# Contrast and Boosted Trees

#### Jerome Friedman

#### 2023-11-21

Contrast trees are used to assess the accuracy of many types of machine learning estimates that are not amenable to standard validation techniques. These include properties of the conditional distribution \(p_{y}(y\,|\,\mathbf{x})\) (means, quantiles, complete distribution) as functions of \(\mathbf{x}\). Given a set of predictor variables \(\mathbf{x}=(x_{1},x_{2},\)\(,x_{p})\) and two outcome variables \(y\) and \(z\) associated with each \(\mathbf{x}\), a contrast tree attempts to partition the space of \(\mathbf{x}\) values into local regions within which the respective distributions of \(y\,|\,\mathbf{x}\) and \(z\,|\,\mathbf{x}\), or selected properties of those distributions such as means or quantiles, are most different.

## A Tutorial

1. Introduction
2. Examples
3. Package Function Reference