Sieve (version 2.1)

sieve_predict: Predict the outcome of interest for new samples

Description

Use the fitted sieve regression model from sieve_solver. It also returns the testing mean-squared errors.

Usage

sieve_predict(model, testX, testY = NULL)

Value

a list.

predictY

a matrix. Dimension is test sample size (# of rows) x number of penalty hyperparameter lambda (# of columns). For regression problem, that is, when family = "gaussian", each entry is the estimated conditional mean (or predictor of outcome Y). For classification problems (family = "binomial"), each entry is the predicted probability of having Y = 1 (which class is defined as "class 1" depends on the training data labeling).

MSE

For regression problem, when testY is provided, the algorithm also calculates the mean-sqaured errors using testing data. Each entry of MSE correponds to one value of penalization hyperparameter lambda

Arguments

model

a list. Use the fitted model from sieve_solver.

testX

a data frame. Dimension equals to test sample size x feature diemnsion. Should be of a similar format as the training feature provided to sieve_preprocess.

testY

a vector. The outcome of testing samples (if known). Default is NULL. For regression problems, the algorithm also returns the testing mean-squared errors.

Examples

xdim <- 1 #1 dimensional feature
#generate 1000 training samples
TrainData <- GenSamples(s.size = 1000, xdim = xdim)
#use 50 cosine basis functions
type <- 'cosine'
basisN <- 50 
sieve.model <- sieve_preprocess(X = TrainData[,2:(xdim+1)], 
                                basisN = basisN, type = type)
sieve.fit<- sieve_solver(model = sieve.model, Y = TrainData$Y)
#generate 1000 testing samples
TestData <- GenSamples(s.size = 1000, xdim = xdim)
sieve.prediction <- sieve_predict(model = sieve.fit, 
                                  testX = TestData[,2:(xdim+1)], 
                                  testY = TestData$Y)
###if the outcome is binary, 
###need to solve a nonparametric logistic regression problem
xdim <- 1
TrainData <- GenSamples(s.size = 1e3, xdim = xdim, y.type = 'binary', frho = 'nonlinear_binary')
sieve.model <- sieve_preprocess(X = TrainData[,2:(xdim+1)], 
                                basisN = basisN, type = type)
sieve.fit<- sieve_solver(model = sieve.model, Y = TrainData$Y,
                         family = 'binomial')
                         
###the predicted value is conditional probability (of taking class 1).
TrainData <- GenSamples(s.size = 1e3, xdim = xdim, y.type = 'binary', frho = 'nonlinear_binary')
sieve.prediction <- sieve_predict(model = sieve.fit, 
                                  testX = TestData[,2:(xdim+1)])