Journal of Complexity最新文献

英文中文

Hammersley point sets and inverse of star-discrepancy 哈默斯利点集与星差逆

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-10-28 DOI: 10.1016/j.jco.2025.101998

Christian Weiß

We establish the existence of N-point sets in dimension d whose star-discrepancy is bounded above by

2.4631832 \sqrt{\frac{d}{N}}

, where the numerical constant improves upon all previously known bounds. This improvement is obtained by combining a recent result by Gnewuch on bracketing numbers in high dimensions with discrepancy bounds for Hammersley point sets due to Atanassov in dimensions

1 \leq d \leq 4

我们建立了d维n点集的存在性，其星差在上面的边界为2.4631832dN，其中的数值常数在所有已知的边界上都有所提高。这种改进是通过结合Gnewuch最近关于高维的括号数的结果和由于Atanassov在1≤d≤4维的Hammersley点集的差异界得到的。

引用次数: 0

Jonathan Siegel is the winner of the 2025 Joseph F. Traub Information-Based Complexity Young Researcher Award 乔纳森·西格尔是2025年约瑟夫·f·特劳布信息复杂性青年研究员奖的获得者

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-10-13 DOI: 10.1016/j.jco.2025.101996

Matthieu Dolbeault, Erich Novak, Kateryna Pozharska, Mathias Sonnleitner, Henryk Woźniakowski

引用次数: 0

Changes of the Editorial Board 编辑委员会的变动

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-10-13 DOI: 10.1016/j.jco.2025.101997

Josef Dick, Erich Novak, Friedrich Pillichshammer, Klaus Ritter, Jan Vybíral, Henryk Woźniakowski

引用次数: 0

Statistical analysis of prediction in functional polynomial quantile regression 函数多项式分位数回归预测的统计分析

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-24 DOI: 10.1016/j.jco.2025.101995

Hongzhi Tong

We consider in this paper the quantile regression in a functional polynomial model, where the conditional quantile of a scalar response is modeled by a polynomial of functional predictor. It extends beyond the standard functional linear setting to accommodate more general functional polynomial model. A Tikhonov regularized functional polynomial quantile regression approach is introduced and investigated. By utilizing some techniques of empirical processes, we establish the explicit convergence rates of the prediction error of the proposed estimator under mild assumptions.

本文考虑一个泛函多项式模型中的分位数回归，其中标量响应的条件分位数是用一个泛函预测器的多项式来建模的。它超越了标准的函数线性设置，以适应更一般的函数多项式模型。介绍并研究了一种吉洪诺夫正则泛函多项式分位数回归方法。利用经验过程的一些技巧，我们建立了在温和假设下所提出的估计量的预测误差的显式收敛速率。

引用次数: 0

A high-efficiency fourth-order iterative method for nonlinear equations: Convergence and computational gains 非线性方程的高效四阶迭代法：收敛性与计算增益

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-23 DOI: 10.1016/j.jco.2025.101994

Amir Naseem , Krzysztof Gdawiec , Sania Qureshi , Ioannis K. Argyros , Muhammad Aziz ur Rehman , Amanullah Soomro , Evren Hincal , Kamyar Hosseini , Ausif Padder

This study introduces an optimal fourth-order iterative method derived by combining two established methods, resulting in enhanced convergence when solving nonlinear equations. Through rigorous convergence analysis using both Taylor expansion and the Banach space framework, the fourth-order optimality condition is verified. We demonstrate the superior efficiency and stability of this new method compared to traditional alternatives. Numerical experiments confirm its effectiveness, showing a reduction in the average number of iterations and computational time. Visual analysis with polynomiographs confirms the method's robustness, focusing on convergence area index, iteration count, computational time, fractal dimension, and Wada measure of basins. These findings underscore the potential of this optimal method for tackling complex nonlinear problems in various scientific and engineering fields.

本文引入了一种将两种已有方法结合起来的四阶最优迭代方法，从而提高了求解非线性方程的收敛性。通过Taylor展开式和Banach空间框架的严格收敛分析，验证了四阶最优性条件。与传统方法相比，我们证明了这种新方法的效率和稳定性。数值实验证实了该方法的有效性，表明该方法减少了平均迭代次数和计算时间。在收敛面积指数、迭代次数、计算时间、分形维数和Wada测度等方面，通过多项式图的可视化分析证实了该方法的鲁棒性。这些发现强调了这种解决各种科学和工程领域复杂非线性问题的最佳方法的潜力。

引用次数: 0

Borell's inequality and mean width of random polytopes via discrete inequalities 离散不等式与随机多面体的平均宽度

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-22 DOI: 10.1016/j.jco.2025.101993

David Alonso-Gutiérrez, Luis C. García-Lirola

<div><div>Borell's inequality states the existence of a positive absolute constant <math><mi>C</mi><mo>></mo><mn>0</mn></math> such that for every <math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>q</mi></math><math><msup><mrow><mo>(</mo><mi>E</mi><mo>|</mo><mo>〈</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>〉</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup><mo>≤</mo><msup><mrow><mo>(</mo><mi>E</mi><mo>|</mo><mo>〈</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>〉</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac></mrow></msup><mo>≤</mo><mi>C</mi><mfrac><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></mfrac><msup><mrow><mo>(</mo><mi>E</mi><mo>|</mo><mo>〈</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>〉</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup><mo>,</mo></math> whenever X is a random vector uniformly distributed on any convex body <math><mi>K</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> and <math><msubsup><mrow><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math> is the standard canonical basis in <math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. In this paper, we will prove a discrete version of this inequality, which will hold whenever X is a random vector uniformly distributed on <math><mi>K</mi><mo>∩</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup></math> for any convex body <math><mi>K</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> containing the origin in its interior. We will also make use of such discrete version to obtain discrete inequalities from which we can recover the estimate <math><mi>E</mi><mi>w</mi><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>)</mo><mo>∼</mo><mi>w</mi><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>log</mi><mo>⁡</mo><mi>N</mi></mrow></msub><mo>(</mo><mi>K</mi><mo>)</mo><mo>)</mo></math> for any convex body K containing the origin in its interior, where <math><msub><mrow><mi>K</mi></mrow><mrow><mi>N</mi></mrow></msub></math> is the centrally symmetric random polytope <math><msub><mrow><mi>K</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>=</mo><mtext>conv</mtext><mo>{</mo><mo>±</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub

Borell不等式表明存在一个正的绝对常数C>；0，使得当X是均匀分布在任意凸体K≤Rn上的随机向量，且（ei）i=1n是Rn中的标准正则基时，对于每1≤p≤q(E b| < X,en > |p)1p≤(E| < X,en > |q)1q≤Cqp(E| < X,en > |p)1p。在本文中，我们将证明该不等式的一个离散版本，当X是一个均匀分布在K∩Zn上的随机向量时，对于任何在其内部包含原点的凸体K≠Rn，该不等式成立。我们还将利用这种离散版本来获得离散不等式，从中我们可以恢复对任何包含其内部原点的凸体K的估计Ew(KN) ~ w(Zlog ln N(K))，其中KN是由均匀分布在K上的独立随机向量生成的中心对称随机多面体KN=conv{±X1，…，±XN}, Zp(K)是K的任意p≥1的lp质心体，w（⋅）表示平均宽度。

引用次数: 0

Sampling and entropy numbers in the uniform norm 均匀范数中的抽样和熵数

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-16 DOI: 10.1016/j.jco.2025.101992

Mario Ullrich

We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.

在有界函数的有界凸集的一致范数中，证明了抽样数与熵数之间的一个锐界。

引用次数: 0

Generalization bounds of adversarial bipartite ranking with pairwise perturbation 对偶扰动下对抗性二部排序的概化界

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-10 DOI: 10.1016/j.jco.2025.101991

Wen Wen , Han Li , Yutao Hu , Lingjuan Wu , Hong Chen

Investigating the generalization and robustness of adversarial learning is an active research topic due to its implications in designing robust models for a wide range of machine learning tasks. In this paper, we aim to investigate the adversarially robust generalization of bipartite ranking against pairwise perturbation attacks from the lens of learning theory. We establish high-probability generalization error bounds of linear hypotheses and multi-layer neural networks for bipartite ranking under adversarial attacks, by developing Rademacher complexity over i.i.d. sample blocks and covering numbers. Our results provide a theoretical characterization of the interplay between generalization error and perturbation-related factors, revealing the important impact of feature dimension and weight regularization for achieving good generalization performance. Experimental results on real-world datasets validate the effectiveness of our theoretical findings.

研究对抗性学习的泛化和鲁棒性是一个活跃的研究课题，因为它对设计广泛的机器学习任务的鲁棒模型具有重要意义。本文从学习理论的角度出发，研究了对偶摄动攻击的二部排序的对抗性鲁棒泛化。我们建立了线性假设和多层神经网络的高概率泛化误差界，用于对抗性攻击下的二部排序，通过在iid样本块和覆盖数上发展Rademacher复杂度。我们的研究结果提供了泛化误差与扰动相关因素之间相互作用的理论表征，揭示了特征维数和权值正则化对实现良好泛化性能的重要影响。在实际数据集上的实验结果验证了我们理论发现的有效性。

引用次数: 0

Accelerated convergence of error quantiles using robust randomized quasi Monte Carlo methods 基于鲁棒随机拟蒙特卡罗方法的误差分位数加速收敛

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-02 DOI: 10.1016/j.jco.2025.101989

Emmanuel Gobet , Matthieu Lerasle , David Métivier

We aim to calculate an expectation

μ (F) = E (F (U))

for functions

F : {[0, 1]}^{d} \mapsto R

using a family of estimators

{\hat{μ}}_{B}

with a budget of B evaluation points. The standard Monte Carlo method achieves a root mean squared risk of order

1 / \sqrt{B}

, both for a fixed square integrable function F and for the worst-case risk over the class

F

of functions with

{‖ F ‖}_{L_{2}} \leq 1

. Using a sequence of Randomized Quasi Monte Carlo (RQMC) methods, in contrast, we achieve faster convergence

σ_{B} ≪ 1 / \sqrt{B}

for the risk

σ_{B} = σ_{B} (F)

when fixing a function F, compared to the worst-case risk which is still of order

1 / \sqrt{B}

. We address the convergence of quantiles of the absolute error, namely, for a given confidence level

1 - δ

this is the minimal ε such that

P (| {\hat{μ}}_{B} (F) - μ (F) | > ε) \leq δ

holds. We show that a judicious choice of a robust aggregation method coupled with RQMC methods allows reaching improved convergence rates for ε depending on δ and B when fixing a function F. This study includes a review on concentration bounds for the empirical mean as well as sub-Gaussian mean estimates and is supported by numerical experiments, ranging from bounded F to heavy-tailed

F (U)

, the latter being well suited to functions F with a singularity. The different methods we have tested are available in a Julia package.

我们的目标是用一组估计量μ μ B计算函数F:[0,1]d∈R的期望μ(F)=E（F(U)）。对于固定平方可积函数F和‖F‖L2≤1的函数的F类的最坏情况风险，标准蒙特卡罗方法均可获得1/B阶的均方根风险。相比之下，使用随机化拟蒙特卡罗（RQMC）方法序列，我们在确定函数F时，对σB=σB(F)的风险实现了更快的收敛σB≪1/B，而最坏情况的风险仍为1/B阶。我们处理绝对误差的分位数的收敛性，即对于给定的置信水平1 - δ，这是使P(|μ δ B(F)−μ(F)|>ε)≤δ成立的最小ε。我们表明，在固定函数F时，明智地选择鲁棒聚合方法与RQMC方法相结合，可以提高ε依赖于δ和B的收敛率。该研究包括对经验均值和亚高斯均值估计的浓度界的回顾，并得到数值实验的支持，范围从有界F到重尾F(U)，后者非常适合具有奇点的函数F。我们测试过的不同方法都可以在Julia包中找到。

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引用次数: 0

On the packing functions of some linear sets of Lebesgue measure zero 若干Lebesgue测度为0的线性集的填充函数

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-09-01 DOI: 10.1016/j.jco.2025.101990

Austin Anderson , Steven Damelin

We use a characterization of Minkowski measurability to study the asymptotics of best packing on cut-out subsets of the real line with Minkowski dimension

d \in (0, 1)

. Our main result is a proof that Minkowski measurability is a sufficient condition for the existence of best packing asymptotics on monotone rearrangements of these sets. For each such set, the main result provides an explicit constant of proportionality

p_{d}

, depending only on the Minkowski dimension d, that relates its packing limit and Minkowski content. We later use the Digamma function to study the limiting value of

p_{d}

d \to 1^{-}

. This study further provides two sharpness results illustrating the necessity of the hypotheses of the main result. Finally, the aforementioned characterization of Minkowski measurability motivates the asymptotic study of an infinite multiple subset sum problem.

我们利用Minkowski可测性的一个表征，研究了Minkowski维数d∈(0,1)的实线切出子集上的最佳填充的渐近性。我们的主要结果证明了Minkowski可测性是这些集合单调重排上存在最佳填充渐近的充分条件。对于每一个这样的集合，主要结果提供了一个显式的比例常数pd，仅依赖于闵可夫斯基维d，它将其包装极限与闵可夫斯基含量联系起来。我们随后利用Digamma函数研究了d→1−时pd的极限值。本研究进一步提供了两个清晰的结果，说明了主要结果假设的必要性。最后，上述闵可夫斯基可测性的表征激励了无穷多子集和问题的渐近研究。

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引用次数: 0

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Journal of Complexity

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