The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making
This provides a more efficient and flexible divergence measure for conditional distributions, useful for researchers and practitioners working with time-series data and sequential decision making, though it is an incremental extension of an existing method.
The authors extended the classic Cauchy-Schwarz divergence to quantify closeness between conditional distributions, showing it can be estimated via kernel density estimators and demonstrating advantages like rigorous faithfulness guarantees and lower computational complexity over alternatives. They applied it to time series clustering and uncertainty-guided exploration for sequential decision making, showing compelling performance.
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.