Dimension reduction in semi-supervised multiple quantile regression

Music City Center 

In this work, we propose a new semi-supervised method for multiple quantile regression method . Traditional multiple quantile regression methods often have the problem of quantile crossing, where a lower quantile estimate ends up being higher than a larger quantile estimate. To address this, we introduce a non-crossing penalty term that enforces the natural ordering of quantiles. Our framework natural allows for regularization of the regression coefficient matrix. To compute our estimator, we utilize a splitting algorithm. In simulation studies, we show that our method can lead to improved performance over existing estimators.

Alternating direction method of multipliers

Constrained optimization

Quantile regression

Dimension reduction 

Section on Statistical Learning and Data Science