A Comparison on the Effectiveness of Two Heuristics for Importance Sampling

Given a good importance function, importance sampling is able to achieve satisfactory precisions within a reasonable time. In addition to the well known requirement that the importance function should have a similar shape to the target density (Rubinstein, 1981), it is also highly recommended that the importance function possess heavy tails (Geweke, 1989; MacKay, 1998; Yuan and Druzdzel, 2004). To achieve this, the -cutoff heuristic (Cheng and Druzdzel, 2000; Yuan and Druzdzel, 2003) was used to cut off extremely small probabilities in the importance function (Yuan and Druzdzel, 2003). However, cutoff demonstrates inconsistent performance on different networks. In this paper, we analyze the underlying reasons and propose another heuristic, if-tempering, based on simulated tempering. We test the new heuristic on three large real Bayesian networks and observe that if-tempering consistently helps the EPIS-BN algorithm (Yuan and Druzdzel, 2003) achieve better precisions than -cutoff.