Conformalized Quantile Regression

Heteroscedasticity

Conditional quantiles

Oracle predictions

Quantile regression

• pinball loss?

Multiple deep quantile regression models

Quantile regression in action

We can fit conditional quantiles but without guarantees.

Generalized residuals for quantile regression

residuals as $Z_i = |Y_i - \hat{f}(X_i)|$ ? no... we need a difference score we would like to have $Z_i < 0$ when you have the correct prediction inside the $[\hat{q}_{\alpha/2}(X_i), \hat{q}_{\alpha}(X_i)]$

Split conformal + quantile regression