arXiv research

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

Estimates sub-Gaussian parameter with consistent and optimal rates.

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

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

Quantum algorithm estimates mean with sub-Gaussian error.

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

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

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 …

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

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

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…

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…

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…

New method tightens sub-Gaussian concentration inequalities.

Paper proposes a 1-bit quantization scheme for high-dimensional statistical estimation.

New method estimates hidden binary mixture model centers efficiently.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

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 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…

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.

Study non-parametric frequency-domain system identification from finite samples.

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.

Paper presents robust clustering methods for general mixture models.

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

DP-PCA improves privacy in PCA computations with optimal statistical error.

New algorithm converts data into sub-gaussian designs efficiently.

The study examines conditions for achieving a simple lower bound in estimating mean from samples.

The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.

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.

Cluster Quilting clusters fragmented data sets for neuroscience and genomics.

Proposes a new model for clustering with heavier tails.

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

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…

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

Study on using random subspaces for ERM with various loss functions.

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.

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming that the random vector has bounded mean and covariance. Polynomial-time solutio…

Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.

Paper improves SLCB regret bound for bounded noise.

New bandit algorithm for non-i.i.d. noise, improving standard rates.

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…