发表机构
University of Greenwich（格林威治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于Kolmogorov-Arnold网络集成的新算法，用于预测随机系统中向量值目标的联合分布，并引入新的差异度量及拟合优度检验以验证和校准该识别技术。
AI 中文摘要
本文提出了一种新颖的算法，用于预测随机系统中向量值目标的条件联合分布，其中随机性本质上是内在的，而非源于观测误差或加性噪声。多变量分位数回归也涉及对条件联合分布的建模，但这是一个相对不那么具有挑战性的任务。它预测向量值目标落入预定义区域的概率，识别与预定义概率水平相对应的区域，或同时执行这两项任务。所提出的识别技术采用Kolmogorov-Arnold网络（KANs）的集成作为灵活的函数逼近器。尽管所提出的技术在理论上并不局限于KANs，但KANs特别适合所提出的构造，因此在整个研究中使用。除了训练过程外，这项工作还引入了一种新的联合分布差异度量以及基于该度量的拟合优度（GoF）检验。该GoF检验最初是为了验证和校准所提出的识别技术而开发的，在此处以特设方式使用。尽管该检验可以制成表格以供更广泛使用，但本文未进行此类制表。该检验也适用于更一般的情况。
英文摘要
This paper introduces a novel algorithm for predicting conditional joint distributions of vector-valued targets in stochastic systems whose randomness is intrinsic rather than arising from observation errors or additive noise. Multivariate quantile regression also involves modeling conditional joint distributions but represents a less challenging task. It predicts the probability that vector-valued targets fall within predefined regions, identifies regions corresponding to predefined probability levels, or performs both tasks simultaneously. The proposed identification technique employs ensembles of Kolmogorov--Arnold networks (KANs) as flexible function approximators. Although the suggested technique is not theoretically restricted to KANs, KANs are particularly well suited to the proposed construction and are therefore used throughout this study. In addition to the training procedure, this work introduces a new discrepancy measure for joint distributions and a goodness-of-fit (GoF) test based on it. This GoF test was initially developed to validate and calibrate the proposed identification technique and is used here in an ad hoc manner. Although the test could be tabulated for broader use, such a tabulation is not pursued in this work. The test is also applicable more generally.
