biasVarCov: Bias-Variance-Covariance Decomposition

In randomUniformForest: Random Uniform Forests for Classification, Regression and Unsupervised Learning

Bias-Variance-Covariance Decomposition

Description

Bias-Variance-Covariance decomposition for Mean Squared Error (MSE) or test error in binary classification, between a response vector and its estimate, over the test sample. For every estimate, based on training examples, MSE on the test sample, between values of the response and values of the estimate, can be decomposed in noise (variance of the response), squared bias (between response and estimate), variance (of the estimate) and covariance (of the response and the estimate). Same decomposition arrives for binary classification with responses in {0, 1}.

Usage

biasVarCov(predictions, target, regression = FALSE, idx = 1:length(target))

Arguments

predictions	vector of predictions for the test sample.
target	response vector for the test sample.
regression	if TRUE, decomposition is done for regression. If FALSE, for classification.
idx	not currently used.

Value

a list with the following components :

MSE, predError	mean squared error or test error for the test sample.
squaredBias	squared bias.
predictionsVar	variance of the estimate.
predictionsTargetCov	covariance between estimate and response.

Author(s)

Saip Ciss [e-mail]

Examples

n = 100;  p = 10
# simulate 'p' gaussian vectors with random parameters between -10 and 10.
X <- simulationData(n,p)

# make a rule to create response vector
epsilon1 = runif(n,-1,1)
epsilon2 = runif(n,-1,1)
rule = 2*(X[,1]*X[,2] + X[,3]*X[,4]) + epsilon1*X[,5] + epsilon2*X[,6]

# Classification
Y <- as.factor(ifelse(rule > mean(rule), 1, 0))

# define random train and test sample of (X,Y)
trainTestIdx <- cut(sample(1:nrow(X), nrow(X)), 2, labels= FALSE)

# training sample
Xtrain = X[trainTestIdx == 1,]
Ytrain = Y[trainTestIdx == 1]

# test sample
Xtest = X[trainTestIdx == 2,]
Ytest = Y[trainTestIdx == 2]

# learning model
synthDataset.ruf <- randomUniformForest(Xtrain, Ytrain, threads = 1, 
ntree = 20, BreimanBounds = FALSE)
synthDataset.pred.ruf <- predict(synthDataset.ruf, Xtest)

# test error
testError = 1 - sum(synthDataset.pred.ruf == Ytest)/length(Ytest)
testError

# test error decomposition
testError.dec <- biasVarCov(synthDataset.pred.ruf, Ytest, regression = FALSE)

# Regression
Y = rule

# training sample
Xtrain = X[trainTestIdx == 1,]
Ytrain = Y[trainTestIdx == 1]

# test sample
Xtest = X[trainTestIdx == 2,]
Ytest = Y[trainTestIdx == 2]

# learning model
synthDataset.ruf <- randomUniformForest(Xtrain, Ytrain, threads = 1,
ntree = 20, BreimanBounds = FALSE)
synthDataset.pred.ruf <- predict(synthDataset.ruf, Xtest)

# MSE
MSE <- sum((synthDataset.pred.ruf - Ytest)^2)/length(Ytest)

# test error decomposition
MSE.dec <- biasVarCov(synthDataset.pred.ruf, Ytest, regression = TRUE)

randomUniformForest documentation built on June 22, 2022, 1:05 a.m.