On Estimation of Conditional Modes Using Multiple Quantile Regressions

TL;DR

This paper introduces a new method for estimating the conditional mode in high-dimensional settings by leveraging multiple quantile regressions to estimate the conditional density, offering computational stability and statistical efficiency.

Contribution

It presents a novel approach that combines quantile regressions to estimate the conditional density and then finds the mode, improving stability and efficiency over existing methods.

Findings

Outperforms existing methods in synthetic data experiments

Demonstrates effectiveness on real-world datasets

Achieves fast convergence and computational stability

Abstract

We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate the conditional mode by finding the maximum of the estimated conditional density. The proposed method has two advantages in that it is computationally stable because it has no initial parameter dependencies, and it is statistically efficient with a fast convergence rate. Synthetic and real-world data experiments demonstrate the better performance of the proposed method compared to other existing ones.