# Quantile Regression for Large-scale Applications

arXiv: https://arxiv.org/abs/1305.0087 · HTML: https://mlsanity.com/paper/1305.0087/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2013.

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

- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Efficient Strongly Polynomial Algorithms for Quantile Regression](https://mlsanity.com/paper/2307.08706/) (2023)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)

## Abstract (arXiv)

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and, with appropriate preprocessing, interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, emph(e.g.), involving data up to and beyond the terabyte regime, remains a challenge. Here, we present a randomized algorithm that runs in nearly linear time in the size of the input and that, with constant probability, computes a (1+ε) approximate solution to an arbitrary quantile regression problem. As a key step, our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that in addition it can be implemented in MapReduce-like environments and applied to terabyte-sized problems.