arXiv research

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

New robust estimators achieve subgaussian bounds using VC-dimension.

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

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

New algorithms exploit mean bounds to improve bandit problem performance.

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

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

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

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

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.

Estimates change point in high dimensional time series 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…

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

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

New algorithm for robust regression with subgaussian error bound.

Deep neural networks help recover two signals from noisy mixtures.

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

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…

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…

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…

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

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…

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

Robustly estimates linear regression coefficients with adversarial and noisy data.

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

Diffusion models learn multi-modal distributions with optimal efficiency.

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

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…

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…

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

New bounds derived for machine learning algorithms using convex functions.

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 …

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…

Bandit algorithms struggle with consistent performance and robustness.

New insights into natural exponential families improve regret bounds for bandit problems.

We study tilting subweibull distributions and their tail behavior.

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

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

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with al…

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…

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 stability bounds for Sinkhorn's algorithm in entropic optimal transport.

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