smile.base.cart

Class CART

java.lang.Object

smile.base.cart.CART

All Implemented Interfaces:

java.io.Serializable, SHAP<smile.data.Tuple>

Direct Known Subclasses:

DecisionTree, RegressionTree

public abstract class CART
extends java.lang.Object
implements SHAP<smile.data.Tuple>, java.io.Serializable

Classification and regression tree.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected smile.data.formula.Formula	formula The model formula.
protected double[]	importance Variable importance.
protected int[]	index An index of samples to their original locations in training dataset.
protected int	maxDepth The maximum depth of the tree.
protected int	maxNodes The maximum number of leaf nodes in the tree.
protected int	mtry The number of input variables to be used to determine the decision at a node of the tree.
protected int	nodeSize The number of instances in a node below which the tree will not split, setting nodeSize = 5 generally gives good results.
protected int[][]	order An index of training values.
protected smile.data.type.StructField	response The schema of response variable.
protected Node	root The root of decision tree.
protected int[]	samples The samples for training this node.
protected smile.data.type.StructType	schema The schema of predictors.
protected smile.data.DataFrame	x The training data.

Constructor Summary

Constructors

Constructor and Description
CART(smile.data.DataFrame x, smile.data.type.StructField y, int maxDepth, int maxNodes, int nodeSize, int mtry, int[] samples, int[][] order) Constructor.
CART(smile.data.formula.Formula formula, smile.data.type.StructType schema, smile.data.type.StructField response, Node root, double[] importance) Constructor.

Method Summary

Modifier and Type	Method and Description
protected void	clear() Clear the workspace of building tree.
java.lang.String	dot() Returns the graphic representation in Graphviz dot format.
protected abstract java.util.Optional<Split>	findBestSplit(LeafNode node, int column, double impurity, int lo, int hi) Finds the best split for given column.
protected java.util.Optional<Split>	findBestSplit(LeafNode node, int lo, int hi, boolean[] unsplittable) Finds the best attribute to split on a set of samples.
double[]	importance() Returns the variable importance.
protected abstract double	impurity(LeafNode node) Returns the impurity of node.
protected abstract LeafNode	newNode(int[] nodeSamples) Creates a new leaf node.
static int[][]	order(smile.data.DataFrame x) Returns the index of ordered samples for each ordinal column.
protected smile.data.Tuple	predictors(smile.data.Tuple x) Returns the predictors by the model formula if it is not null.
Node	root() Returs the root node.
double[]	shap(smile.data.DataFrame data) Returns the average of absolute SHAP values over a data frame.
double[]	shap(smile.data.Tuple x) Returns the SHAP values.
int	size() Returns the number of nodes in the tree.
protected boolean	split(Split split, java.util.PriorityQueue<Split> queue) Split a node into two children nodes.
java.lang.String	toString() Returns a text representation of the tree in R's rpart format.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface smile.feature.SHAP

shap

Field Detail

formula

protected smile.data.formula.Formula formula

The model formula.

schema

protected smile.data.type.StructType schema

The schema of predictors.

response

protected smile.data.type.StructField response

The schema of response variable.

root

protected Node root

The root of decision tree.

maxDepth

protected int maxDepth

The maximum depth of the tree.

maxNodes

protected int maxNodes

The maximum number of leaf nodes in the tree.

nodeSize

protected int nodeSize

The number of instances in a node below which the tree will not split, setting nodeSize = 5 generally gives good results.

mtry

protected int mtry

The number of input variables to be used to determine the decision at a node of the tree.

importance

protected double[] importance

Variable importance. Every time a split of a node is made on variable the (GINI, information gain, etc.) impurity criterion for the two descendent nodes is less than the parent node. Adding up the decreases for each individual variable over the tree gives a simple measure of variable importance.

x

protected transient smile.data.DataFrame x

The training data.

samples

protected transient int[] samples

The samples for training this node. Note that samples[i] is the number of sampling of dataset[i]. 0 means that the datum is not included and values of greater than 1 are possible because of sampling with replacement.

index

protected transient int[] index

An index of samples to their original locations in training dataset.

order

protected transient int[][] order

An index of training values. Initially, order[i] is a set of indices that iterate through the training values for attribute i in ascending order. During training, the array is rearranged so that all values for each leaf node occupy a contiguous range, but within that range they maintain the original ordering. Note that only numeric attributes will be sorted; non-numeric attributes will have a null in the corresponding place in the array.

Constructor Detail

CART

public CART(smile.data.formula.Formula formula,
            smile.data.type.StructType schema,
            smile.data.type.StructField response,
            Node root,
            double[] importance)

Constructor.

CART

public CART(smile.data.DataFrame x,
            smile.data.type.StructField y,
            int maxDepth,
            int maxNodes,
            int nodeSize,
            int mtry,
            int[] samples,
            int[][] order)

Constructor.

Parameters:

x - the data frame of the explanatory variable.

y - the response variables.

maxDepth - the maximum depth of the tree.

maxNodes - the maximum number of leaf nodes in the tree.

nodeSize - the minimum size of leaf nodes.

mtry - the number of input variables to pick to split on at each node. It seems that sqrt(p) give generally good performance, where p is the number of variables.

samples - the sample set of instances for stochastic learning. samples[i] is the number of sampling for instance i.

order - the index of training values in ascending order. Note that only numeric attributes need be sorted.

Method Detail

size

public int size()

Returns the number of nodes in the tree.

order

public static int[][] order(smile.data.DataFrame x)

Returns the index of ordered samples for each ordinal column.

predictors

protected smile.data.Tuple predictors(smile.data.Tuple x)

Returns the predictors by the model formula if it is not null. Otherwise return the input tuple.

clear

protected void clear()

Clear the workspace of building tree.

split

protected boolean split(Split split,
                        java.util.PriorityQueue<Split> queue)

Split a node into two children nodes. Returns a new InternalNode if split success. Otherwise, return the node.

findBestSplit

protected java.util.Optional<Split> findBestSplit(LeafNode node,
                                                  int lo,
                                                  int hi,
                                                  boolean[] unsplittable)

Finds the best attribute to split on a set of samples. at the current node. Returns null if a split doesn't exists to reduce the impurity.

Parameters:

node - the leaf node to split.

lo - the inclusive lower bound of the data partition in the reordered sample index array.

hi - the exclusive upper bound of the data partition in the reordered sample index array.

unsplittable - unsplittable[j] is true if the column j cannot be split further in the node.

impurity

protected abstract double impurity(LeafNode node)

Returns the impurity of node.

newNode

protected abstract LeafNode newNode(int[] nodeSamples)

Creates a new leaf node.

findBestSplit

protected abstract java.util.Optional<Split> findBestSplit(LeafNode node,
                                                           int column,
                                                           double impurity,
                                                           int lo,
                                                           int hi)

Finds the best split for given column.

importance

public double[] importance()

Returns the variable importance. Every time a split of a node is made on variable the (GINI, information gain, etc.) impurity criterion for the two descendent nodes is less than the parent node. Adding up the decreases for each individual variable over the tree gives a simple measure of variable importance.

Returns:

the variable importance

root

public Node root()

Returs the root node.

Returns:

root node.

dot

public java.lang.String dot()

Returns the graphic representation in Graphviz dot format. Try http://viz-js.com/ to visualize the returned string.

toString

public java.lang.String toString()

Returns a text representation of the tree in R's rpart format. A semi-graphical layout of the tree. Indentation is used to convey the tree topology. Information for each node includes the node number, split, size, deviance, and fitted value. For the decision tree, the class probabilities are also printed.

Overrides:

toString in class java.lang.Object

shap

public double[] shap(smile.data.DataFrame data)

Returns the average of absolute SHAP values over a data frame.

shap

public double[] shap(smile.data.Tuple x)

Description copied from interface: SHAP

Returns the SHAP values. For regression, the length of SHAP values is same as the number of features. For classification, SHAP values are of p x k, where p is the number of features and k is the classes. The first k elements are the SHAP values of first feature over k classes, respectively. The rest features follow accordingly.

Specified by:

shap in interface SHAP<smile.data.Tuple>

Parameters:

x - an instance.

Returns:

the SHAP values.