We give a polynomial-time algorithm for the problem of robustly estimating a mixture of k
arbitrary Gaussians in ℝ d, for any fixed k, in the presence of a constant fraction of arbitrary …

We obtain robust and computationally efficient estimators for learning several linear models
that achieve statistically optimal convergence rate under minimal distributional assumptions …

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of testable
learning, where the goal is to replace hard-to-verify distributional assumptions (such as …

We design new polynomial-time algorithms for recovering planted cliques in the semi-
random graph model introduced by Feige and Kilian. The previous best algorithms for this …

Linear dynamical systems are the foundational statistical model upon which control theory is
built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge …

A set of high dimensional points X ={x_1,x_2,...,x_n\}⊆R^d in isotropic position is said to be
δ-anti concentrated if for every direction v, the fraction of points in X satisfying …

Learning from data in the presence of outliers is a fundamental problem in statistics. Until
recently, no computationally efficient algorithms were known to compute the mean of a high …

We study the problem of list-decodable sparse mean estimation. Specifically, for a
parameter $\alpha\in (0, 1/2) $, we are given $ m $ points in $\mathbb {R}^ n $, $\lfloor\alpha …

We study the problem of list-decodable linear regression, where an adversary can corrupt a
majority of the examples. Specifically, we are given a set $ T $ of labeled examples $(x …

We give the first polynomial time algorithm for list-decodable covariance estimation. For any
α> 0, our algorithm takes input a sample Y⊆ d of size n≥ d poly (1/α) obtained by …