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Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in the literature to date, particularly considering that it includes many standard inference problems as special cases. In this paper, we propose two algorithms ...

In this paper we consider a stylized multidimensional rare-event simulation problem for a heavy-tailed process. More precisely, the problem of e¢ cient estimation via simulation of …rst passage time probabilities for a multidimensional random walk with t distributed increments. This problem is a natural generalization of ruin probabilities in insurance, in which the focus is a one dimensional r...

FALL 1999 This article develops a variance-reduction technique for pricing derivatives by simulation in highdimensional multifactor models. A premise of this work is that the greatest gains in simulation efficiency come from taking advantage of the structure of both the cash flows of a security and the model in which it is priced. For this to be feasible in practice requires automating the iden...

We present a new technique called Multiple Vertex Next Event Estimation, which outperforms current direct lighting techniques in forward scattering, optically dense media with the Henyey-Greenstein phase function. Instead of a one-segment connection from a vertex within the medium to the light source, an entire sub path of arbitrary length can be created and we show experimentally that 4-10 seg...

In this paper we propose a fast adaptive Importance Sampling method for the efficient simulation of buffer overffow probabilities in queueing networks. The method comprises three stages. First we estimate the minimum Cross-Entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer le...

which can be shown to be equivalent to MMDH(q, p) 2 = Ex,x′∼p[k(x, x′)]− 2Ex∼p;y∼q[k(x, y)] + Ey,y′∼q[k(y, y′)]. We show that kernelized discrepancy is equivalent to MMDHp(q, p), equipped with the p-Steinalized kernel kp(x, x ′). Proposition 1.1. Assume (3) is true, we have S(q, p) = MMDHp(q, p). Proof. Simply note that Ex′∼p[kp(x, x′)] = 0 for any x, we have MMDHp(q, p) 2 = Ex,x′∼q[kp(x, x′)] ...

We provide a comparative study of several widely used off-policy estimators (Empirical Average, Basic Importance Sampling and Normalized Importance Sampling), detailing the different regimes where they are individually suboptimal. We then exhibit properties optimal estimators should possess. In the case where examples have been gathered using multiple policies, we show that fused estimators dom...

Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying black-box importance sampling methods that calculate importance weights for samples generated from any unknown proposal or black-box mechanism. Our method all...

We present algorithms for Bayesian learning of decomposable models from data. Priors of a certain form admit exact averaging in O(3nn3) time and sampling T graphs from the posterior in O(4n + nT) time. To target a broader class of priors we associate each sample with an importance weight. Empirically, we compare averaging to optimization and demonstrate the accuracy of our importance sampling e...