research on efficient Bayesian network inference, such as computing a most probable explanation or belief updating, since they allow controlled experimentation to determine the impact of imp...
متن کامل