Citation

Steven Siwei Ye and Oscar Hernan Madrid Padilla. Non-parametric quantile regression via the K-NN fused lasso. Journal of Machine Learning Research, Vol. 22, No. 111, 1-38, 2021.

Codes

• linear programming
• ADMM and ADMM with BIC model selection
• Majorize-Minimize
• K-NN fused lasso

Note that all algorithms require the usage of nearestneighbour.m by Richard Brown. See details in https://www.mathworks.com/matlabcentral/fileexchange/12574-nearestneighbour-m.

For ADMM, we use parametric max-flow algorithm from "On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows" by Antonin Chambolle and Jérôme Darbon (https://link.springer.com/article/10.1007/s11263-009-0238-9). Users need to compile "TVexact" first to enable the "graphtv" function.

Datasets

• California housing data
• Chicago crime data

Demo

• comparison between quantile K-NN fused lasso and K-NN fused lasso