# 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

![](https://1687157657-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FKLjYi16C9OsVCRdrTcrH%2Fuploads%2Fx4npyORC3mjEImjHQ3hg%2FScreenshot%202023-06-04%20at%2011.20.36%20AM.png?alt=media\&token=48b97280-3eac-4ebf-bc98-3cf88d1fd1dd)





