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Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…

The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…

We motive and calculate Newton--Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…

Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data)…

We investigate the finite sample performance of sample splitting, cross-fitting and averaging for the estimation of the conditional average treatment effect. Recently proposed methods, so-called meta-learners, make use of machine learning…

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is…

Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…

Bagging can significantly improve the generalization performance of unstable machine learning algorithms such as trees or neural networks. Though bagging is now widely used in practice and many empirical studies have explored its behavior,…

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We…

Auxiliary variable is extensively used in survey sampling to improve the precision of estimates. Whenever there is availability of auxiliary information, we want to utilize it in the method of estimation to obtain the most efficient…