11 accepted papers
Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective typically precludes …
Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context, casting the minimizer as the invariant distribution of a McKea…
An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to-date it has remained unclear how to exploit modern reinforcement learning technologies for adaptive MCMC. The aim of this paper is t…
We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct good…
Stein discrepancies have emerged as a powerful tool for retrospective improvement of Markov chain Monte Carlo output. However, the question of how to design Markov chains that are well-suited to such post-processing has yet to be addressed. This paper studies Stein importance sampling, in which we…
Proxy causal learning (PCL) is a method for estimating the causal effect of treatments on outcomes in the presence of unobserved confounding, using proxies (structured side information) for the confounder. This is achieved via two-stage regression: in the first stage, we model relations among the tr…
Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either a…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function p(y|x) and a joint sample, decide whether the sample is drawn from p(y|x)q(x) for some density q(x). Our tests, formulated with a Stein operator, can be a…
Given two candidate models, and a set of target observations, we address the problem of measuring the relative goodness of fit of the two models. We propose two new statistical tests which are nonparametric, computationally efficient (runtime complexity is linear in the sample size), and interpretab…
We investigate the statistical efficiency of a nonparametric Gaussian process method for a nonlinear tensor estimation problem. Low-rank tensor estimation has been used as a method to learn higher order relations among several data sources in a wide range of applications, such as multi-task learning…
We investigate the statistical performance and computational efficiency of the alternating minimization procedure for nonparametric tensor learning. Tensor modeling has been widely used for capturing the higher order relations between multimodal data sources. In addition to a linear model, a nonl…