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Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state space models, but offer an alternative to MCMC in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC…

We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…

Estimating the gradients for binary variables is a task that arises frequently in various domains, such as training discrete latent variable models. What has been commonly used is a REINFORCE based Monte Carlo estimation method that uses…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…

This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional…

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…

Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…

Antithetic sampling, which goes back to the classical work by Hammersley and Morton (1956), is one of the well-known variance reduction techniques for Monte Carlo integration. In this paper we investigate its application to digital nets…

Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…

This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…

Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…

Gaussian Processes (GPs) provide a powerful framework for making predictions and understanding uncertainty for classification with kernels and Bayesian non-parametric learning. Building such models typically requires strong prior knowledge…

We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…

Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…