Related papers: Stochastic mirror descent for nonparametric adapti…
We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…
In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs…
Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
The paper deals with the still-to-video face recognition for the small sample size problem based on computation of distances between high-dimensional deep bottleneck features. We present the novel statistical recognition method, in which…
The joint probabilistic data association (JPDA) filter is a popular tracking methodology for problems involving well-spaced targets, but it is rarely applied in problems with closely-spaced targets due to its complexity in these cases, and…
The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is…
This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a $k$-sparse signal $\mathbf{x}^\star\in\mathbb{R}^n$ from a set of quadratic Gaussian measurements corrupted by…
We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate…