Introduction to Machine Learning Classification and Regression Trees - PowerPoint PPT Presentation

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Introduction to Machine Learning Classification and Regression Trees (CART): Basics compstat-lmu.github.io/lecture_i2ml TREE MODEL AND PREDICTION Classification and Regression Trees, introduced by Breiman Binary splits are constructed top-down

Introduction to Machine Learning Classification and Regression Trees (CART): Basics compstat-lmu.github.io/lecture_i2ml
TREE MODEL AND PREDICTION Classification and Regression Trees, introduced by Breiman Binary splits are constructed top-down Constant prediction in each terminal node (leaf): either a numerical value, a class label or a probability vector over class labels. � c Introduction to Machine Learning – 1 / 5
TREE MODEL AND PREDICTION For predictions, observations are passed down the tree, according to the splitting rules in each node An observation will end up in exactly one leaf node All observations in a leaf node are assigned the same prediction for the target � c Introduction to Machine Learning – 2 / 5
TREE MODEL AND PREDICTION For predictions, observations are passed down the tree, according to the splitting rules in each node An observation will end up in exactly one leaf node All observations in a leaf node are assigned the same prediction for the target -1.20 -0.42 0.98 -0.20 -0.01 � c Introduction to Machine Learning – 3 / 5
TREES AS AN ADDITIVE MODEL Each point in X is assigned to exactly one leaf, and each leaf has a set of input points leading to it, through axis-parallel splits. Hence, trees divide the feature space X into rectangular regions : M � f ( x ) = c m I ( x ∈ Q m ) , m = 1 where a tree with M leaf nodes defines M “rectangles” Q m . c m is the predicted numerical response, class label or class distribution in the respective leaf node. Iris Data 2.5 Species 2.0 Petal.Width ● setosa 1.5 versicolor 1.0 virginica ● 0.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 2 4 6 Petal.Length � c Introduction to Machine Learning – 4 / 5
TREES The hypothesis space of a CART is the set of all step functions over rectangular partitions of X : M � f ( x ) = c m I ( x ∈ Q m ) , m = 1 Classification: Regression: Iris Data 2.5 -1.20 -0.42 0.98 -0.20 -0.01 2.0 Species Petal.Width 1.5 ● setosa versicolor 1.0 virginica ● 0.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 2 4 6 Petal.Length � c Introduction to Machine Learning – 5 / 5

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