Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Learning hybrid Bayesian networks from data
Learning in graphical models
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Learning bayesian networks from Markov random fields: An efficient algorithm for linear models
ACM Transactions on Knowledge Discovery from Data (TKDD)
International Journal of Systems and Service-Oriented Engineering
Sub-local constraint-based learning of Bayesian networks using a joint dependence criterion
The Journal of Machine Learning Research
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In this paper we present a method of computing the posterior probability of conditional independence of two or more continuous variables from data, examined at several resolutions. Our approach is motivated by the observation that the appearance of continuous data varies widely at various resolutions, producing very different independence estimates between the variables involved. Therefore, it is difficult to ascertain independence without examining discretized data at several carefully selected resolutions. In our paper, we accomplish this using the exact computation of the posterior probability of independence, calculated analytically given a resolution. At each examined resolution and boundary placement, we assume a multinomial distribution with Dirichlet priors for the discretized table parameters, and compute the posterior using Bayesian integration. Across resolutions, we use a search procedure to approximate the Bayesian integral of probability over an exponential number of possible boundary placements. Our method generalizes to an arbitrary number variables in a straightforward manner. The test is suitable for Bayesian network learning algorithms that use independence tests to infer the network structure, in domains that contain any mix of continuous, ordinal discrete, and categorical variables.