# Robust Local Polynomial Regression with Similarity Kernels

arXiv: https://arxiv.org/abs/2501.10729 · HTML: https://mlsanity.com/paper/2501.10729/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 18 Jan 2025.

## Builds on (most cited first, 2 of 2)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Robust nonparametric regression: review and practical considerations](https://mlsanity.com/paper/2211.08376/) (2022)

## Abstract (arXiv)

Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of the data, weighted by proximity. However, traditional LPR is sensitive to outliers and high-leverage points, which can significantly affect estimation accuracy. This paper revisits the kernel function used to compute regression weights and proposes a novel framework that incorporates both predictor and response variables in the weighting mechanism. The focus of this work is a conditional density kernel that robustly estimates weights by mitigating the influence of outliers through localized density estimation. The proposed method is implemented in Python and is publicly available at https://github.com/yaniv-shulman/rsklpr. The population analysis quantifies the bias induced by density-based robust weighting, and the reported experiments show lower empirical bias than iterative robust LOWESS while remaining competitive with standard LOWESS. This advancement provides a promising extension to traditional LPR, opening new possibilities for robust regression applications.