Quantile Regression

Quantile regression estimates how different parts of an outcome distribution change with input features, rather than modeling only the average. Common approaches minimize pinball loss using linear models, kernels, trees, or neural networks, with extensions for multiple quantiles, online learning, and high-dimensional data. These estimates support uncertainty-aware forecasting, survival analysis, causal studies, and risk-sensitive decisions, while statistical inference and conformal methods help assess their reliability. Key challenges include accurate extreme-tail estimates, preventing quantile crossings, and maintaining calibration under dependence, distribution shift, or limited data.