6 papers
Quasi-Monte Carlo Beyond Hardy-Krause II: Samples Suffice
Ekene Ezeunala, Agastya Vibhuti Jha, Haotian Jiang
Numerical integration studies how well one can estimate the integral of a function over using sample points. The two classical methods, Monte Carlo (MC) and quasi…
A Simpler Analysis of the Bansal-Jiang Quasi Monte-Carlo Algorithm via Haar Wavelets
Jiaheng Chen, Agastya Vibhuti Jha, Haotian Jiang
Numerical integration---approximating the integral of a function using point evaluations---is a central task in science and engineering. The two main paradigms for this pro…
An Exposition of the Bound for the Komlós Problem
Nikhil Bansal, Haotian Jiang
A conjecture of Komlós states that the combinatorial discrepancy of any matrix whose columns have Euclidean norm at most one is bounded by a universal c…
Near-Optimal Constructive Bounds for Prefix Discrepancy and Steinitz Problems via Affine Spectral Independence
Kunal Dutta, Agastya Vibhuti Jha, Haotian Jiang
A classical result of Steinitz from 1913 \cite{Ste13}, answering an earlier question of Riemann and Lévy (e.g., \cite{Lev05}), states that for any norm in $\mathbb{R}^d…
Decoupling via Affine Spectral-Independence: Beck-Fiala and Komlós Bounds Beyond Banaszczyk
Nikhil Bansal, Haotian Jiang
The Beck-Fiala Conjecture [Discrete Appl. Math, 1981] asserts that any set system of elements with degree has combinatorial discrepancy . A substantial general…
An Improved Bound for the Beck-Fiala Conjecture
Nikhil Bansal, Haotian Jiang
In 1981, Beck and Fiala [Discrete Appl. Math, 1981] conjectured that given a set system with degree at most (i.e., each column of has at most $…