Importance Sampling based Estimation over AND/OR Search Spaces for Graphical Mode

Vibhav Gogate and Rina Dechter

It is well known that the accuracy of importance sampling can be improved by reducing the variance of its sample mean and therefore variance reduction schemes have been the subject of much research. In this paper, we introduce a family of variance reduction schemes that generalize the sample mean from the conventional OR search space to the AND/OR search space for graphical models. The new sample means allow trading time and space with variance. At one end is the AND/OR sample tree mean which has the same time and space complexity as the conventional OR sample tree mean but has smaller variance. At the other end is the AND/OR sample graph mean which requires more time and space to compute but has the smallest variance. Theoretically, we show that the variance is smaller in the AND/OR space because the AND/OR sample mean is defined over a larger virtual sample size compared with the OR sample mean. Empirically, we demonstrate that the AND/OR sample mean is far closer to the true mean than the OR sample mean.