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About 10,000 papers for “Importance sampling”
Supersampling Multisampling, Expected Value, Mit Eecs · 2012
• Prove its convergence speed – Error: notion of variance • For all this, we need to study what happens to expected value and variance when we had tons of random samples • Apply to ray tracing Today’s lecture • Expected value and variance
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Saul I. Gass, Michael C. Fu · 2013
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Tomáš Hovorka · Digital Repository (National Repository of Grey Literature) · 2008
In the present work we study the important sampling method. This method serves as a variance reduction technique for the Monte Carlo simulations. The basic theoretical properties of important sampling estimators are shown. A number of methods how to choose an alternative density is presented and compared on many examples. Among others: translation and scaling of original density, dominating point method, random translation over the surface of d-dimensional sphere method and method combining translation and scaling of original density. In the conclusion we attempted to set up some rules for choosing an appropriate method in dependence on the form of the problem to be solved.
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Jordan Frank, Shie Mannor, Doina Precup · 2008
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Masashi Sugiyama, Taiji Suzuki, Takafumi Kanamori · Cambridge University Press eBooks · 2012
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Josef Leydold, Wolfgang Hörmann A, Josef Leydold A · 2015
ePubWU, the institutional repository of the WU Vienna University of Economics and Business, is provided by the University Library and the IT-Services. The aim is to enable open access to the scholarly output of the WU.
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Thomas Müller, Brian McWilliams, Fabrice Rousselle et al. · arXiv (Cornell University) · 2018
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial coupling transforms that greatly increase the modeling power of individual coupling layers. Second, we propose to preprocess the inputs of neural networks using one-blob encoding, which stimulates localization of computation and improves inference. Third, we derive a gradient-descent-based optimization for the KL and the $\chi^2$ divergence for the specific application of Monte Carlo integration with unnormalized stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independently of the dimensionality of the integration domain. We show its benefits on generating natural images and in two applications to light-transport simulation: first, we demonstrate learning of joint path-sampling densities in the primary sample space and importance sampling of multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the product of incident illumination and the BSDF in the rendering equation, and we leverage the densities for path guiding. In all applications, our approach yields on-par or higher performance than competing techniques at equal sample count.
Cited by 13Open access
Finnegan Southey, Dale Schuurmans, Ali Ghodsi · 1999
Abstract Greedy importance sampling is an unbiased estimation technique that re-duces the variance of standard importance sampling by explicitly searching for modes in the estimation objective. Previous work has demon-strated the feasibility of implementing this method and proved that the technique is unbiased in both discrete and continuous domains. In thispaper we present a reformulation of greedy importance sampling that eliminates the free parameters from the original estimator, and introducesa new regularization strategy that further reduces variance without compromising unbiasedness. The resulting estimator is shown to be effectivefor difficult estimation problems arising in Markov random field inference. In particular, improvements are achieved over standard MCMCestimators when the distribution has multiple peaked modes. 1 Introduction Many inference problems in graphical models can be cast as determining the expectedvalue of a random variable of interest, f, given observations drawn according to a tar-get distribution P. That is, we are interested in computing EP (x)f (x). Unfortunately, innatural situations
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Benjamin Virrion · arXiv (Cornell University) · 2020
We present a generic path-dependent importance sampling algorithm where the Girsanov induced change of probability on the path space is represented by a sequence of neural networks taking the past of the trajectory as an input. At each learning step, the neural networks' parameters are trained so as to reduce the variance of the Monte Carlo estimator induced by this change of measure. This allows for a generic path dependent change of measure which can be used to reduce the variance of any path-dependent financial payoff. We show in our numerical experiments that for payoffs consisting of either a call, an asymmetric combination of calls and puts, a symmetric combination of calls and puts, a multi coupon autocall or a single coupon autocall, we are able to reduce the variance of the Monte Carlo estimators by factors between 2 and 9. The numerical experiments also show that the method is very robust to changes in the parameter values, which means that in practice, the training can be done offline and only updated on a weekly basis.
Cited by 0Open access
Ping Zhang · Journal of the American Statistical Association · 1996
Abstract Importance sampling is a widely used variance reduction simulation technique for the evaluation of high-dimensional integrals. A key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated. Parametric sampling distributions, if available at all, are often inadequate for high-dimensional integrals over irregular regions. One possible remedy is to use a nonparametric method to estimate the unknown optimal sampling function. We show that the nonparametric approach yields integral estimates that converge faster than estimates obtained from parametric approaches. We also demonstrate that an adaptive method, which has been used successfully in parametric settings, does not yield better results than simple one-step methods in the nonparametric setting.
Cited by 108
Michael L. Evans, Tim B. Swartz · 2000
Abstract We use the term independent importance sampling to refer to what might be considered the most straightforward Monte Carlo integration technique; namely generating independent values x1, ... , Xn from a density w and then taking a weighted average of the integrand evaluated at the sampled points with the weights given by the reciprocal of w evaluated at the sample values.
Cited by 0Open access
Thomas Müller, Brian McWilliams, Fabrice Rousselle et al. · ACM Transactions on Graphics · 2019
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial coupling transforms that greatly increase the modeling power of individual coupling layers. Second, we propose to preprocess the inputs of neural networks using one-blob encoding, which stimulates localization of computation and improves inference. Third, we derive a gradient-descent-based optimization for the Kullback-Leibler and the χ 2 divergence for the specific application of Monte Carlo integration with unnormalized stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independently of the dimensionality of the integration domain. We show its benefits on generating natural images and in two applications to light-transport simulation: first, we demonstrate learning of joint path-sampling densities in the primary sample space and importance sampling of multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the product of incident illumination and the BSDF in the rendering equation, and we leverage the densities for path guiding. In all applications, our approach yields on-par or higher performance than competing techniques at equal sample count.
Cited by 12Open access
Ingmar Schuster · arXiv (Cornell University) · 2015
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case ergodicity can only be guaranteed if adaptation is diminished at a certain rate. Importance Sampling approaches offer a way to circumvent this limitation and design sampling algorithms that keep adapting. Here I present a gradient informed variant of SMC (and its special case Population Monte Carlo) for static problems.
Cited by 13Open access
Benjamin Peherstorfer, Tiangang Cui, Youssef Marzouk et al. · Computer Methods in Applied Mechanics and Engineering · 2015
Cited by 137Open access
Jyotishka Datta, Nicholas G. Polson · Brazilian Journal of Probability and Statistics · 2025
In Bayesian inference, the approximation of integrals of the form ψ=EFl(X)=∫χl(x)dF(x) is a fundamental challenge. Such integrals are crucial for evidence estimation, which is important for various purposes, including model selection and numerical analysis. The existing strategies for evidence estimation are classified into four categories: deterministic approximation, density estimation, importance sampling and vertical representation (SIAM Review 65 (2023) 3–58). In this paper, we show that the Riemann sum estimator due to (SIAM Journal on Numerical Analysis 15 (1978) 1289–1300) can be used in the context of nested sampling (Bayesian Analysis 1 (2006) 833–859) to achieve a O(n−4) rate of convergence, faster than the usual ergodic central limit theorem, under certain regularity conditions. We provide a brief overview of the literature on the Riemann sum estimators and the nested sampling algorithm and its connections to vertical likelihood Monte Carlo. We provide theoretical and numerical arguments to show how merging these two ideas may result in improved and more robust estimators for evidence estimation, especially in higher-dimensional spaces. We also briefly discuss the idea of simulating the Lorenz curve that avoids the problem of intractable Λ functions, essential for the vertical representation and nested sampling.
Cited by 0Open access
Nayden Dimitrov Kambouchev, David Darmofal, Nayden Dimitrov Kambouchev · 2004
The probability of instability is computed via a new approach based on Impor-tance Sampling and a dynamic compression system model. In contrast to ordinary Monte Carlo methods Importance Sampling offers reduced confidence intervals, re-duced number of samples and reduced model execution times. The new approach avoids some of the problematic details associated with the traditional stability mar-gin methodology including the additivity, linearity and normality assumptions. It also captures successfully the phase interaction effects between inlet distortion and sta-tionary asymmetric tip clearance. The phase interaction is an example of a case when the stability margin approach fails to capture both the quantitative and qualitative
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Kevin Lopez (14551892), Huan Li (120482), Hyung Paek (14551895) et al. · Figshare · 2023
<p>Permutation importance sampling was performed to test the global significance of each feature in model predictions. Four features showed statistical significance with p < 0.05: Tenure, Exponential Weighted panel complexity, Exponential weighted teamwork on inbox, and rolling slope of the panel count.</p> <p>(DOCX)</p>
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Daniel Sanz-Alonso, Andrew M. Stuart, Armeen Taeb · Cambridge University Press eBooks · 2023
In this chapter we introduce Monte Carlo sampling and importance sampling. These are two general techniques for estimating expectations with respect to a given pdf π. Monte Carlo generates independent samples from π and combines them with equal weights, whilst importance sampling uses independent samples, weighted appropriately, from a different distribution. In quantifying the error in Monte Carlo and importance sampling, we will use a distance on random probability measures that reduces to total variation in the case of deterministic probability measures; and we will introduce the χ2 divergence.
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Markov Chain Monte Carlo Methods · 2013
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Gareth E, Jonathan M, G. Yu. Sofronov et al. · 2014
The genomes of complex organisms, including the human genome, are highly structured. This structure takes the form of segmental patterns of variation in various properties, and may be caused by the division of genomes into regions of distinct function, by the contingent evolutionary processes that gave rise to genomes, or by a combination of both. Whatever the cause, identifying the change-points between segments is potentially important, as a means of discovering the functional components of a genome, understanding the evolutionary processes involved, and fully describing genomic architecture. One property of genomes that is known to display a segmental pattern of variation is GC content. Genomes are composed of DNA: a long, doublestranded, linear polymer built up from four nucleotide bases, namely adenine, cytosine, guanine, and thymine (A, C, G, and T). The two strands of a DNA molecule form a double-helix, held together by hydrogen bonds formed between G and C nucleotide pairs, and between A and T nucleotide pairs, as illustrated in Figure 1. The two strands are thus complementary; the sequence of either strand can be deduced from that of the other by interconverting G with C, and A with T. Figure 1. The DNA structure. Source:
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