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Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…

Machine Learning · Statistics 2022-07-06 Jonathan Schmidt , Nicholas Krämer , Philipp Hennig

Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once. The goal of both is to decide on fractions of each…

Data Structures and Algorithms · Computer Science 2013-07-22 Paul Duetting , Robert Kleinberg

In this paper, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA…

Data Structures and Algorithms · Computer Science 2020-06-18 Zhihao Jiang , Debmalya Panigrahi , Kevin Sun

Prophet inequalities are a cornerstone in optimal stopping and online decision-making. Traditionally, they involve the sequential observation of $n$ non-negative independent random variables and face irrevocable accept-or-reject choices.…

Computer Science and Game Theory · Computer Science 2024-08-22 Sebastian Perez-Salazar , Victor Verdugo

We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items…

Machine Learning · Computer Science 2016-09-26 Reinhard Heckel , Nihar B. Shah , Kannan Ramchandran , Martin J. Wainwright

Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…

Data Structures and Algorithms · Computer Science 2024-05-13 Mohammad Taghi Hajiaghayi , Dariusz R. Kowalski , Piotr Krysta , Jan Olkowski

The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and…

Data Structures and Algorithms · Computer Science 2016-06-28 Yajun Wang , Sam Chiu-wai Wong

The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…

Machine Learning · Statistics 2011-09-06 Antony Joseph

Ordinal regression with anchored reference samples (ORARS) has been proposed for predicting the subjective Mean Opinion Score (MOS) of input stimuli automatically. The ORARS addresses the MOS prediction problem by pairing a test sample with…

Machine Learning · Computer Science 2022-07-07 Bin Su , Shaoguang Mao , Frank Soong , Zhiyong Wu

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

Other Computer Science · Computer Science 2020-02-18 W. W. Koczkodaj , R. Smarzewski , J. Szybowski

We consider a fair resource allocation problem in the no-regret setting against an unrestricted adversary. The objective is to allocate resources equitably among several agents in an online fashion so that the difference of the aggregate…

Machine Learning · Computer Science 2023-03-14 Abhishek Sinha , Ativ Joshi , Rajarshi Bhattacharjee , Cameron Musco , Mohammad Hajiesmaili

The prophet inequalities problem has received significant study over the past decades and has several applications such as to online auctions. In this paper, we study two variants of the i.i.d. prophet inequalities problem, namely the…

Data Structures and Algorithms · Computer Science 2020-12-01 William Marshall , Nolan Miranda , Albert Zuo

We introduce a new decomposition technique for random variables that maps a generic instance of the prophet inequalities problem to a new instance where all but a constant number of variables have a tractable structure that we refer to as…

Data Structures and Algorithms · Computer Science 2020-11-10 Allen Liu , Renato Paes Leme , Martin Pal , Jon Schneider , Balasubramanian Sivan

Motivated by the least squares solver Blendenpik, we investigate three strategies for uniform sampling of rows from m x n matrices Q with orthonormal columns. The goal is to determine, with high probability, how many rows are required so…

Numerical Analysis · Mathematics 2014-03-06 Ilse C. F. Ipsen , Thomas Wentworth

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we…

Logic in Computer Science · Computer Science 2023-06-22 Roberto Bruni , Hernán Melgratti , Ugo Montanari

Pairwise comparisons between alternatives are a well-known method for measuring preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the…

Artificial Intelligence · Computer Science 2019-06-20 László Csató

Online resource allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints, with applications ranging from online advertising to revenue management. In this work, we study a broader setting…

Computer Science and Game Theory · Computer Science 2026-05-12 Eleonora Fidelia Chiefari , Francesco Emanuele Stradi , Matteo Castiglioni , Alberto Marchesi

We introduce various quantities that can be defined for an arbitrary matroid, and show that certain conditions on these quantities imply that a matroid is not representable over $\mathbb{F}_q$ where $q$ is a prime power. Mostly, for a…

Combinatorics · Mathematics 2023-06-01 J. Sun , S. B. Damelin

Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the…

Machine Learning · Statistics 2013-01-24 Yuyang Wang , Roni Khardon , Dmitry Pechyony , Rosie Jones

Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…

Machine Learning · Statistics 2021-10-28 Christina Lee Yu