13 accepted papers
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb R^d \times \mathbb R$ with $x \sim \mathcal N(0,I_d)$ and $y = x^\top \beta + z$, wh…
We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a *corrupted* set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in \mathbb{R}^d$ is constrained to be $k$-sparse. A series of prior…
We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with optimal error guarantees, within constant factors. All prior ef…
We study the problem of list-decodable Gaussian covariance estimation. Given a multiset $T$ of $n$ points in $\mathbb{R}^d$ such that an unknown $\alpha<1/2$ fraction of points in $T$ are i.i.d. samples from an unknown Gaussian $\mathcal{N}(\mu, \Sigma)$, the goal is to output a list of $O(1/\alpha)…
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time algorithms with optimal error guarantees for both thes…
We study principal component analysis (PCA), where given a dataset in $\mathbb R^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$. Despite being a classical task, standard estimators fail drast…
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 $\mathbb{R}^n$, $\lfloor \alpha m \rfloor$ of which are i.i.d. samples from a distribution $D$ with unknown $k$-sparse mean $\mu$. No assumptions are made on…
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean $\mu$ is guaranteed to be sparse, the goal is to efficient…
We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust statistics tasks. Unfortunately, all previous algorithms require storing the entire dataset, incurring memory at least…
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 $(x, y) \in \mathbb{R}^d \times \mathbb{R}$ and a parameter $0< \alpha <1/2$ such that an $\alpha$-fraction of the points in $…
The strong lottery ticket hypothesis (LTH) postulates that one can approximate any target neural network by only pruning the weights of a sufficiently over-parameterized random network. A recent work by Malach et al. [MYSS20] establishes the first theoretical analysis for the strong LTH: one can pr…
We study the problem of outlier robust high-dimensional mean estimation under a bounded covariance assumption, and more broadly under bounded low-degree moment assumptions. We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponential…
We present a probabilistic framework for multi-label learning based on a deep generative model for the binary label vector associated with each observation. Our generative model learns deep multi-layer latent embeddings of the binary label vector, which are conditioned on the input features of the o…