We study high-dimensional distribution learning in an agnostic setting where an adversary is
allowed to arbitrarily corrupt an ε-fraction of the samples. Such questions have a rich history …

Robust estimation is much more challenging in high-dimensions than it is in one-dimension:
Most techniques either lead to intractable optimization problems or estimators that can …

We describe a general technique that yields the first Statistical Query lower bounds for a
range of fundamental high-dimensional learning problems involving Gaussian distributions …

We use the Sum of Squares method to develop new efficient algorithms for learning well-
separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that …

We study the problem of estimating $ k $-ary distributions under $\eps $-local differential
privacy. $ n $ samples are distributed across users who send privatized versions of their …

We prove new upper and lower bounds on the sample complexity of (ε, δ) differentially
private algorithms for releasing approximate answers to threshold functions. A threshold …

Diffusion models have made rapid progress in generating high-quality samples across
various domains. However, a theoretical understanding of the Lipschitz continuity and …

We give new upper and lower bounds on the minimax sample complexity of differentially
private mean estimation of distributions with bounded $ k $-th moments. Roughly speaking …

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 study the fundamental problem of learning the parameters of a high-dimensional
Gaussian in the presence of noise—where an ε-fraction of our samples were chosen by an …