arXiv research

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

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.

New robust estimators achieve subgaussian bounds using VC-dimension.

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

Deep neural networks help recover two signals from noisy mixtures.

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

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

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…

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…

New algorithms exploit mean bounds to improve bandit problem performance.

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…

Robustly estimates linear regression coefficients with adversarial and noisy data.

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

New algorithm for robust regression with subgaussian error bound.

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

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

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

New bounds derived for machine learning algorithms using convex functions.

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

Estimates change point in high dimensional time series models.

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

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.

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…

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…

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

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.

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…

New TS algorithms improve performance in non-stationary multi-armed bandit problems.

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

This paper analyzes the sample complexity of SPS method for scalar linear regression.

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

Diffusion models learn multi-modal distributions with optimal efficiency.

Estimates mean from heavy-tailed data without variance.

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

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…

New coherence parameter for GNNs with Fourier measurements improves signal recovery.

Study reduces human labeling in LLM-based classification systems.

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

New SQ lower bound shows complexity nearly matches known upper bound for smoothed agnostic learning.

Existing strategies for finite-armed stochastic bandits mostly depend on a parameter of scale that must be known in advance. Sometimes this is in the form of a bound on the payoffs, or the knowledge of a variance or subgaussian parameter. The notable exceptions are the analysis of Gaussian bandits with unknown mean and…

"No free lunch" results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling. Some models are expensive (strong assumptions, such as as subgaussian tails), others are cheap (simply finite variance). As it is well known, the more you pay, the…

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…