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Related papers: Statistically Near-Optimal Hypothesis Selection

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In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the…

Machine Learning · Computer Science 2022-11-17 Lunjia Hu , Charlotte Peale

We consider the problem of heteroscedastic linear regression, where, given $n$ samples $(\mathbf{x}_i, y_i)$ from $y_i = \langle \mathbf{w}^{*}, \mathbf{x}_i \rangle + \epsilon_i \cdot \langle \mathbf{f}^{*}, \mathbf{x}_i \rangle$ with…

Machine Learning · Statistics 2023-07-04 Dheeraj Baby , Aniket Das , Dheeraj Nagaraj , Praneeth Netrapalli

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

Machine Learning · Statistics 2026-01-23 Lei Qian , Wu Su , Yanqi Huang , Song Xi Chen

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Artificial Intelligence · Computer Science 2012-12-12 David Ephraim Larkin

The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…

Machine Learning · Computer Science 2023-01-25 Xiao Zhou , Renjie Pi , Weizhong Zhang , Yong Lin , Tong Zhang

Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…

Data Structures and Algorithms · Computer Science 2024-05-22 Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all…

Information Theory · Computer Science 2016-11-17 Naira Grigoryan , Ashot Harutyunyan , Svyatoslav Voloshynovskiy , Oleksiy Koval

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

Optimization and Control · Mathematics 2025-01-08 Dimitris Bertsimas , Jean Pauphilet , Bart Van Parys

The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are…

Information Theory · Computer Science 2009-04-30 Maxim Raginsky

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…

Data Structures and Algorithms · Computer Science 2026-05-25 Clément L. Canonne , Yash Pote , Jonathan Scarlett , Joy Qiping Yang

Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…

Machine Learning · Computer Science 2022-11-21 Wenxuan Guo , YoonHaeng Hur , Tengyuan Liang , Christopher Ryan

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated -- amongst the inputs that receive…

Machine Learning · Statistics 2021-07-14 Shengjia Zhao , Michael P. Kim , Roshni Sahoo , Tengyu Ma , Stefano Ermon

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

Methodology · Statistics 2015-11-24 Rong Zhu , Ping Ma , Michael W. Mahoney , Bin Yu

We consider a basic problem in unsupervised learning: learning an unknown \emph{Poisson Binomial Distribution}. A Poisson Binomial Distribution (PBD) over $\{0,1,\dots,n\}$ is the distribution of a sum of $n$ independent Bernoulli random…

Data Structures and Algorithms · Computer Science 2015-02-18 Constantinos Daskalakis , Ilias Diakonikolas , Rocco A. Servedio

We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…

Machine Learning · Computer Science 2020-03-18 Yi Hao , Alon Orlitsky

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…

Machine Learning · Statistics 2016-06-10 Shuyang Gao , Greg Ver Steeg , Aram Galstyan

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

Data Structures and Algorithms · Computer Science 2023-10-25 Andre Linhares , Chaitanya Swamy

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

Data Structures and Algorithms · Computer Science 2016-05-10 Ilias Diakonikolas , Daniel M. Kane

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Machine Learning · Computer Science 2020-07-23 Hassan Ashtiani , Shai Ben-David , Nick Harvey , Christopher Liaw , Abbas Mehrabian , Yaniv Plan

A popular approach to model compression is to train an inexpensive student model to mimic the class probabilities of a highly accurate but cumbersome teacher model. Surprisingly, this two-step knowledge distillation process often leads to…

Machine Learning · Statistics 2021-04-21 Tri Dao , Govinda M Kamath , Vasilis Syrgkanis , Lester Mackey