Related papers: Polynomial-Time Robust Multiclass Linear Classific…
We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…
We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is…
A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test-time natural example. In contrast, the attacker only needs to…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
Online classification is a central problem in optimization, statistical learning and data science. Classical algorithms such as the perceptron offer efficient updates and finite mistake guarantees on linearly separable data, but they do not…
We give a simple, multiplicative-weight update algorithm for learning undirected graphical models or Markov random fields (MRFs). The approach is new, and for the well-studied case of Ising models or Boltzmann machines, we obtain an…
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…
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…
In this work, we give a ${\rm poly}(d,k)$ time and sample algorithm for efficiently learning the parameters of a mixture of $k$ spherical distributions in $d$ dimensions. Unlike all previous methods, our techniques apply to heavy-tailed…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…
We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testable learning framework, the goal is to develop a…
It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly…
On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…