  The paper analyzes theoretically and empirically the performance of
likelihood weighting (LW) on a subset of nodes in Bayesian networks. The
proposed scheme requires fewer samples to converge due to reduction in sampling
variance. The method exploits the structure of the network to bound the
complexity of exact inference used to compute sampling distributions, similar
to Gibbs cutset sampling. Yet, the extension of the previosly proposed cutset
sampling principles to likelihood weighting is non-trivial due to differences
in the sampling processes of Gibbs sampler and LW. We demonstrate empirically
that likelihood weighting on a cutset (LWLC) is effective time-wise and has a
lower rejection rate than LW when applied to networks with many deterministic
probabilities. Finally, we show that the performance of likelihood weighting on
a cutset can be improved further by caching computed sampling distributions
and, consequently, learning 'zeros' of the target distribution.
