条件 Cauchy-Schwarz 散度及其在时间序列数据和序贯决策中的应用
The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making
AI总结：
本文提出可由核密度估计的条件 CS 散度，用于衡量条件分布接近度，并在时间序列聚类与不确定性引导的序贯决策探索中验证其优势。
摘要：
Cauchy-Schwarz（CS）散度由 Príncipe 等人于 2000 年提出。本文将经典 CS 散度扩展，用于量化两个条件分布之间的接近程度，并表明所提出的条件 CS 散度可以根据给定样本通过核密度估计器简单地进行估计。我们阐述了条件 CS 散度相对于条件 KL 散度和条件最大均值差异等既有方法的优势，例如严格的保真性保证、更低的计算复杂度、更高的统计功效，以及在广泛应用中更强的灵活性。我们还展示了条件 CS 散度在两个与时间序列数据和序贯推断相关的机器学习任务中的出色性能，即时间序列聚类和序贯决策中由不确定性引导的探索。条件 CS 散度的代码可在 https://github.com/SJYuCNEL/conditional_CS_divergence 获取。
英文摘要：
The Cauchy-Schwarz (CS) divergence was developed by Príncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS divergence can be simply estimated by a kernel density estimator from given samples. We illustrate the advantages (e.g., rigorous faithfulness guarantee, lower computational complexity, higher statistical power, and much more flexibility in a wide range of applications) of our conditional CS divergence over previous proposals, such as the conditional KL divergence and the conditional maximum mean discrepancy. We also demonstrate the compelling performance of conditional CS divergence in two machine learning tasks related to time series data and sequential inference, namely time series clustering and uncertainty-guided exploration for sequential decision making. The code of conditional CS divergence is available at https://github.com/SJYuCNEL/conditional_CS_divergence.
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