arXiv research

Proves subgaussian distributions are SoS-certifiably subgaussian, enabling efficient algorithms for various statistical tasks.

New robust estimators achieve subgaussian bounds using VC-dimension.

New algorithms robustly estimate mean with near-optimal error rates.

Paper estimates EOT maps for non-compactly supported measures with subGaussian target.

Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and $β$-mixing condition to establish consistency of lasso when data comes from a $β…

Robustly estimates linear regression coefficients with adversarial and noisy data.

New algorithms exploit mean bounds to improve bandit problem performance.

New algorithms allocate sampling budget to estimate group means without exploration.

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.

Note on subgaussian bounds for sign-quantized linear maps.

Improved mean estimation for symmetric distributions with finite-sample guarantees.

We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We provide a generic method for proving performance guar…

Estimates change point in high dimensional time series models.

Estimates score function from data with optimal rate in high dimensions.

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…

Deep neural networks help recover two signals from noisy mixtures.

The paper provides entrywise bounds for Sparse PCA, improving upon previous results.

New algorithm for robust regression with subgaussian error bound.

We solve robust regression and matrix completion problems with sparse and low-rank models.

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower e…

Thompson Sampling shows polynomial regret for combinatorial semi-bandits with subgaussian rewards.

Estimates mean from heavy-tailed data without variance.

The study analyzes the performance of a nonparametric estimator for dynamical systems.

Ridge regression performs optimally in noisy environments with heavy-tailed distributions.

We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured spars…

Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.

RONM method reduces regret in stochastic convex bandits with decreasing noise.

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* + ε\\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^f$ is a noise vector…

This work establishes near-minimax optimal guarantees for ODE-based samplers under mild assumptions.

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…

We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for …

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…

New bounds derived for machine learning algorithms using convex functions.

New algorithm optimizes convex functions with noisy evaluations in one dimension.

New bounds for learning polynomial surrogates with $L_\infty$ guarantees.

The classical asymptotic theory for parametric $M$-estimators guarantees that, in the limit of infinite sample size, the excess risk has a chi-square type distribution, even in the misspecified case. We demonstrate how self-concordance of the loss allows to characterize the critical sample size sufficient to guarantee …

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially o…

Bandit algorithms struggle with consistent performance and robustness.

We study tilting subweibull distributions and their tail behavior.

This paper tackles open problem of tight bounds for KBs with Bernoulli rewards.

We study the problem of high-dimensional sparse mean estimation in the presence of an $ε$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance subgaussian distributions. In this work, we develop the first efficient algorithms for rob…

New result on tensor recovery without strong assumptions.

I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a hori…

We solve ReLU regression with efficient approximations for various distributions.

Paper presents an efficient algorithm for estimating Lipschitz functions from noisy data.

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi, Reingold and Roth introd…

Improves treatment effect estimation by reducing sample size needed.