arXiv research

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

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

New algorithm for robust regression with subgaussian error bound.

Deep neural networks help recover two signals from noisy mixtures.

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…

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…

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

Robustly estimates linear regression coefficients with adversarial and noisy data.

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.

New bounds derived for machine learning algorithms using convex functions.

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…

Note on subgaussian bounds for sign-quantized linear maps.

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 robust estimators achieve subgaussian bounds using VC-dimension.

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

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

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…

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

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

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…

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…

Diffusion models learn multi-modal distributions with optimal efficiency.

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

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 algorithms allocate sampling budget to estimate group means without exploration.

"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…

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

Study reduces human labeling in LLM-based classification systems.

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 …

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

Estimates change point in high dimensional time series models.

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

Study finds the minimum number of finite Gaussian mixtures for best approximation.

Optimal sample complexity for learning Gaussian DAG models established.

We study a variant of the bandit problem where side information in the form of bounds on the mean of each arm is provided. We prove that these translate to tighter estimates of subgaussian factors and develop novel algorithms that exploit these estimates. In the linear setting, we present the Restricted-set OFUL (R-OFU…

Unified framework for information-theoretic bounds on learning algorithms.

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…

New algorithm reduces clustering cost in bandit feedback.

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.

New algorithm optimizes robust estimation under mixed local and global corruptions.

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

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

The paper proves a non-asymptotic test error approximation for KRR.