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Related papers: Optimal Non-Adaptive Tolerant Junta Testing via Lo…

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This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance…

Data Structures and Algorithms · Computer Science 2019-04-12 Marco Gaboardi , Ryan Rogers , Or Sheffet

The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…

Statistics Theory · Mathematics 2008-01-22 Patricia Reynaud-Bouret , Vincent Rivoirard

An algorithm is given for determining an optimal $b$-step approximation of weighted data, where the error is measured with respect to the $L_\infty$ norm. For data presorted by the independent variable the algorithm takes $\Theta(n + \log n…

Data Structures and Algorithms · Computer Science 2015-05-05 Quentin F. Stout

We provide an example of a monotone Boolean function on the hypercube given by a low depth decision tree that is not well approximated by any k-junta for small k.

Discrete Mathematics · Computer Science 2013-06-17 Daniel M. Kane

We investigate adaptive sublinear algorithms for detecting monotone patterns in an array. Given fixed $2 \leq k \in \mathbb{N}$ and $\varepsilon > 0$, consider the problem of finding a length-$k$ increasing subsequence in an array $f \colon…

Data Structures and Algorithms · Computer Science 2019-11-05 Omri Ben-Eliezer , Shoham Letzter , Erik Waingarten

We study the problem of estimating the number of edges in an $n$-vertex graph, accessed via the Bipartite Independent Set query model introduced by Beame et al. (ITCS '18). In this model, each query returns a Boolean, indicating the…

Data Structures and Algorithms · Computer Science 2022-07-07 Raghavendra Addanki , Andrew McGregor , Cameron Musco

We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…

Machine Learning · Statistics 2025-04-21 Robert Busa-Fekete , Umar Syed

We study monotonicity testing of functions $f \colon \{0,1\}^d \to \{0,1\}$ using sample-based algorithms, which are only allowed to observe the value of $f$ on points drawn independently from the uniform distribution. A classic result by…

Data Structures and Algorithms · Computer Science 2024-08-21 Hadley Black

Monotonicity testing of Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$, is a classic topic in property testing. Determining the non-adaptive complexity of this problem is an important open question. For arbitrary $n$,…

Data Structures and Algorithms · Computer Science 2025-05-20 Hadley Black , Deeparnab Chakrabarty , C. Seshadhri

We study the relative-error property testing model for Boolean functions that was recently introduced in the work of Chen et al. (SODA 2025). In relative-error testing, the testing algorithm gets uniform random satisfying assignments as…

Computational Complexity · Computer Science 2025-04-15 Xi Chen , William Pires , Toniann Pitassi , Rocco A. Servedio

Inspired by a recent classical distribution-free junta tester by Chen, Liu, Serverdio, Sheng, and Xie (STOC'18), we construct a quantum tester for the same problem with complexity $O(k/\varepsilon)$, which constitutes a quadratic…

Quantum Physics · Physics 2019-03-21 Aleksandrs Belovs

The problem of testing monotonicity for Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$ is a classic topic in property testing. When $n=2$, the domain is the hypercube. For the hypercube case, a breakthrough result of…

Data Structures and Algorithms · Computer Science 2022-11-11 Hadley Black , Deeparnab Chakrabarty , C. Seshadhri

We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access…

Computational Complexity · Computer Science 2023-09-06 William He , Shivam Nadimpalli

Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…

Data Structures and Algorithms · Computer Science 2024-12-24 Ziao Wang , Nadim Ghaddar , Banghua Zhu , Lele Wang

We study the problems of learning and testing junta distributions on $\{-1,1\}^n$ with respect to the uniform distribution, where a distribution $p$ is a $k$-junta if its probability mass function $p(x)$ depends on a subset of at most $k$…

Data Structures and Algorithms · Computer Science 2020-04-28 Xi Chen , Rajesh Jayaram , Amit Levi , Erik Waingarten

We revisit the problem of tolerant distribution testing. That is, given samples from an unknown distribution $p$ over $\{1, \dots, n\}$, is it $\varepsilon_1$-close to or $\varepsilon_2$-far from a reference distribution $q$ (in total…

Data Structures and Algorithms · Computer Science 2021-11-10 Clément L. Canonne , Ayush Jain , Gautam Kamath , Jerry Li

We provide the first known algorithm that provably achieves $\varepsilon$-optimality within $\widetilde{\mathcal{O}}(1/\varepsilon)$ function evaluations for the discounted discrete-time LQR problem with unknown parameters, without relying…

Systems and Control · Electrical Eng. & Systems 2025-06-18 Amirreza Neshaei Moghaddam , Alex Olshevsky , Bahman Gharesifard

For a function $f \colon \{0,1\}^n \to \{0,1\}$, the junta testing problem asks whether $f$ depends on only $k$ variables. If $f$ depends on only $k$ variables, the feature selection problem asks to find those variables. We prove that these…

Machine Learning · Computer Science 2025-07-23 Lorenzo Beretta , Nathaniel Harms , Caleb Koch

The (tolerant) Hamiltonian locality testing problem, introduced in [Bluhm, Caro,Oufkir `24], is to determine whether a Hamiltonian $H$ is $\varepsilon_1$-close to being $k$-local (i.e. can be written as the sum of weight-$k$ Pauli…

Quantum Physics · Physics 2025-05-13 John Kallaugher , Daniel Liang

We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube ${0,1}^n$. Informally, a function $f:{0,1}^n \rightarrow \mathbb{R}$ is self-bounding if for every $x…

Machine Learning · Computer Science 2019-06-04 Vitaly Feldman , Pravesh Kothari , Jan Vondrák