论文标题
在非线性动力学中推断出具有变化高斯工艺的非线性动力学统计数据
Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes
论文作者
论文摘要
伪造是检验现有假设的基础，当结果错误拒绝我们先前的概念（误报）时，就会构成巨大的危险。尽管发现耦合的非参数和非线性探索方法为研究网络配置提供了灵活的框架，但多次比较分析使误报更有可能，从而加剧了对其控制的需求。我们旨在通过变异贝叶斯高斯过程建模（VGP-CCM）来鲁棒性促进融合交叉映射（GP-CCM）方法。我们通过平均场近似值来减轻与条件高参数分布的集成的计算成本。该近似模型与零分布的置换采样结合，允许与点超参数的置换采样更强大的显着性统计。模拟的单向Lorenz-Rossler系统以及神经血管系统的机械模型用于评估该方法。结果表明，所提出的方法产生了提高的特异性，表明有望打击假阳性
Falsification is the basis for testing existing hypotheses, and a great danger is posed when results incorrectly reject our prior notions (false positives). Though nonparametric and nonlinear exploratory methods of uncovering coupling provide a flexible framework to study network configurations and discover causal graphs, multiple comparisons analyses make false positives more likely, exacerbating the need for their control. We aim to robustify the Gaussian Processes Convergent Cross-Mapping (GP-CCM) method through Variational Bayesian Gaussian Process modeling (VGP-CCM). We alleviate computational costs of integrating with conditional hyperparameter distributions through mean field approximations. This approximation model, in conjunction with permutation sampling of the null distribution, permits significance statistics that are more robust than permutation sampling with point hyperparameters. Simulated unidirectional Lorenz-Rossler systems as well as mechanistic models of neurovascular systems are used to evaluate the method. The results demonstrate that the proposed method yields improved specificity, showing promise to combat false positives
