Consistency of permutation tests for HSIC and dHSIC

Kernel-based Tests for Joint Independence

We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but allows for an arbitrary number of variables. We embed the $d$-dimensional joint distribution and the product of the marginals into a reproducing kernel Hilbert space and define the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) as the squared distance between the embeddings. In the population case, the value of dHSIC is zero if and only if the $…

A Permutation-Free Kernel Independence Test

In nonparametric independence testing, we observe i.i.d.\ data $\{(X_i,Y_i)\}_{i=1}^n$, where $X \in \mathcal{X}, Y \in \mathcal{Y}$ lie in any general spaces, and we wish to test the null that $X$ is independent of $Y$. Modern test statistics such as the kernel Hilbert-Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics. Thus, in practice, one often resorts to using permutation testing, which provides a nonasymptotic guarantee at the expense of recalculating the quadratic-time statistics …

差分隐私联合独立性检验

Differentially Private Joint Independence Test

针对隐私约束下的多随机向量联合依赖检测问题，提出基于差分隐私置换的dHSIC检验方法，实现有效水平、点态一致性和极小极大最优功效。

基于HSIC的混合不确定性灵敏度分析：面向具有偶然-认知分离的高维响应

Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation

提出双空间张量积RKHS框架，通过分解核函数和双重Möbius反演，将全局依赖度量正交分解为纯偶然效应、纯认知效应及其交互贡献，实现高维响应下混合不确定性的灵敏度分析。

Efficient Aggregated Kernel Tests using Incomplete $U$-statistics

We propose a series of computationally efficient nonparametric tests for the two-sample, independence, and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC), and Kernel Stein Discrepancy (KSD), respectively. Our test statistics are incomplete $U$-statistics, with a computational cost that interpolates between linear time in the number of samples, and quadratic time, as associated with classical $U$-statistic tests. The three proposed tests aggregate over several kernel bandwidths to detect departures from the null on various scale…

廉价排列检验

Cheap Permutation Testing

研究如何加速排列检验，提出将数据点分组为箱并仅对箱排列的方法，证明该廉价排列检验对U和V统计量有运行快、功效近似标准检验的特性，继承了标准检验的优点且优于多种其他检验。