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Related papers: Efficient Robust Proper Learning of Log-concave Di…

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We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…

Data Structures and Algorithms · Computer Science 2018-12-14 Ilias Diakonikolas , Anastasios Sidiropoulos , Alistair Stewart

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…

Data Structures and Algorithms · Computer Science 2024-06-14 Gautam Chandrasekaran , Adam R. Klivans , Vasilis Kontonis , Konstantinos Stavropoulos , Arsen Vasilyan

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this…

Optimization and Control · Mathematics 2014-10-03 Zizhuo Wang , Peter Glynn , Yinyu Ye

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on…

Machine Learning · Computer Science 2023-02-14 Ilias Diakonikolas , Daniel M. Kane , Lisheng Ren

We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as…

Machine Learning · Computer Science 2009-01-22 Shai Ben-David , Tyler Lu , David Pal , Miroslava Sotakova

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…

Machine Learning · Computer Science 2023-09-13 Abhin Shah , Devavrat Shah , Gregory W. Wornell

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on…

Statistics Theory · Mathematics 2018-12-06 Timothy Carpenter , Ilias Diakonikolas , Anastasios Sidiropoulos , Alistair Stewart

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…

Data Structures and Algorithms · Computer Science 2025-05-21 Jane Lange , Arsen Vasilyan

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

Machine Learning · Computer Science 2018-06-04 Ilias Diakonikolas , Weihao Kong , Alistair Stewart

We study the problem, introduced by Qiao and Valiant, of learning from untrusted batches. Here, we assume $m$ users, all of whom have samples from some underlying distribution $p$ over $1, \ldots, n$. Each user sends a batch of $k$ i.i.d.…

Data Structures and Algorithms · Computer Science 2019-11-07 Sitan Chen , Jerry Li , Ankur Moitra

We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…

Machine Learning · Computer Science 2023-07-06 Nikita Puchkin , Nikita Zhivotovskiy

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse…

Optimization and Control · Mathematics 2019-10-14 Salar Fattahi , Nikolai Matni , Somayeh Sojoudi

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…

Optimization and Control · Mathematics 2021-06-15 Mengmeng Li , Tobias Sutter , Daniel Kuhn

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Computation · Statistics 2016-12-06 Arnak S. Dalalyan

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Optimization and Control · Mathematics 2017-12-27 Kun Yuan , Bicheng Ying , Xiaochuan Zhao , Ali H. Sayed

Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…

Machine Learning · Computer Science 2012-03-19 Kaizhu Huang , Rong Jin , Zenglin Xu , Cheng-Lin Liu

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Data Structures and Algorithms · Computer Science 2026-04-29 Michał Szyfelbein

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear…

Machine Learning · Computer Science 2013-04-29 Maria Florina Balcan , Philip M. Long

Current deep learning solutions are well known for not informing whether they can reliably classify an example during inference. One of the most effective ways to build more reliable deep learning solutions is to improve their performance…

Machine Learning · Computer Science 2022-08-09 David Macêdo

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

Machine Learning · Computer Science 2019-06-12 Yu Cheng , Ilias Diakonikolas , Rong Ge , David Woodruff