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It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights $(1-|z|)^{-c}, \ 0\leq c<…

Functional Analysis · Mathematics 2025-04-16 David Norrbo

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…

Computational Complexity · Computer Science 2023-12-13 Marcel Dall'Agnol , Tom Gur , Oded Lachish

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

The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…

Machine Learning · Computer Science 2021-01-14 Tsimboy Olga , Yermek Kapushev , Evgeny Burnaev , Ivan Oseledets

Compositional verification algorithms are well-studied in the context of model checking. Properly selecting components for verification is important for efficiency, yet has received comparatively less attention. In this paper, we address…

Formal Languages and Automata Theory · Computer Science 2024-08-19 Ian Dardik , April Porter , Eunsuk Kang

We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ and sampling oracle access to an unknown distribution…

Discrete Mathematics · Computer Science 2015-11-12 Xi Chen , Jinyu Xie

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Combinatorics · Mathematics 2021-10-15 Bingchen Qian , Xin Wang , Gennian Ge

Meta-learning and few-shot prompting are viable methods to induce certain types of compositional behaviour. However, these methods can be very sensitive to the choice of support examples used. Choosing good supports from the training data…

Computation and Language · Computer Science 2024-10-15 Sam Spilsbury , Pekka Marttinen , Alexander Ilin

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

Data Structures and Algorithms · Computer Science 2020-09-15 Ilias Diakonikolas , Themis Gouleakis , Daniel M. Kane , John Peebles , Eric Price

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

Compositionality supports the manipulation of large systems by working on their components. For model-based testing, this means that large systems can be tested by modelling and testing their components: passing tests for all components…

Software Engineering · Computer Science 2025-08-01 Gijs van Cuyck , Lars van Arragon , Jan Tretmans

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to…

Machine Learning · Computer Science 2017-11-28 Mostafa Rahmani , George Atia

For the purpose of proving the strong openness conjecture of multiplier ideal sheaves, Jonsson-Musta\c{t}\u{a} posed an enhanced conjecture and proved the two-dimensional case, which says that: the Lebesgue measure of the set…

Complex Variables · Mathematics 2024-04-02 Shijie Bao , Qi'an Guan , Zheng Yuan

Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…

Logic in Computer Science · Computer Science 2024-05-24 Mayuko Kori , Kazuki Watanabe , Jurriaan Rot , Shin-ya Katsumata

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Machine Learning · Computer Science 2021-03-23 Rui Zhang , Hongyuan Zhang , Xuelong Li

It is preferred that feature selectors be \textit{stable} for better interpretabity and robust prediction. Ensembling is known to be effective for improving the stability of feature selectors. Since ensembling is time-consuming, it is…

Machine Learning · Computer Science 2021-08-04 Rina Onda , Zhengyan Gao , Masaaki Kotera , Kenta Oono

We give new proofs for the hardness amplification of efficiently samplable predicates and of weakly verifiable puzzles which generalize to new settings. More concretely, in the first part of the paper, we give a new proof of Yao's XOR-Lemma…

Cryptography and Security · Computer Science 2010-12-30 Thomas Holenstein , Grant Schoenebeck

We introduce a new model for testing graph properties which we call the \emph{rejection sampling model}. We show that testing bipartiteness of $n$-nodes graphs using rejection sampling queries requires complexity $\widetilde{\Omega}(n^2)$.…

Computational Complexity · Computer Science 2018-05-04 Amit Levi , Erik Waingarten

A function $f\colon\{0,1\}^n\to \{0,1\}$ is called an approximate AND-homomorphism if choosing ${\bf x},{\bf y}\in\{0,1\}^n$ randomly, we have that $f({\bf x}\land {\bf y}) = f({\bf x})\land f({\bf y})$ with probability at least…

Discrete Mathematics · Computer Science 2019-11-04 Yuval Filmus , Noam Lifshitz , Dor Minzer , Elchanan Mossel

A combinatorial theory of associative $n$-categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising as a combinatorial notion of homotopy with a natural…

Category Theory · Mathematics 2019-02-12 David Reutter , Jamie Vicary