The paper introduces robust independence tests with non-asymptotically
guaranteed significance levels for stochastic linear time-invariant systems,
assuming that the observed outputs are synchronous, which means that the
systems are driven by jointly i.i.d. noises. Our method provides bounds for the
type I error probabilities that are distribution-free, i.e., the innovations
can have arbitrary distributions. The algorithm combines confidence region
estimates with permutation tests and general dependence measures, such as the
Hilbert-Schmidt independence criterion and the distance covariance, to detect
any nonlinear dependence between the observed systems. We also prove the
consistency of our hypothesis tests under mild assumptions and demonstrate the
ideas through the example of autoregressive systems.

该论文引入了具有非渐近显著性水平保证的鲁棒独立性检验，假设观测输出是同步的，这意味着系统受到联合独立和同分布噪声的驱动。我们的方法提供了分布无关的第一类错误概率的界限，即创新可以具有任意分布。该算法将置信区间估计与排列检验和一般的依赖度量（如 Hilbert-Schmidt 独立性准则和距离协方差）结合在一起，用于检测观测系统之间的任何非线性依赖关系。我们还证明了我们的假设检验的一致性在温和的假设下，并通过自回归系统的示例演示了这些思想。

用于同步随机线性系统的具有有限样本保证的鲁棒独立性检验

Robust Independence Tests with Finite Sample Guarantees for Synchronous  Stochastic Linear Systems

We consider the problem of inferring causal relationships between two or more
passively observed variables. While the problem of such causal discovery has
been extensively studied especially in the bivariate setting, the majority of
current methods assume a linear causal relationship, and the few methods which
consider non-linear dependencies usually make the assumption of additive noise.
Here, we propose a framework through which we can perform causal discovery in
the presence of general non-linear relationships. The proposed method is based
on recent progress in non-linear independent component analysis and exploits
the non-stationarity of observations in order to recover the underlying sources
or latent disturbances. We show rigorously that in the case of bivariate causal
discovery, such non-linear ICA can be used to infer the causal direction via a
series of independence tests. We further propose an alternative measure of
causal direction based on asymptotic approximations to the likelihood ratio, as
well as an extension to multivariate causal discovery. We demonstrate the
capabilities of the proposed method via a series of simulation studies and
conclude with an application to neuroimaging data.

研究非线性关系下的因果发现问题，提出基于非线性独立成分分析的方法，通过一系列独立性检验来推断具有双边因果关系的变量之间的因果方向，并扩展到多变量因果发现，最终通过神经成像数据证明该方法的有效性。