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We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size $N$ into $m$ machines, and estimates a local sparse LDA…

Machine Learning · Statistics 2016-10-18 Lu Tian , Quanquan Gu

In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However,…

Machine Learning · Computer Science 2023-04-19 Ishaq Aden-Ali , Yeshwanth Cherapanamjeri , Abhishek Shetty , Nikita Zhivotovskiy

We present differentially private algorithms for high-dimensional mean estimation. Previous private estimators on distributions over $\mathbb{R}^d$ suffer from a curse of dimensionality, as they require $\Omega(d^{1/2})$ samples to achieve…

Machine Learning · Computer Science 2024-11-04 Yuval Dagan , Michael I. Jordan , Xuelin Yang , Lydia Zakynthinou , Nikita Zhivotovskiy

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

Data Structures and Algorithms · Computer Science 2024-10-31 Anders Aamand , Alexandr Andoni , Justin Y. Chen , Piotr Indyk , Shyam Narayanan , Sandeep Silwal , Haike Xu

We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average $L_p$ distance between the learned classifier and the…

Information Theory · Computer Science 2017-11-20 Matthew Nokleby , Ahmad Beirami , Robert Calderbank

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

Statistics Theory · Mathematics 2025-02-25 Erik Learned-Miller

In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using…

Statistics Theory · Mathematics 2018-02-14 Olivier Catoni , Ilaria Giulini

This paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the Cramer-Rao lower bound (CRLB) on the variance of distributed…

Information Theory · Computer Science 2015-06-17 Salvatore Talarico , Natalia A. Schmid , Marwan Alkhweldi , Matthew C. Valenti

We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…

Optimization and Control · Mathematics 2022-07-28 Miroslav Rada , Michal Černý , Ondřej Sokol

The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA…

Optimization and Control · Mathematics 2024-02-28 Johannes Milz , Michael Ulbrich

We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true,…

Machine Learning · Computer Science 2025-02-03 Arnab Bhattacharyya , Davin Choo , Philips George John , Themis Gouleakis

We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…

Information Theory · Computer Science 2015-04-24 Aolin Xu , Maxim Raginsky

Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed…

Applications · Statistics 2014-12-18 Yasin Yilmaz , George V. Moustakides , Xiaodong Wang

We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first…

Statistics Theory · Mathematics 2025-12-09 Nicolas Conanec , Claire Lacour , Thanh Mai Pham Ngoc

We consider the class of noisy multi-layered sigmoid recurrent neural networks with $w$ (unbounded) weights for classification of sequences of length $T$, where independent noise distributed according to $\mathcal{N}(0,\sigma^2)$ is added…

Machine Learning · Statistics 2023-05-31 Alireza Fathollah Pour , Hassan Ashtiani

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…

Machine Learning · Computer Science 2020-12-01 Ruizhi Liao , Daniel Moyer , Polina Golland , William M. Wells

We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error,…

Machine Learning · Computer Science 2026-04-24 Natalie Collina , Jiuyao Lu , Georgy Noarov , Aaron Roth

We propose a scalable divergence estimation method based on hashing. Consider two continuous random variables $X$ and $Y$ whose densities have bounded support. We consider a particular locality sensitive random hashing, and consider the…

Information Theory · Computer Science 2018-01-03 Morteza Noshad , Alfred O. Hero

A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…

Statistics Theory · Mathematics 2017-12-21 Ben Berckmoes , Geert Molenberghs

In probably approximately correct (PAC) reinforcement learning (RL), an agent is required to identify an $\epsilon$-optimal policy with probability $1-\delta$. While minimax optimal algorithms exist for this problem, its instance-dependent…

Machine Learning · Computer Science 2022-10-25 Andrea Tirinzoni , Aymen Al-Marjani , Emilie Kaufmann