Related papers: Robustly Learning a Gaussian: Getting Optimal Erro…

We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…

In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…

We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…

It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and…

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…

Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions…

Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In…

There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime…

Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…