Methods of Reducing Sample Size in Monte Carlo Computations

By H. Kahn, A. W. Marshall. 1953

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Citations in the corpus

Federated Visual Classification with Real-World Data Distribution (2020, methodology): “Importance sampling is a classic technique for variance reduction in Monte Carlo methods [12,9] and has been used widely in domain adaption literature for countering covariate and target shift [24,36,22].”
Learning to Reweight Examples for Robust Deep Learning (2018, methodology): “Importance sampling (Kahn & Marshall, 1953), a classical method in statistics, assigns weights to samples in order to match one distribution to another.”
Off-policy learning based on weighted importance sampling with linear computational complexity (2015, methodology): “A Monte Carlo technique known as importance sampling (Kahn & Marshall 1953, Rubinstein 1981) is often used to resolve this mismatch in policies (Sutton & Barto 1998, Dann, Neumann & Peters 2014, Geist & Scherrer 2014).”
Transfer Learning in Deep Reinforcement Learning: A Survey (2020, background): “Importance sampling is usually applied to the off-policy approaches in order to transform the expectation of returns from the behavior policy to the target policy [14], [15].”
Choosing the Sample with Lowest Loss makes SGD Robust (2020, background): “Weighted sampling is one of the popular variants of SGD that can be used for matching one distribution to another (importance sampling), improving the rate of convergence, variance reduction or all of them and has been considered in [16, 33, 38, 19].”
What is the Effect of Importance Weighting in Deep Learning? (2018, background): “…is a fundamental tool in statistics and machine learning often used when we want to estimate a quantity on some target distribution, but can only sample from a diﬀerent source distribution [Horvitz and Thompson, 1952, Kahn and Marshall, 1953, Rubinstein and Kroese, 2016, Koller et al., 2009].”
Generalized Multiple Importance Sampling (2015, background): “Furthermore, the variance of Î and Ĩ is directly related to the discrepancy between π̃(x)|g(x)| and q(x) [Robert and Casella, 2004; Kahn and Marshall, 1953].”
Efficient high-dimensional importance sampling (2007, background): “See Lerman and Manski (1981), McFadden (1989), Pakes and Pollard (1989) or Börsch-Supan and Hajivassiliou (1990).”
Hamiltonian Annealed Importance Sampling for partition function estimation (2012, background): “Importance sampling Kahn & Marshall (1953) allows an unbiased estimate Ẑp of the partition function (or normalization constant) Zp of a non-analytically-normalizable target distribution p (x) over x ∈ RM , p (x) = e−Ep(x) Zp (1) Zp = ∫ dx e−Ep(x), (2) to be calculated.”
Weighted importance sampling for off-policy learning with linear function approximation (2014, background): “Importance sampling (Kahn & Marshall 1953, Rubinstein 1981, Koller & Friedman 2009) is a wellknown Monte Carlo technique for estimating an expectation under one distribution given samples from a different distribution.”
Rethinking the Effective Sample Size (2018, methodology): “, Robert and Casella, 2004; Kahn and Marshall, 1953]. Third, other approximations can be derived from the simulated sample, including unbiased estimates of Eq[W 2H2] and E(2)q [WH], obtained at the same cost as the original estimates, as well as bootstrap versions. At last, we point out the most det”
Dice Loss for Data-imbalanced NLP Tasks (2019, background): “Importance sampling (Kahn and Marshall, 1953) assigns weights to different samples and changes the data distribution.”
Testing the assumptions behind importance sampling (2009, methodology): “Failure of this condition can lead to slow and unstable convergence of the estimator as the central limit theorem governing convergence fails to hold.”
On Ensuring that Intelligent Machines Are Well-Behaved (2017, methodology): “This decision will both simplify the use of importance sampling [Kahn and Marshall, 1953] by removing the product over time that usually appears when using importance sampling for reinforcement learning [Precup et al.”