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Robust Estimators in High Dimensions without the Computational Intractability
This work obtains the first computationally efficient algorithms for agnostically learning several fundamental classes of high-dimensional distributions: a single Gaussian, a product distribution on the hypercube, mixtures of two product distributions (under a natural balancedness condition), and k Gaussians with identical spherical covariances.
Being Robust (in High Dimensions) Can Be Practical
This work addresses sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions.
Sever: A Robust Meta-Algorithm for Stochastic Optimization
This work introduces a new meta-algorithm that can take in a base learner such as least squares or stochastic gradient descent, and harden the learner to be resistant to outliers, and finds that in both cases it has substantially greater robustness than several baselines.
Optimal Testing for Properties of Distributions
This work provides a general approach via which sample-optimal and computationally efficient testers for discrete log-concave and monotone hazard rate distributions are obtained.
Robust Estimators in High-Dimensions Without the Computational Intractability
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich hist...
The Discrete Gaussian for Differential Privacy
This work theoretically and experimentally shows that adding discrete Gaussian noise provides essentially the same privacy and accuracy guarantees as the addition of continuousGaussian noise, and presents an simple and efficient algorithm for exact sampling from this distribution.
Robustly Learning a Gaussian: Getting Optimal Error, Efficiently
This work gives robust estimators that achieve estimation error $O(\varepsilon)$ in the total variation distance, which is optimal up to a universal constant that is independent of the dimension.
Faster and Sample Near-Optimal Algorithms for Proper Learning Mixtures of Gaussians
An improved and generalized algorithm for selecting a good candidate distribution from among competing hypotheses, which improves previous such results from a quadratic dependence of the running time on $N$ to quasilinear.
An analysis of one-dimensional schelling segregation
This analysis is the first rigorous analysis of the Schelling dynamics of segregation in which a society of n individuals live in a ring and the average size of monochromatic neighborhoods in the final stable state is considered.
Privately Learning High-Dimensional Distributions
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product