On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Kernel methods in Reproducing Kernel Hilbert Space (RKHS) learning face challenges with selecting optimal training data points for kernel functions.
• Traditional squared norm penalties in RKHS do not inherently perform data selection, potentially impacting model efficiency and performance.

Purpose of the Study:

• To address the issue of training data selection in RKHS learning by proposing a novel data sparsity constraint.
• To investigate the effectiveness of this data sparsity constraint in the context of quantile regression.

Main Methods:

• A data sparsity constraint is proposed, which involves thresholding kernel function coefficients to achieve a sparse kernel representation.
• The method is applied to quantile regression, a specific application within RKHS learning.

Main Results:

• The proposed data sparsity method demonstrates competitive prediction performance in certain scenarios.
• Its performance is comparable to traditional squared norm penalty methods in other cases.
• Theoretical properties of the data sparsity constraint method were derived.

Conclusions:

• The data sparsity constraint offers a competitive alternative to the traditional squared norm penalty for RKHS learning.
• The method's usefulness is validated through simulations and real-world data analysis.