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We consider the \emph{approximate minimum selection} problem in presence of \emph{independent random comparison faults}. This problem asks to select one of the smallest $k$ elements in a linearly-ordered collection of $n$ elements by only…

Data Structures and Algorithms · Computer Science 2020-07-08 Stefano Leucci , Chih-Hung Liu

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…

Machine Learning · Computer Science 2012-03-19 Miika Pihlaja , Michael Gutmann , Aapo Hyvarinen

Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…

Discrete Mathematics · Computer Science 2024-11-15 Yiqiao Bao , Sampath Kannan , Erik Waingarten

We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product…

Machine Learning · Computer Science 2021-05-25 Mark Braverman , Elad Hazan , Max Simchowitz , Blake Woodworth

Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly…

Machine Learning · Computer Science 2026-05-18 Zhankun Luo , Antesh Upadhyay , M. Berk Sahin , Sang Bin Moon , Anuran Makur , Abolfazl Hashemi

We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace…

Data Structures and Algorithms · Computer Science 2021-10-27 Prathamesh Dharangutte , Christopher Musco

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

Machine Learning · Computer Science 2016-06-02 Andriy Mnih , Danilo J. Rezende

We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…

Computational Complexity · Computer Science 2015-11-17 Aleksandrs Belovs , Eric Blais

In this paper, we study estimators for geometric optimization problems in the sublinear geometric model. In this model, we have oracle access to a point set with size $n$ in a discrete space $[\Delta]^d$, where queries can be made to an…

Computational Geometry · Computer Science 2025-04-23 Anne Driemel , Morteza Monemizadeh , Eunjin Oh , Frank Staals , David P. Woodruff

The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is…

Data Structures and Algorithms · Computer Science 2021-01-15 Thomas Erlebach , Michael Hoffmann , Murilo S. de Lima

Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…

Applications · Statistics 2022-06-22 Yupeng Chen , Zhiguo Wang , Xiaojing Shen

We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an…

Statistics Theory · Mathematics 2025-07-15 Aaron Abrams , Sandy Ganzell , Henry Landau , Zeph Landau , James Pommersheim , Eric Zaslow

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

Machine Learning · Computer Science 2022-03-22 Nhat Ho , Koulik Khamaru , Raaz Dwivedi , Martin J. Wainwright , Michael I. Jordan , Bin Yu

We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…

We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…

Statistics Theory · Mathematics 2026-05-18 Fan Chen , Sinho Chewi , Constantinos Daskalakis , Alexander Rakhlin

We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…

Data Structures and Algorithms · Computer Science 2025-04-15 Gleb Novikov

We study least-squares trace regression when the parameter is the sum of a $r$-low-rank matrix and a $s$-sparse matrix and a fraction $\epsilon$ of the labels is corrupted. For subgaussian distributions and feature-dependent noise, we…

Statistics Theory · Mathematics 2024-01-08 Philip Thompson

Four types of explicit estimators are proposed here to estimate the loss rates of the links in a network with the tree topology and all of them are derived by the maximum likelihood principle. One of the four is developed from an estimator…

Networking and Internet Architecture · Computer Science 2017-07-05 Weiping Zhu

In this paper, we study the problem of mean estimation under 1-bit communication constraints. We propose a novel adaptive mean estimator based solely on randomized threshold queries, where each 1-bit outcome indicates whether a given sample…

Machine Learning · Statistics 2026-05-25 Ivan Lau , Jonathan Scarlett

Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…

Quantum Physics · Physics 2023-07-04 Y. S. Teo