Black-box Importance Sampling

By Qiang Liu, Jason D. Lee. 2016

78 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Black-box Off-policy Estimation for Infinite-Horizon Reinforcement Learning (2020, methodology): “Our black-box estimator is inspired by previous work for black-box importance sampling [20].”
Batch Stationary Distribution Estimation (2020, methodology): “A more relevant approach is Stein importance sampling (Liu and Lee, 2017), where the ratio is estimated by minimizing the kernelized Stein discrepancy (Liu et al., 2016).”
Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning (2016, methodology): “…there exist methods that use no explicit information of q ( x ) , which, seemingly counter-intuitively, give better asymptotic variance or converge rates than the typical IS that uses the proposal information (e.g., Liu & Lee, 2016; Briol et al., 2015; Henmi et al., 2007; Delyon & Portier, 2014).”
Measuring Sample Quality with Diffusions (2016, background): “While our chief motivation is sample quality measurement, our work is also directly applicable to a variety of inferential tasks that currently rely on the Langevin operator, including control variate design [66, 67], one sample hypothesis testing [? 57], variational inference [56], and importance s”
Action-depedent Control Variates for Policy Optimization via Stein's Identity (2017, unknown): “An incomplete list includes Gorham & Mackey (2015), Oates et al. (2017), Oates et al. (2016), Chwialkowski et al. (2016), Liu et al. (2016), Sedghi et al. (2016), Liu & Wang (2016), Feng et al. (2017), Liu & Lee (2017).”
Measuring Sample Quality with Kernels (2017, methodology): “Proposition 9 applies to common kernels like the Gaussian, Mat´ern, and IMQ kernels, and its proof in Section I provides an explicit upper bound on the KSD in terms of the Wasserstein distance (Liu et al., 2016, Thm. 4.1) ) rate under continuity and integrability assumptions on µ .”
Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences (2018, background): “For instance, Liu and Lee [2017] proposed to optimize the weights under a constraint that the weights be non-negative.”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “This analysis provides important insight into the strong performance that has been observed for these estimators in certain lowdimensional applications [23,35].”