2 research outputs found
Mix-nets: Factored Mixtures of Gaussians in Bayesian Networks With Mixed Continuous And Discrete Variables
Recently developed techniques have made it possible to quickly learn accurate
probability density functions from data in low-dimensional continuous space. In
particular, mixtures of Gaussians can be fitted to data very quickly using an
accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999).
In this paper, we propose a kind of Bayesian networks in which low-dimensional
mixtures of Gaussians over different subsets of the domain's variables are
combined into a coherent joint probability model over the entire domain. The
network is also capable of modeling complex dependencies between discrete
variables and continuous variables without requiring discretization of the
continuous variables. We present efficient heuristic algorithms for
automatically learning these networks from data, and perform comparative
experiments illustrated how well these networks model real scientific data and
synthetic data. We also briefly discuss some possible improvements to the
networks, as well as possible applications.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
A Variational Approximation for Bayesian Networks with Discrete and Continuous Latent Variables
We show how to use a variational approximation to the logistic function to
perform approximate inference in Bayesian networks containing discrete nodes
with continuous parents. Essentially, we convert the logistic function to a
Gaussian, which facilitates exact inference, and then iteratively adjust the
variational parameters to improve the quality of the approximation. We
demonstrate experimentally that this approximation is faster and potentially
more accurate than sampling. We also introduce a simple new technique for
handling evidence, which allows us to handle arbitrary distributions on
observed nodes, as well as achieving a significant speedup in networks with
discrete variables of large cardinality.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in
Artificial Intelligence (UAI1999