# Non-parametric Quantile Regression via the K-NN Fused Lasso

arXiv: https://arxiv.org/abs/2012.01758 · HTML: https://mlsanity.com/paper/2012.01758/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Multivariate Trend Filtering for Lattice Data](https://mlsanity.com/paper/2112.14758/) (2021)
- [Variance estimation in graphs with the fused lasso](https://mlsanity.com/paper/2207.12638/) (2022)
- [Varying-coefficients for regional quantile via KNN-based LASSO with applications to health outcome study](https://mlsanity.com/paper/2308.04212/) (2023)
- [Risk Bounds For Distributional Regression](https://mlsanity.com/paper/2505.09075/) (2025)

## Abstract (arXiv)

Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than l2-based methods. By using the fused lasso penalty over a K-nearest neighbors graph, we propose an adaptive quantile estimator in a non-parametric setup. We show that the estimator attains optimal rate of n-1/d up to a logarithmic factor, under mild assumptions on the data generation mechanism of the d-dimensional data. We develop algorithms to compute the estimator and discuss methodology for model selection. Numerical experiments on simulated and real data demonstrate clear advantages of the proposed estimator over state of the art methods.