独立性检验的大规模核方法
Large-Scale Kernel Methods for Independence Testing
摘要：
再生核希尔伯特空间中的概率测度表示为独立性的完全非参数假设检验提供了一个灵活的框架，它可以捕获任何类型的独立性偏离，包括非线性关联和多变量相互作用。然而，这些方法在观测的数量上具有至少二次的计算成本，这在许多应用中可能是禁止的。可以说，正是在这种大规模的数据集，捕捉任何类型的依赖是感兴趣的，所以罢工之间的计算效率和测试性能内核独立性测试的有利的权衡将有直接影响其在实践中的适用性。在这方面的贡献，我们提供了一个广泛的研究使用大规模的内核近似的独立性测试，对比基于块，Nystrom和随机傅立叶特征的方法。通过各种合成数据的实验，它表明，我们的新的大规模的方法提供了与现有的方法相当的性能，同时使用显着更少的计算时间和内存。
英文摘要：
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including nonlinear associations and multivariate interactions. However, these approaches come with an at least quadratic computational cost in the number of observations, which can be prohibitive in many applications. Arguably, it is exactly in such large-scale datasets that capturing any type of dependence is of interest, so striking a favourable tradeoff between computational efficiency and test performance for kernel independence tests would have a direct impact on their applicability in practice. In this contribution, we provide an extensive study of the use of large-scale kernel approximations in the context of independence testing, contrasting block-based, Nystrom and random Fourier feature approaches. Through a variety of synthetic data experiments, it is demonstrated that our novel large scale methods give comparable performance with existing methods whilst using significantly less computation time and memory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
