20 accepted papers
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\\mathbf{\Sigma}$, whose top eigenvector $\\mathbf{v} \in \\mathbb{R}^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categor…
To recognize and mitigate the harms of generative AI systems, it is crucial to consider whether and how different societal groups are represented by these systems. A critical gap emerges when naively measuring or improving *who* is represented, as this does not consider *how* people are represented.…
Estimating the geometric median of a dataset is a robust counterpart to mean estimation, and is a fundamental problem in computational geometry. Recently, [HSU24] gave an $(\epsilon, \delta)$-differentially private algorithm obtaining an $\alpha$-multiplicative approximation to the geometric median…
Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called *iterative polynomial filtering* and show a number of striking applications for supervised learning with contamination: (1) We show that any function class that can be approximated by low-…
We study the problem of PAC learning $\gamma$-margin halfspaces with Massart noise. We propose a simple proper learning algorithm, the Perspectron, that has sample complexity $\widetilde{O}((\epsilon\gamma)^{-2})$ and achieves classification error at most $\eta+\epsilon$ where $\eta$ is the Massart…
We study the problem of differentially private stochastic convex optimization (DP-SCO) with heavy-tailed gradients, where we assume a $k^{\text{th}}$-moment bound on the Lipschitz constants of sample functions, rather than a uniform bound. We propose a new reduction-based approach that enables us to…
We consider the well-studied problem of completing a rank-$r$, $\mu$-incoherent matrix $\mathbf{M} \in \mathbb{R}^{d \times d}$ from incomplete observations. We focus on this problem in the semi-random setting where each entry is independently revealed with probability at least $p = \frac{\textup{po…
In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model calibration have remained relatively less well-explored. Mo…
We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $\widetilde{O}(\sqrt{m + n}\cdot \epsilon^{-2.5} +…
We investigate area convexity [Sherman17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with conventional analyses of extragradient methods [Nemirovski04, Nesterov07]. We also give imp…
We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including: Diagonal preconditioning. We give an algorithm which, given…
Robust statistics has traditionally focused on designing estimators tolerant to a minority of contaminated data. {\em List-decodable learning}~\cite{CharikarSV17} studies the more challenging regime where only a minority $\tfrac 1 k$ fraction of the dataset, $k \geq 2$, is drawn from the distributio…
We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to well-conditioned distributions. Our main result is a nearly-tigh…
We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the \emph{robust gradient descent}…
Consider an oracle which takes a point x and returns the minimizer of a convex function f in an l
We develop two methods for the following fundamental statistical task: given an $\eps$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our first robust PCA algorithm runs in polynomial time, returns a $1 -…
Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two $n$-dimensional distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves the problem to additive $\epsilon$ accuracy with $\tilde{…
We present a randomized primal-dual algorithm that solves the problem min
Word embedding is a useful approach to capture co-occurrence structures in large text corpora. However, in addition to the text data itself, we often have additional covariates associated with individual corpus documents—e.g. the demographic of the author, time and venue of publication—and we would…
Consider the following estimation problem: there are $n$ entities, each with an unknown parameter $p_i \in [0,1]$, and we observe $n$ independent random variables, $X_1,\ldots,X_n$, with $X_i \sim $ Binomial$(t, p_i)$. How accurately can one recover the ``histogram'' (i.e. cumulative density functi…