Measuring the Hardness of Stochastic Sampling on Bayesian Networks with Deterministic Causalities: the k-Test
Haohai Yu, Robert van Engelen
Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local Variance Bound (LVB) to measure the approximation hardness of Bayesian inference on Bayesian networks, assuming the networks model strictly positive joint probability distributions, i.e. zero probabilities are not permitted. This paper introduces the k-test to measure the approximation hardness of inference on Bayesian networks with deterministic causalities in the probability distribution, i.e. when zero conditional probabilities are permitted. Approximation by stochastic sampling is a widely-used inference method that is known to suffer from inefficiencies due to sample rejection. The k-test predicts when rejection rates of stochastic sampling a Bayesian network will be low, modest, high, or when sampling is intractable.
PDF Link: /papers/11/p786-yu.pdf
AUTHOR = "Haohai Yu
and Robert van Engelen",
TITLE = "Measuring the Hardness of Stochastic Sampling on Bayesian Networks with Deterministic Causalities: the k-Test",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "786--795"