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Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…

Data Structures and Algorithms · Computer Science 2019-11-26 Tobias Mömke , Andreas Wiese

We study the efficient learnability of high-dimensional Gaussian mixtures in the outlier-robust setting, where a small constant fraction of the data is adversarially corrupted. We resolve the polynomial learnability of this problem when the…

Data Structures and Algorithms · Computer Science 2020-05-14 Ilias Diakonikolas , Samuel B. Hopkins , Daniel Kane , Sushrut Karmalkar

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…

Artificial Intelligence · Computer Science 2018-07-02 Brendan Juba

Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…

Machine Learning · Statistics 2022-06-22 Yi Hao , Ayush Jain , Alon Orlitsky , Vaishakh Ravindrakumar

The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…

Computational Complexity · Computer Science 2019-02-20 Manuel Arora , Gábor Ivanyos , Marek Karpinski , Nitin Saxena

We give new differentially private algorithms for the classic problems of learning decision lists and large-margin halfspaces in the PAC and online models. In the PAC model, we give a computationally efficient algorithm for learning…

Machine Learning · Computer Science 2026-02-10 Mark Bun , William Fang

We study the problem of learning a mixture of two subspaces over $\mathbb{F}_2^n$. The goal is to recover the individual subspaces, given samples from a (weighted) mixture of samples drawn uniformly from the two subspaces $A_0$ and $A_1$.…

Data Structures and Algorithms · Computer Science 2021-02-16 Aidao Chen , Anindya De , Aravindan Vijayaraghavan

A Forster transform is an operation that turns a distribution into one with good anti-concentration properties. While a Forster transform does not always exist, we show that any distribution can be efficiently decomposed as a disjoint…

Machine Learning · Computer Science 2021-07-13 Ilias Diakonikolas , Daniel M. Kane , Christos Tzamos

We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…

Computational Complexity · Computer Science 2023-04-06 Pál András Papp , Georg Anegg , A. N. Yzelman

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

Machine Learning · Computer Science 2024-06-13 Fan Chen , Constantinos Daskalakis , Noah Golowich , Alexander Rakhlin

In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be…

Machine Learning · Statistics 2023-05-25 Ying Huang , Liang Chen

In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…

Machine Learning · Computer Science 2025-05-02 Gautam Chandrasekaran , Adam Klivans , Vasilis Kontonis , Raghu Meka , Konstantinos Stavropoulos

We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…

Machine Learning · Computer Science 2015-03-13 Pranjal Awasthi , Maria-Florina Balcan , Nika Haghtalab , Ruth Urner

In this paper we revisit some classic problems on classification under misspecification. In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$. In a recent work, Diakonikolas, Goulekakis, and Tzamos…

Machine Learning · Computer Science 2023-09-21 Sitan Chen , Frederic Koehler , Ankur Moitra , Morris Yau

We investigate the computational efficiency of multitask learning of Boolean functions over the $d$-dimensional hypercube, that are related by means of a feature representation of size $k \ll d$ shared across all tasks. We present a…

Machine Learning · Computer Science 2022-09-08 Konstantina Bairaktari , Guy Blanc , Li-Yang Tan , Jonathan Ullman , Lydia Zakynthinou

We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. Here the task is to construct a hypothesis mixture of…

Machine Learning · Computer Science 2007-05-23 Jon Feldman , Ryan O'Donnell , Rocco A. Servedio

We consider the problem of clustering mixtures of mean-separated Gaussians in high dimensions. We are given samples from a mixture of $k$ identity covariance Gaussians, so that the minimum pairwise distance between any two pairs of means is…

Data Structures and Algorithms · Computer Science 2021-12-02 Jerry Li , Allen Liu

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…

Data Structures and Algorithms · Computer Science 2026-05-22 Alkis Kalavasis , Pravesh K. Kothari , Shuchen Li , Manolis Zampetakis

This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise…

Machine Learning · Statistics 2020-10-20 Ioannis Anagnostides , Themis Gouleakis , Ali Marashian

We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the…

Data Structures and Algorithms · Computer Science 2013-04-18 Brendan Juba