Black-box Importance Sampling
نویسندگان
چکیده
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 allows us to use better and richer proposals to solve difficult problems, and (somewhat counter-intuitively) also has the additional benefit of improving the estimation accuracy beyond typical importance sampling. Both theoretical and empirical analyses are provided.
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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′)] ...
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