arXiv research

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

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

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

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

Paper improves SLCB regret bound for bounded noise.

New method tightens sub-Gaussian concentration inequalities.

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

Estimates sub-Gaussian parameter with consistent and optimal rates.

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

Improved median of means estimator with tighter bounds.

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 …

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

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

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

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,…

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

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…

New bounds for kernel regression under non-Gaussian noise.

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

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.

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

Score-based diffusion models achieve optimal error bounds under non-parametric assumptions.

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…

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

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

Paper tackles online control of linear systems with unbounded noise.

RS-NSGD improves SGD convergence for heavy-tailed noise.

New algorithm guarantees performance on noisy data.

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

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

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…

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

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

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…

In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_λ^d$ or matrix-version LASSO estimator $\hat{A}_λ^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. Suppose $\textrm…

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…

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…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …

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…

New method for robust linear regression in nearly linear time.

We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex optimization problem, which is then solved using the alternating direction method of m…

LinMED is a new linear bandit algorithm with near-optimal regret bound.

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

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

The paper explores how linear neural networks can overfit without bias when data is well-behaved.

New method estimates gradients accurately with sharp bounds.

Improved generalization bounds for SGD in non-convex learning.