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Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube…

Machine Learning · Computer Science 2025-11-14 Arnab Bhattacharyya , Davin Choo , Philips George John , Themis Gouleakis

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

Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…

Statistics Theory · Mathematics 2019-12-10 Octavio César Mesner , Cosma Rohilla Shalizi

We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…

Data Structures and Algorithms · Computer Science 2013-08-20 Siu-On Chan , Ilias Diakonikolas , Gregory Valiant , Paul Valiant

We study the problem of mean estimation for high-dimensional distributions, assuming access to a statistical query oracle for the distribution. For a normed space $X = (\mathbb{R}^d, \|\cdot\|_X)$ and a distribution supported on vectors $x…

Data Structures and Algorithms · Computer Science 2019-02-08 Jerry Li , Aleksandar Nikolov , Ilya Razenshteyn , Erik Waingarten

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on…

Artificial Intelligence · Computer Science 2023-10-23 Qianli Shen , Wai Hoh Tang , Zhun Deng , Apostolos Psaros , Kenji Kawaguchi

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

Machine Learning · Statistics 2020-12-24 Noam Finkelstein , Roy Adams , Suchi Saria , Ilya Shpitser

We propose an estimation procedure for discrete choice models of differentiated products with possibly high-dimensional product attributes. In our model, high-dimensional attributes can be determinants of both mean and variance of the…

Econometrics · Economics 2020-04-21 Masayuki Sawada , Kohei Kawaguchi

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

Methodology · Statistics 2014-10-29 Nicolas Brunel , Quentin Clairon

We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…

Machine Learning · Statistics 2025-03-11 Gilles Blanchard , Jean-Baptiste Fermanian , Hannah Marienwald

This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

Statistics Theory · Mathematics 2018-08-29 Stanislav Minsker , Nate Strawn

We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data…

Data Structures and Algorithms · Computer Science 2020-12-17 Yeshwanth Cherapanamjeri , Jelani Nelson

We present an approximate distance oracle for a point set S with n points and doubling dimension {\lambda}. For every {\epsilon}>0, the oracle supports (1+{\epsilon})-approximate distance queries in (universal) constant time, occupies space…

Data Structures and Algorithms · Computer Science 2010-08-10 Yair Bartal , Lee-Ad Gottlieb , Tsvi Kopelowitz , Moshe Lewenstein , Liam Roditty

Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$…

Computational Complexity · Computer Science 2013-06-05 Hamed Hatami , Shachar Lovett

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Optimization and Control · Mathematics 2019-12-05 Xiaokai Chang , Sanyang Liu , Jianchao Bai , Jun Yang

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

Systems and Control · Computer Science 2018-07-19 Luca Cardelli , Mirco Tribastone , Max Tschaikowski , Andrea Vandin

Accurate and explainable out-of-distribution (OOD) detection is required to use machine learning systems safely. Previous work has shown that feature distance to decision boundaries can be used to identify OOD data effectively. In this…

Machine Learning · Computer Science 2025-08-15 Maria Stoica , Francesco Leofante , Alessio Lomuscio

We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets.…

Machine Learning · Statistics 2015-05-05 Bohan Liu , Ernest Fokoue

In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be…

Statistics Theory · Mathematics 2026-02-26 Patrick Kramer , Edward H. Kennedy , Isaac M. Opper