Related papers: List Decodable Mean Estimation in Nearly Linear Ti…
We consider the problem of clustering mixtures of mean-separated Gaussians in high dimensions. We are given samples from a mixture of $k$ identity covariance Gaussians, so that the minimum pairwise distance between any two pairs of means is…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
In the problem of compressive phase retrieval, one wants to recover an approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem has…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…
We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…
We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator…
This paper shows how to adapt several simple and classical sampling-based algorithms for the $k$-means problem to the setting with outliers. Recently, Bhaskara et al. (NeurIPS 2019) showed how to adapt the classical $k$-means++ algorithm to…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…
Real-world network applications must cope with failing nodes, malicious attacks, or, somehow, nodes facing corrupted data --- classified as outliers. One enabling application is the geographic localization of the network nodes. However,…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Standard classification theory assumes that the distribution of images in the test and training sets are identical. Unfortunately, real-life scenarios typically feature unseen data (``out-of-distribution data") which is different from data…