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We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…

Quantum Physics · Physics 2020-08-19 Patrick Rall

We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume…

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows to sample high dimensional probability measures. It relies on the integration of the Hamiltonian dynamics to propose a move which is then accepted or rejected…

Numerical Analysis · Mathematics 2023-08-08 Tony Lelièvre , Régis Santet , Gabriel Stoltz

Single-site Markov Chain Monte Carlo (MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site…

We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…

Quantum Physics · Physics 2018-09-10 Patrick Rebentrost , Brajesh Gupt , Thomas R. Bromley

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Machine Learning · Statistics 2016-06-03 Jinghui Chen , Quanquan Gu

We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…

Cosmology and Nongalactic Astrophysics · Physics 2025-02-28 Denitsa Staicova

We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…

Methodology · Statistics 2015-05-05 Michalis K. Titsias , Christopher Yau

Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…

Algebraic Geometry · Mathematics 2019-02-21 Tianran Chen

A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo…

Machine Learning · Computer Science 2022-11-03 Carol Mak , Fabian Zaiser , Luke Ong

Volume is a natural geometric measure for comparing polyhedral relaxations of non-convex sets. Speakman and Lee gave volume formulae for comparing relaxations of trilinear monomials, quantifying the strength of various natural relaxations.…

Optimization and Control · Mathematics 2018-10-18 Emily Speakman , Han Yu , Jon Lee

Viewpoint estimation from 2D rendered images is helpful in understanding how users select viewpoints for volume visualization and guiding users to select better viewpoints based on previous visualizations. In this paper, we propose a…

Graphics · Computer Science 2019-02-04 Neng Shi , Yubo Tao

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Probability · Mathematics 2025-11-04 Andrea Bertazzi , Paul Dobson , Pierre Monmarché

We make an experimental comparison of methods for computing the numerical radius of an $n\times n$ complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a…

Numerical Analysis · Mathematics 2023-10-10 Tim Mitchell , Michael L. Overton

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

Computation · Statistics 2017-03-16 Alexandros Beskos , Ajay Jasra , Kody Law , Youssef Marzouk , Yan Zhou

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…

Statistical Mechanics · Physics 2024-05-17 Jarod Tall , Steven Tomsovic

State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…

Methodology · Statistics 2020-06-18 Thi Tuyet Trang Chau , Pierre Ailliot , Valérie Monbet

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…

Mathematical Physics · Physics 2015-06-05 Jean-Pierre Magnot

Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…

Machine Learning · Computer Science 2025-08-15 Dmitrii Dobrynin , Masoud Mohseni , John Paul Strachan

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Machine Learning · Computer Science 2018-03-14 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart