## Sampling-based Lower Bounds for Counting Queries

Citations: | 1 - 0 self |

### BibTeX

@MISC{Gogate_sampling-basedlower,

author = {Vibhav Gogate and Rina Dechter},

title = {Sampling-based Lower Bounds for Counting Queries},

year = {}

}

### OpenURL

### Abstract

Itiswellknownthatcomputingrelativeapproximationsofweightedcountingqueries such as the probability of evidence in a Bayesian network, the partition function of a Markov network, and the number of solutions of a constraint satisfaction problem is NP-hard. In this paper, we settle therefore on an easier problem of computing highconfidence lower bounds and propose an algorithm based on importance sampling and Markov inequality for it. However, a straight-forward application of Markov inequality often yields poor lower bounds because it uses only one sample. We therefore propose several new schemes that extend it to multiple samples. Empirically, we show that our new schemes are quite powerful, often yielding substantially higher (better) lower bounds than state-of-the-art schemes. 1