A Comparison on the Effectiveness of Two Heuristics for Importance Sampling
Changhe Yuan, Marek J. Drużdżel · 2004
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 ɛ-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, ɛ-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 ɛ-cutoff. 1