# Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive Filtering

arXiv: https://arxiv.org/abs/1608.00441 · HTML: https://mlsanity.com/paper/1608.00441/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2016.

## Built on by (most cited first, 3 of 3)

- [Error Loss Networks](https://mlsanity.com/paper/2106.03722/) (2021)
- [Study of Proximal Normalized Subband Adaptive Algorithm for Acoustic Echo Cancellation](https://mlsanity.com/paper/2108.10219/) (2021)
- [Study of General Robust Subband Adaptive Filtering](https://mlsanity.com/paper/2208.08856/) (2022)

## Abstract (arXiv)

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian signal processing and machine learning. In this work, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.