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.

Optimizes sub-Gaussian matrices for preserving data distances.

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

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…

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.

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

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.

Robust clustering algorithm for datasets with outliers.

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

New algorithm converts data into sub-gaussian designs efficiently.

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.

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…

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

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.