# Nonparametric modal regression

arXiv: https://arxiv.org/abs/1412.1716 · HTML: https://mlsanity.com/paper/1412.1716/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2014.

## Built on by (most cited first, 8 of 8)

- [Convergence Analysis of Mean Shift](https://mlsanity.com/paper/2305.08463/) (2023)
- [Uniform Consistency in Nonparametric Mixture Models](https://mlsanity.com/paper/2108.14003/) (2021)
- [Adaptive Conditional Quantile Neural Processes](https://mlsanity.com/paper/2305.18777/) (2023)
- [Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm](https://mlsanity.com/paper/2104.10103/) (2021)
- [Regularized Modal Regression on Markov-dependent Observations: A Theoretical Assessment](https://mlsanity.com/paper/2112.04779/) (2021)
- [Generative Distribution Prediction: A Unified Approach to Multimodal Learning](https://mlsanity.com/paper/2502.07090/) (2025)
- [Bump hunting through density curvature features](https://mlsanity.com/paper/2208.00174/) (2022)
- [A Monotone Single-Index Modal Regression Powered by Deep Neural Networks for Non-Gaussian Periodontal Data](https://mlsanity.com/paper/2505.02153/) (2025)

## Abstract (arXiv)

Modal regression estimates the local modes of the distribution of Y given X=x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of Y and X. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is used to select the smoothing bandwidth of the underlying KDE. The idea behind modal regression is connected to many others, such as mixture regression and density ridge estimation, and we discuss these ties as well.