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The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…

The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a…

We develop and describe online algorithms for performing online semiparametric regression analyses. Earlier work on this topic is in Luts, Broderick & Wand (J. Comput. Graph. Statist., 2014) where online mean field variational Bayes was…

We provide a framework which admits a number of ``marginal'' sequential Monte Carlo (SMC) algorithms as particular cases -- including the marginal particle filter [Klaas et al., 2005, in: Proceedings of Uncertainty in Artificial…

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…

Selecting from or ranking a set of candidates variables in terms of their capacity for predicting an outcome of interest is an important task in many scientific fields. A variety of methods for variable selection and ranking have been…

In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally…

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…

We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in $L^p$ and almost surely. The results also apply to Markov chains…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…

We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…

We consider the $\mathcal{H}^2$-formatted compression and computational estimation of covariance functions on a compact set in $\mathbb{R}^d$. The classical sample covariance or Monte Carlo estimator is prohibitively expensive for many…

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…