Related papers: Quasi-Monte Carlo Feature Maps for Shift-Invariant…

Effective sample size is a standard summary of Markov chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinate-wise…

We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo…

In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of…

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Recently, iterative Quasi-Monte Carlo (iQMC) was introduced as a new method of neutron transport which combines deterministic iterative methods and quasi-Monte Carlo simulation for more efficient solutions to the neutron transport equation.…

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…

We study multivariate integration of functions that are invariant under the permutation (of a subset) of their arguments. Recently, in Nuyens, Suryanarayana, and Weimar (Adv. Comput. Math. (2016), 42(1):55--84), the authors derived an upper…

Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base…

Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…

Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are $o(1/n)$ as $n\to\infty$, changing even…

Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

We propose an end-to-end integrated strategy to produce highly accurate quantum chemistry (QC) synthetic datasets (energies and forces) aimed at deriving Foundation Machine Learning models for molecular simulation. Starting from Density…

We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models…

We apply diffusion quantum Monte Carlo (DMC) to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and DFT based theories. The test set includes…

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives:…