Studies in Lower Bounding Probabilities of Evidence using the Markov Inequality
Vibhav Gogate, Bozhena Bidyuk, Rina Dechter
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on probability of evidence but does not have any guarantees in terms of relative or absolute error. Our proposed approximation is a randomized importance sampling scheme that uses the Markov inequality. However, a straight-forward application of the Markov inequality may lead to poor lower bounds. We therefore propose several heuristic measures to improve its performance in practice. Empirical evaluation of our scheme with state-of- the-art lower bounding schemes reveals the promise of our approach.
PDF Link: /papers/07/p141-gogate.pdf
AUTHOR = "Vibhav Gogate
and Bozhena Bidyuk and Rina Dechter",
TITLE = "Studies in Lower Bounding Probabilities of Evidence using the Markov Inequality",
BOOKTITLE = "Proceedings of the Twenty-Third Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-07)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2007",
PAGES = "141--148"