Sampling Algorithms
Yves Śampling · Springer series in statistics · 2006
Cited by 10
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About 10,000 papers for “sampling algorithms”
Yves Śampling · Springer series in statistics · 2006
Cited by 10
Yves Tillé · International Encyclopedia of Statistical Science · 2025
Cited by 0
Ayori Mitsutake, Y. Mori, Yuko Okamoto · Methods in molecular biology · 2012
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.
Cited by 67
Howie Choset, Kevin Lynch, Seth Hutchinson et al. · 2005
This chapter contains sections titled: Probabilistic Roadmaps, Single-Query Sampling-Based Planners, Integration of Planners: Sampling-Based Roadmap of Trees, Analysis of PRM, Beyond Basic Path Planning, Problems
Cited by 3
Michael L. Evans, Tim B. Swartz · 2000
Abstract Monte Carlo methods are an essential part of any practitioner’s toolkit when considering the approximation of integrals. Typically this will require the ability to generate from a wide variety of probability distributions. In fact, a major constraint on the implementation of Monte Carlo methods can be the lack of a suitable algorithm for generation in a given context.
Cited by 0
2010
Cited by 0
Ayori Mitsutake, Y. Mori, Yuko Okamoto · arXiv (Cornell University) · 2010
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.
Cited by 0Open access
Wilmer Prentius, Authors of the dependent Rust crates · 2025
Fast tools for unequal probability sampling in multi-dimensional spaces, implemented in Rust for high performance. The package offers a wide range of methods, including Sampford (Sampford, 1967, <<a href="https://doi.org/10.1093%2Fbiomet%2F54.3-4.499" target="_top">doi:10.1093/biomet/54.3-4.499</a>>) and correlated Poisson sampling (Bondesson and Thorburn, 2008, <<a href="https://doi.org/10.1111%2Fj.1467-9469.2008.00596.x" target="_top">doi:10.1111/j.1467-9469.2008.00596.x</a>>), pivotal sampling (Deville and Tillé, 1998, <<a href="https://doi.org/10.1093%2Fbiomet%2F91.4.893" target="_top">doi:10.1093/biomet/91.4.893</a>>), and balanced sampling such as the cube method (Deville and Tillé, 2004, <<a href="https://doi.org/10.1093%2Fbiomet%2F91.4.893" target="_top">doi:10.1093/biomet/91.4.893</a>>) to ensure auxiliary totals are respected. Spatially balanced approaches, including the local pivotal method (Grafström et al., 2012, <<a href="https://doi.org/10.1111%2Fj.1541-0420.2011.01699.x" target="_top">doi:10.1111/j.1541-0420.2011.01699.x</a>>), spatially correlated Poisson sampling (Grafström, 2012, <<a href="https://doi.org/10.1016%2Fj.jspi.2011.07.003" target="_top">doi:10.1016/j.jspi.2011.07.003</a>>), and locally correlated Poisson sampling (Prentius, 2024, <<a href="https://doi.org/10.1002%2Fenv.2832" target="_top">doi:10.1002/env.2832</a>>), provide efficient designs when the target variable is linked to auxiliary information.
Cited by 0Open access
Mark Goldberg, David L. Hollinger · Discrete Applied Mathematics · 2001
Cited by 3
Vibhav Giridhar Gogate · 2009
Cited by 0
Götz Uebe · AStA Advances in Statistical Analysis · 2009
Cited by 0
Foto N. Afrati, Paraskevas V. Lekeas, Chen Li · 2008
Cited by 0
Dong Zhang · 2017
For distributions whose probability density functions are log-concave, the adaptive rejection sampling algorithm can be used to build envelope functions for sampling. For others, we can use the modified adaptive rejection sampling algorithm, the concave-convex adaptive rejection sampling algorithm and the adaptive slice sampling algorithm. So we designed an R package mainly including 4 functions: rARS(), rMARS(), rCCARS() and rASS(). These functions can realize sampling based on the algorithms above.
Cited by 0Open access
Cesa-Bianchi, N. · Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) · 2011
We study online algorithms for selective sampling that use regularized least squares (RLS) as base classifier.These algorithms typically perform well in practice, and some of them have formal guarantees on their mistake and query rates.We refine and extend these guarantees in various ways, proposing algorithmic variants that exhibit better empirical behavior while enjoying performance guarantees under much more general conditions.We also show a simple way of coupling a generic gradient-based classifier with a specific RLSbased selective sampler, obtaining hybrid algorithms with combined performance guarantees.
Cited by 0Open access
Yongqiang Lian, Dandan Song, Jizheng Di · 2011
In this paper, we give algorithms to calculate multivariate wavelet coefficients approximately by sampled values of functions. Then we provide two formulae respectively to calculate the outlines and details of functions. Last, as an example, we draw figures of outline and detail of a function. 2000 AMS Classification: 42A65
Cited by 0
Popa, Vladimir, Technische Universität München · 2024
Set-based reachability analysis is used extensively in fields such as robotics in the context of, e.g., motion planning and the formal verification of cyber-physical systems. In order to properly model such systems, various set representations have been used throughout the literature. For certain computational tasks, one needs to be able to sample random points within such set representations. This thesis will introduce two approaches, the Ball Walk Algorithm and the Billiard Walk Algorithm, which are both so-called Markov Chain Monte Carlo methods that allow one to generate random samples within a convex set. In addition, the distribution of these samples can be shown to converge to the uniform distribution. The set representation we will focus our efforts on are spectrahedral shadows, which can be seen as the solution sets of positive semi-definite constraints. As a possible application, this thesis will also present two probabilistic solutions to the containment problem for spectrahedral shadows, using uniform random sampling algorithms.
Cited by 0Open access
Martin Fleury, Adrian F. Clark · IEEE Transactions on Medical Imaging · 1997
This paper investigates the problem of providing suitable interpolation for scanline algorithms. These algorithms are of interest, as they are parallelizable. A structure for analyzing the problem is given. The theory in regard to resampling is developed in the context of a scanline algorithm for image rotation. The theory is compared to results arrived at in practice. Alternative interpolation schemes are discussed, including the use of a cubic Hermite interpolator. The paper points to theoretical limitations of scanline algorithms.
Cited by 3
Karlheinz Gröchenig · Mathematics of Computation · 1992
Cited by 155
Alexandr Andoni, Robert Krauthgamer, Krzysztof Onak · 2011
A technique introduced by Indyk and Woodruff (STOC 2005) has inspired several recent advances in data-stream algorithms. We show that a number of these results follow eas- ily from the application of a single probabilistic method called Precision Sampling. Using this method, we obtain simple data- stream algorithms that maintain a randomized sketch of an input vector x = (x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,...,x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ), which is useful for the following applications: 1) Estimating the F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> -moment of x, for k >; 2. 2) Estimating the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm of x, for p ϵ [1, 2], with small update time. 3) Estimating cascaded norms ℓp(ℓq) for all p,q >; 0. 4) ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sampling, where the goal is to produce an element i with probability (approximately) |x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> |/||x|| <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . It extends to similarly defined ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -sampling, for p ϵ [1, 2]. For all these applications the algorithm is essentially the same: scale the vector x entry-wise by a well-chosen random vector, and run a heavy-hitter estimation algorithm on the resulting vector. Our sketch is a linear function of x, thereby allowing general updates to the vector x. Precision Sampling itself addresses the problem of estimating a sum Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> from weak estimates of each real a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ϵ [0,1]. More precisely, the estimator first chooses a desired precision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ϵ (0,1] for each i ϵ [n], and then it receives an estimate of every a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> within additive u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> . Its goal is to provide a good approximation to Σa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> while keeping a tab on the "approximation cost" Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (1/u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> )- Here we refine previous work (Andoni, Krauthgamer, and Onak, FOCS 2010) which shows that as long as Σa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> = Ω(1), a good multiplicative approximation can be achieved using total precision of only O(n log n).
Cited by 89
Hyeong Soo Chang, Jiaqiao Hu, Michael C. Fu et al. · Communications and control engineering/Communications and control engineering series · 2013
Cited by 2