Quantile Regression: Linear Optimization

This lecture covers the concept of quantile regression, focusing on linear optimization to find the coefficient vector and threshold for predicting outputs. It discusses the use of absolute and squared loss functions, their sensitivity to outliers, and the empirical estimation of quantiles. The lecture also delves into the optimization problem formulation, the dual problem, and the regularization techniques. Practical implementation and comparison with least-squares regression are demonstrated through solving empirical problems. Additionally, it explores the application of quantile regression in electricity price prediction and image reconstruction, emphasizing total variation regularization for denoising and reconstruction.