smile.regression

Class RandomForest

java.lang.Object

smile.regression.RandomForest

All Implemented Interfaces:

java.io.Serializable, Regression<double[]>

public class RandomForest
extends java.lang.Object
implements Regression<double[]>, java.io.Serializable

Random forest for regression. Random forest is an ensemble method that consists of many regression trees and outputs the average of individual trees. The method combines bagging idea and the random selection of features.

Each tree is constructed using the following algorithm:

1. If the number of cases in the training set is N, randomly sample N cases with replacement from the original data. This sample will be the training set for growing the tree.
2. If there are M input variables, a number m << M is specified such that at each node, m variables are selected at random out of the M and the best split on these m is used to split the node. The value of m is held constant during the forest growing.
3. Each tree is grown to the largest extent possible. There is no pruning.

The advantages of random forest are:

• For many data sets, it produces a highly accurate model.
• It runs efficiently on large data sets.
• It can handle thousands of input variables without variable deletion.
• It gives estimates of what variables are important in the classification.
• It generates an internal unbiased estimate of the generalization error as the forest building progresses.
• It has an effective method for estimating missing data and maintains accuracy when a large proportion of the data are missing.

The disadvantages are

• Random forests are prone to over-fitting for some datasets. This is even more pronounced in noisy classification/regression tasks.
• For data including categorical variables with different number of levels, random forests are biased in favor of those attributes with more levels. Therefore, the variable importance scores from random forest are not reliable for this type of data.

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	RandomForest.Trainer Trainer for random forest.

Constructor Summary

Constructors

Constructor and Description
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees) Constructor.
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees, int maxNodes) Constructor.
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees, int maxNodes, int nodeSize) Constructor.
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees, int maxNodes, int nodeSize, int mtry) Constructor.
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees, int maxNodes, int nodeSize, int mtry, double subsample) Constructor.
RandomForest(smile.data.Attribute[] attributes, double[][] x, double[] y, int ntrees, int maxNodes, int nodeSize, int mtry, double subsample, double[] monotonicRegression) Constructor.
RandomForest(smile.data.AttributeDataset data, int ntrees) Constructor.
RandomForest(smile.data.AttributeDataset data, int ntrees, int maxNodes) Constructor.
RandomForest(smile.data.AttributeDataset data, int ntrees, int maxNodes, int nodeSize) Constructor.
RandomForest(smile.data.AttributeDataset data, int ntrees, int maxNodes, int nodeSize, int mtry, double subsample, double[] monotonicRegression) Constructor.
RandomForest(double[][] x, double[] y, int ntrees) Constructor.
RandomForest(double[][] x, double[] y, int ntrees, int maxNodes, int nodeSize, int mtry) Constructor.

Method Summary

Modifier and Type	Method and Description
double	error() Returns the out-of-bag estimation of RMSE.
RegressionTree[]	getTrees() Returns the regression trees.
double[]	importance() Returns the variable importance.
RandomForest	merge(RandomForest other) Merges together two random forests and returns a new forest consisting of trees from both input forests.
double	predict(double[] x) Predicts the dependent variable of an instance.
int	size() Returns the number of trees in the model.
double[]	test(double[][] x, double[] y) Test the model on a validation dataset.
double[][]	test(double[][] x, double[] y, RegressionMeasure[] measures) Test the model on a validation dataset.
void	trim(int ntrees) Trims the tree model set to a smaller size in case of over-fitting.

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.regression.Regression

predict

Constructor Detail

RandomForest

public RandomForest(double[][] x,
                    double[] y,
                    int ntrees)

Constructor. Learns a random forest for regression.

Parameters:

x - the training instances.

y - the response variable.

ntrees - the number of trees.

RandomForest

public RandomForest(double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes,
                    int nodeSize,
                    int mtry)

Constructor. Learns a random forest for regression.

Parameters:

x - the training instances.

y - the response variable.

ntrees - the number of trees.

mtry - the number of input variables to be used to determine the decision at a node of the tree. p/3 seems to give generally good performance, where p is the number of variables.

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

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

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

RandomForest

public RandomForest(smile.data.AttributeDataset data,
                    int ntrees)

Constructor. Learns a random forest for regression.

Parameters:

data - the dataset

ntrees - the number of trees.

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

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

RandomForest

public RandomForest(smile.data.AttributeDataset data,
                    int ntrees,
                    int maxNodes)

Constructor. Learns a random forest for regression.

Parameters:

data - the dataset

ntrees - the number of trees.

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

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes,
                    int nodeSize)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

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

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

RandomForest

public RandomForest(smile.data.AttributeDataset data,
                    int ntrees,
                    int maxNodes,
                    int nodeSize)

Constructor. Learns a random forest for regression.

Parameters:

data - the dataset

ntrees - the number of trees.

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

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

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes,
                    int nodeSize,
                    int mtry)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

mtry - the number of input variables to be used to determine the decision at a node of the tree. p/3 seems to give generally good performance, where dim is the number of variables.

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

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

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes,
                    int nodeSize,
                    int mtry,
                    double subsample)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

mtry - the number of input variables to be used to determine the decision at a node of the tree. p/3 seems to give generally good performance, where dim is the number of variables.

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

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

subsample - the sampling rate for training tree. 1.0 means sampling with replacement. < 1.0 means sampling without replacement.

RandomForest

public RandomForest(smile.data.AttributeDataset data,
                    int ntrees,
                    int maxNodes,
                    int nodeSize,
                    int mtry,
                    double subsample,
                    double[] monotonicRegression)

Constructor. Learns a random forest for regression.

Parameters:

data - the dataset

ntrees - the number of trees.

mtry - the number of input variables to be used to determine the decision at a node of the tree. p/3 seems to give generally good performance, where dim is the number of variables.

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

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

subsample - the sampling rate for training tree. 1.0 means sampling with replacement. < 1.0 means sampling without replacement.

RandomForest

public RandomForest(smile.data.Attribute[] attributes,
                    double[][] x,
                    double[] y,
                    int ntrees,
                    int maxNodes,
                    int nodeSize,
                    int mtry,
                    double subsample,
                    double[] monotonicRegression)

Constructor. Learns a random forest for regression.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

ntrees - the number of trees.

mtry - the number of input variables to be used to determine the decision at a node of the tree. p/3 seems to give generally good performance, where dim is the number of variables.

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

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

subsample - the sampling rate for training tree. 1.0 means sampling with replacement. < 1.0 means sampling without replacement.

Method Detail

merge

public RandomForest merge(RandomForest other)

Merges together two random forests and returns a new forest consisting of trees from both input forests.

error

public double error()

Returns the out-of-bag estimation of RMSE. The OOB estimate is quite accurate given that enough trees have been grown. Otherwise the OOB estimate can bias upward.

Returns:

the out-of-bag estimation of RMSE

importance

public double[] importance()

Returns the variable importance. Every time a split of a node is made on variable the impurity criterion for the two descendent nodes is less than the parent node. Adding up the decreases for each individual variable over all trees in the forest gives a fast measure of variable importance that is often very consistent with the permutation importance measure.

Returns:

the variable importance

size

public int size()

Returns the number of trees in the model.

Returns:

the number of trees in the model

trim

public void trim(int ntrees)

Trims the tree model set to a smaller size in case of over-fitting. Or if extra decision trees in the model don't improve the performance, we may remove them to reduce the model size and also improve the speed of prediction.

Parameters:

ntrees - the new (smaller) size of tree model set.

predict

public double predict(double[] x)

Description copied from interface: Regression

Predicts the dependent variable of an instance.

Specified by:

predict in interface Regression<double[]>

Parameters:

x - the instance.

Returns:

the predicted value of dependent variable.

test

public double[] test(double[][] x,
                     double[] y)

Test the model on a validation dataset.

Parameters:

x - the test data set.

y - the test data response values.

Returns:

RMSEs with first 1, 2, ..., regression trees.

test

public double[][] test(double[][] x,
                       double[] y,
                       RegressionMeasure[] measures)

Test the model on a validation dataset.

Parameters:

x - the test data set.

y - the test data output values.

measures - the performance measures of regression.

Returns:

performance measures with first 1, 2, ..., regression trees.

getTrees

public RegressionTree[] getTrees()

Returns the regression trees.