arXiv research

New method tightens sub-Gaussian concentration inequalities.

We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $α$-stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…

Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.

Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful information. This is done by approximately preserving the distances between data points,…

UCB algorithm adapted for large-scale, non-sub-Gaussian problems.

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

New algorithm converts data into sub-gaussian designs efficiently.

Quantum algorithm estimates mean with sub-Gaussian error.

Sharp comparison for sub-Gaussian random variables in convex order.

Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.

New method reduces summary points for datasets while maintaining quality.

Estimates sub-Gaussian parameter with consistent and optimal rates.

Proposes a new model for clustering with heavier tails.

New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.

New winsorized mean improves robustness to up to 50% contamination.

Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.

The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.

We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is based on a novel concept of a…

Two new algorithms improve robust PCA and Schatten packing.

Paper analyzes SGMs for learning sub-Gaussian distributions without dimensionality constraints.

SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.

Paper improves SLCB regret bound for bounded noise.

Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher variables in the bounding expression by arbitrary idd symmetric and sub-gaussian var…

Improved median of means estimator with tighter bounds.

Flexible model captures varying scales in data clusters.

Study shows how over-parameterized classifiers can still perform well on noisy data.

One-bit clustering method for two-component sub-Gaussian mixture models

New characterization limits sampling with inexact scores.

Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential f…

Paper analyzes neural network models for sub-Gaussian distributions, proving approximation and generalization abilities.

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …

SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.

We improve bounds for stochastic processes, especially those with heavy tails.

New estimator accurately estimates mean of real-valued distributions without variance knowledge.

The paper strengthens the classical result of MLE convergence to a Gaussian distribution.

The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.

GROS combines estimators robustly in metric spaces.

We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has finite mean and covariance; in particular, we mak…

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

Sharp rates found for learning with dependent data, avoiding sample size deflation.

The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some $ε\in (0,1]$. Surprisingly, moments of order 2 (i.e., finite variance) are suffi…

Paper presents robust clustering methods for general mixture models.

Paper tackles online control of linear systems with unbounded noise.

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of in…

Paper solves robust convex problems with heavy-tailed noise.

The paper tackles resource allocation for arms with unknown and random rewards, achieving optimal regret bounds.