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Related papers: Optimal Bounds for Noisy Sorting

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The problem of estimating frequency moments of a data stream has attracted a lot of attention since the onset of streaming algorithms [AMS99]. While the space complexity for approximately computing the $p^{\rm th}$ moment, for $p\in(0,2]$…

Data Structures and Algorithms · Computer Science 2013-06-27 Alexandr Andoni , Huy L. Nguyen , Yury Polyanskiy , Yihong Wu

System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an…

Systems and Control · Electrical Eng. & Systems 2025-06-12 Xiong Zeng , Jing Yu , Necmiye Ozay

We give a general approach for solving optimization problems on noisy minor free graphs, where a \delta-fraction of edges and vertices are adversarially corrupted. The noisy setting was first considered by Magen and Moharrami and they gave…

Data Structures and Algorithms · Computer Science 2017-02-03 Nikhil Bansal , Daniel Reichman , Seeun William Umboh

Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…

Data Structures and Algorithms · Computer Science 2007-07-12 Constantinos Daskalakis , Richard M. Karp , Elchanan Mossel , Samantha Riesenfeld , Elad Verbin

We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…

Data Structures and Algorithms · Computer Science 2010-05-06 Jean Cardinal , Samuel Fiorini , Gwenaël Joret , Raphaël M. Jungers , J. Ian Munro

The dynamic optimality conjecture, postulating the existence of an $O(1)$-competitive online algorithm for binary search trees (BSTs), is among the most fundamental open problems in dynamic data structures. Despite extensive work and some…

Data Structures and Algorithms · Computer Science 2019-12-24 Parinya Chalermsook , Julia Chuzhoy , Thatchaphol Saranurak

We study a general clustering setting in which we have $n$ elements to be clustered, and we aim to perform as few queries as possible to an oracle that returns a noisy sample of the weighted similarity between two elements. Our setting…

Machine Learning · Statistics 2024-11-05 Yuko Kuroki , Atsushi Miyauchi , Francesco Bonchi , Wei Chen

The element distinctness problem takes as input a list $I$ of $n$ values from a totally ordered universe and the goal is to decide whether $I$ contains any duplicates. It is a well-studied problem with a classical worst-case $\Omega(n \log…

Data Structures and Algorithms · Computer Science 2025-11-06 Ivor van der Hoog , Eva Rotenberg , Daniel Rutschmann

In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of $n$ bins (knapsacks) of equal size. The gain of an~algorithm is equal to the sum of sizes…

Data Structures and Algorithms · Computer Science 2020-04-29 Marcin Bienkowski , Maciej Pacut , Krzysztof Piecuch

Sparse subspace clustering (SSC) using greedy-based neighbor selection, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known as a popular computationally-efficient alternative to the conventional…

Machine Learning · Statistics 2020-02-04 Jwo-Yuh Wu , Wen-Hsuan Li , Liang-Chi Huang , Yen-Ping Lin , Chun-Hung Liu , Rung-Hung Gau

The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >=…

Machine Learning · Computer Science 2007-05-23 Barak A. Pearlmutter

We give the first sorting algorithm with bounds in terms of higher-order entropies: let $S$ be a sequence of length $m$ containing $n$ distinct elements and let (H_\ell (S)) be the $\ell$th-order empirical entropy of $S$, with (n^{\ell + 1}…

Data Structures and Algorithms · Computer Science 2007-05-23 Travis Gagie

Let $0 < p < 2$. Let $\{X, X_{n}; n \geq 1\}$ be a sequence of independent and identically distributed $\mathbf{B}$-valued random variables and set $S_{n} = \sum_{i=1}^{n}X_{i},~n \geq 1$. In this paper, a supplement to the classical laws…

Probability · Mathematics 2020-07-13 Deli Li , Yu Miao

We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum…

Information Theory · Computer Science 2016-08-24 Babak Mamandipoor , Dinesh Ramasamy , Upamanyu Madhow

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…

Machine Learning · Computer Science 2025-10-30 Phuc Tran , Nisheeth K. Vishnoi

Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on…

Machine Learning · Computer Science 2023-10-30 Bohan Wang , Jingwen Fu , Huishuai Zhang , Nanning Zheng , Wei Chen

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and has numerous practical applications. One of the defining features of group testing is…

Information Theory · Computer Science 2021-11-12 Bernard Teo , Jonathan Scarlett

Motivated by the concept of probe storage, we study the problem of information retrieval using a large array of N nano-mechanical probes, N ~ 4000. At the nanometer scale it is impossible to avoid errors in the positioning of the array,…

Information Theory · Computer Science 2015-03-18 Oliver Hambrey , Thomas Parnell , Oleg Zaboronski

Noisy label learning aims to train deep neural networks using a large amount of samples with noisy labels, whose main challenge comes from how to deal with the inaccurate supervision caused by wrong labels. Existing works either take the…

Machine Learning · Computer Science 2024-04-03 Sihan Bai

We introduce new stable natural merge sort algorithms, called $2$-merge sort and $\alpha$-merge sort. We prove upper and lower bounds for several merge sort algorithms, including Timsort, Shivers' sort, $\alpha$-stack sorts, and our new…

Data Structures and Algorithms · Computer Science 2019-02-12 Sam Buss , Alexander Knop