Related papers: Efficient Algorithms and Lower Bounds for Robust L…
We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For $s$-sparse polynomial over $n$ variables and $\epsilon=1/s^\beta$, $\beta>1$, our…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…
Training deep neural models in the presence of corrupted supervision is challenging as the corrupted data points may significantly impact the generalization performance. To alleviate this problem, we present an efficient robust algorithm…
The robustness to noise and outliers is an important issue in linear representation in real applications. We focus on the problem that samples are grossly corrupted, which is also the 'sample specific' corruptions problem. A reasonable…
We study the problem of estimating the mean of an identity covariance Gaussian in the truncated setting, in the regime when the truncation set comes from a low-complexity family $\mathcal{C}$ of sets. Specifically, for a fixed but unknown…
Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We present a detailed study of $H$-consistency bounds for regression. We first present new theorems that generalize the tools previously given to establish $H$-consistency bounds. This generalization proves essential for analyzing…
In this paper, we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations. These estimators are robust against high-leverage outliers and they generalize…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model.…
High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…