Approximating the inference probability Pr[X = x / E = e] in any sense, even for a single evidence node E, is NP-hard. This result holds for belief networks that are allowed to contain extreme conditional probabilities-that is, conditional probabilities arbitrarily close to 0. Nevertheless, all previous approximation algorithms have failed to approximate efficiently many inferences, even for belief networks without extreme conditional probabilities. We prove that we can approximate efficiently… CONTINUE READING