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Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…

Machine Learning · Computer Science 2025-02-06 German Martinez Matilla , Jakub Marecek

The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…

Computational Complexity · Computer Science 2019-11-19 Matthew Brennan , Guy Bresler , Wasim Huleihel

Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…

Machine Learning · Computer Science 2015-11-10 Raef Bassily , Kobbi Nissim , Adam Smith , Thomas Steinke , Uri Stemmer , Jonathan Ullman

In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…

Computational Geometry · Computer Science 2018-05-01 Sariel Har-Peled , Piotr Indyk , Sepideh Mahabadi

We consider tradeoffs between the query and update complexities for the (approximate) nearest neighbor problem on the sphere, extending the recent spherical filters to sparse regimes and generalizing the scheme and analysis to account for…

Data Structures and Algorithms · Computer Science 2016-09-13 Thijs Laarhoven

The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…

Data Structures and Algorithms · Computer Science 2026-03-26 Rayen Tan , Viswanath Nagarajan

The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…

Data Structures and Algorithms · Computer Science 2009-07-08 Mihai Patrascu

The use of realistic input models has gained popularity in the theory community. Assuming a realistic input model often precludes complicated hypothetical inputs, and the analysis yields bounds that better reflect the behaviour of…

Computational Geometry · Computer Science 2022-11-15 Joachim Gudmundsson , Zijin Huang , Sampson Wong

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

Statistics Theory · Mathematics 2017-01-23 Yannick Baraud , Lucien Birgé , Mathieu Sart

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

Methodology · Statistics 2017-05-04 Daniel W. Meyer

Dynamic decision-making under distributional shifts is of fundamental interest in theory and applications of reinforcement learning: The distribution of the environment in which the data is collected can differ from that of the environment…

Machine Learning · Computer Science 2024-09-05 Shengbo Wang , Nian Si , Jose Blanchet , Zhengyuan Zhou

One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…

Quantum Physics · Physics 2008-04-26 Masahito Hayashi , Akinori Kawachi , Hirotada Kobayashi

We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to…

Machine Learning · Computer Science 2019-05-30 Mingda Qiao , Gregory Valiant

We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…

Machine Learning · Computer Science 2023-07-06 Bryon Aragam , Wai Ming Tai

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space…

Machine Learning · Computer Science 2017-08-10 Paul Beame , Shayan Oveis Gharan , Xin Yang

In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…

Statistics Theory · Mathematics 2017-07-25 Zuofeng Shang , Guang Cheng

Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…

Computational Geometry · Computer Science 2017-07-18 Peyman Afshani , Anne Driemel

Robust mean estimation is one of the most important problems in statistics: given a set of samples in $\mathbb{R}^d$ where an $\alpha$ fraction are drawn from some distribution $D$ and the rest are adversarially corrupted, we aim to…

Machine Learning · Computer Science 2022-12-07 Shiwei Zeng , Jie Shen

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…

Machine Learning · Computer Science 2024-06-26 Rares-Darius Buhai , Jingqiu Ding , Stefan Tiegel

This paper studies the \emph{subset sampling} problem. The input is a set $\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a random…

Data Structures and Algorithms · Computer Science 2023-07-24 Jinchao Huang , Sibo Wang