Studies in Lower Bounding Probabilities of Evidence using the Markov Inequality
This work addresses a fundamental computational challenge in probabilistic inference, but it is incremental as it focuses on heuristic improvements to an existing approximation approach.
The paper tackles the NP-hard problem of computing the probability of evidence by proposing a randomized importance sampling scheme using the Markov inequality to provide high-confidence lower bounds, with empirical evaluation showing promise compared to state-of-the-art methods.
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.