The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909537862156288 |
|---|---|
| author | Yu, Shujian Li, Hongming Løkse, Sigurd Jenssen, Robert Príncipe, José C. |
| author_facet | Yu, Shujian Li, Hongming Løkse, Sigurd Jenssen, Robert Príncipe, José C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08970 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making Yu, Shujian Li, Hongming Løkse, Sigurd Jenssen, Robert Príncipe, José C. Machine Learning Information Theory 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. |
| title | The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2301.08970 |