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The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both…

Information Theory · Computer Science 2011-02-15 Vincent Y. F. Tan , Animashree Anandkumar , Alan S. Willsky

We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…

Data Structures and Algorithms · Computer Science 2022-08-09 Lisa Hellerstein , Devorah Kletenik , Naifeng Liu , R. Teal Witter

There has been renewed recent interest in developing effective lower bounds for Dynamic Time Warping (DTW) distance between time series. These have many applications in time series indexing, clustering, forecasting, regression and…

Machine Learning · Computer Science 2019-02-15 Chang Wei Tan , Francois Petitjean , Geoffrey I. Webb

We show that in any Euclidean space, an arbitrary probability measure can be reconstructed explicitly by its geometric (or spatial) distribution function. The reconstruction takes the form of a (potentially fractional) linear PDE, where the…

Statistics Theory · Mathematics 2024-04-11 Dimitri Konen

As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…

Numerical Analysis · Mathematics 2017-10-26 You Gao , Tao Qian , Vladimir Temlyakov , Long-fei Cao

The model of relative-error property testing of Boolean functions has been the subject of significant recent research effort [CDH+24][CPPS25a][CPPS25b] In this paper we consider the problem of relative-error testing an unknown and arbitrary…

Computational Complexity · Computer Science 2025-10-27 Xi Chen , Diptaksho Palit , Kabir Peshawaria , William Pires , Rocco A. Servedio , Yiding Zhang

We study sparse polynomials with bounded individual degree and their factors, obtaining the following structural and algorithmic results. 1. A deterministic polynomial-time algorithm to find all sparse divisors of a sparse polynomial of…

Computational Complexity · Computer Science 2026-03-10 Aminadav Chuyoon , Amir Shpilka

The Forward-Forward (FF) algorithm was recently proposed as a local learning method to address the limitations of backpropagation (BP), offering biological plausibility along with memory-efficient and highly parallelized computational…

Neural and Evolutionary Computing · Computer Science 2024-08-28 Yujie Wu , Siyuan Xu , Jibin Wu , Lei Deng , Mingkun Xu , Qinghao Wen , Guoqi Li

Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning…

Machine Learning · Computer Science 2022-03-31 Jonathan Warrell , Mark Gerstein

We study Fourier-sparse Boolean functions over general finite Abelian groups. A Boolean function $f : G \to \{-1,+1\}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. We introduce a general notion of granularity of…

Computational Complexity · Computer Science 2026-02-03 Sourav Chakraborty , Swarnalipa Datta , Pranjal Dutta , Arijit Ghosh , Swagato Sanyal

We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…

Computational Complexity · Computer Science 2017-08-22 Xi Chen , Erik Waingarten , Jinyu Xie

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the Large Deviation Function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools.…

Statistical Mechanics · Physics 2015-06-18 Marija Vucelja , Konstantin S. Turitsyn , Michael Chertkov

The construction by Du et al. (2019) implies that even if a learner is given linear features in $\mathbb R^d$ that approximate the rewards in a bandit with a uniform error of $\epsilon$, then searching for an action that is optimal up to…

Machine Learning · Statistics 2020-02-20 Tor Lattimore , Csaba Szepesvari , Gellert Weisz

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Let f be a Boolean function with…

Computational Complexity · Computer Science 2020-08-04 Nikhil S. Mande , Swagato Sanyal

We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…

Logic in Computer Science · Computer Science 2021-06-22 Carol Mak , C. -H. Luke Ong , Hugo Paquet , Dominik Wagner

The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is $\varepsilon$-far from having that property. We investigate here several types of properties…

Quantum Physics · Physics 2023-06-22 Zhengwei Xie , Daowen Qiu , Guangya Cai , Jozef Gruska , Paulo Mateus

We give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some…

Data Structures and Algorithms · Computer Science 2024-04-23 Shivam Nadimpalli , Shyamal Patel

A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…

Data Structures and Algorithms · Computer Science 2015-04-08 Ishay Haviv , Oded Regev

We prove that the Fourier dimension of any Boolean function with Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof method yields an improved bound of $\widetilde{O}(\sqrt{s})$ assuming a conjecture of…

Computational Complexity · Computer Science 2014-07-15 Swagato Sanyal

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

Machine Learning · Computer Science 2018-11-26 Yu Cheng , Ilias Diakonikolas , Rong Ge