Related papers: Optimal estimation of high-dimensional location Ga…
The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides…
We consider the problem of robust mean and location estimation w.r.t. any pseudo-norm of the form $x\in\mathbb{R}^d\to ||x||_S = \sup_{v\in S}<v,x>$ where $S$ is any symmetric subset of $\mathbb{R}^d$. We show that the deviation-optimal…
Accurate detection of the centerline of a thick linear structure and good estimation of its thickness are challenging topics in many real-world applications such X-ray imaging, remote sensing and lane marking detection in road traffic.…
This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
We study the asymptotics of the expected Wasserstein distance between the empirical measure of a Point Process and the background volume form. The main DPP studied is the harmonic ensemble, where we get the optimal rate of convergence for…
The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a…
We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
It is common in nonparametric estimation problems to impose a certain low-dimensional structure on the unknown parameter to avoid the curse of dimensionality. This paper considers a nonparametric distribution estimation problem with a…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
In the wake of many new ML-inspired approaches for reconstructing and representing high-quality 3D content, recent hybrid and explicitly learned representations exhibit promising performance and quality characteristics. However, their…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
A new methodology is proposed to approximate the time-dependent house price distribution at a fine regional scale using Gaussian mixtures. The means, variances and weights of the mixture components are related to time, location and dwelling…
The purpose of this paper is to analyze the distribution distance between random vectors derived from the magnitude of the analytic wavelet transform of the squared envelopes of Gaussian processes and their large-scale limits. When the…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…