TraceAssist {TraceAssist}

Aggregation of structured sign series for trace regression (ASSIST)

Description

Main function for fitting the nonparametric trace regression. The algorithm uses a learning reduction approach to estimate the nonparametric trace regression via ASSIST.

Usage

TraceAssist(X,y,X_new=NULL,r,sparse_r,sparse_c,H=10,lambda=0,rho.ini=0.1,min,max)

Arguments

X

A list of matrix-valued predictors.

y

A vector of response variables.

X_new

A list of new matrices in the test data. X_new = NULL returns fitted values in the training data.

r

The rank of sign representable function to be fitted.

sparse_r

The number of zero rows in coefficient matrix.

sparse_c

The number of zero columns in coefficient matrix.

H

Resoution parameter that controls the number of classifiers to aggregate.

lambda

Lagrangian multiplier.

rho.ini

Initial step size.

min

Minimum value of the response variables

max

Maximum value of the response variables.

Value

The returned object is a list of components.

B_est - An array that collects a series of coefficient matrices for the classifiers used in the algorithm.

fitted - The predicted responses in the test data.

sign_fitted - A matrix that collects a series of predicted signs for the classifiers used in the algorithm.

References

Lee, C., Li, L., Zhang, H., and Wang, M. (2021). Nonparametric Trace Regression via Sign Series Representation. arXiv preprint arXiv:2105.01783.

Examples

######### Generate matrices in the training data ################
X = list()
for(i in 1:10){
 X[[i]] = matrix(runif(4,-1,1),nrow = 2,ncol = 2)
}

######### Generate coefficient matrix ###########################
B = runif(2,-1,1)%*%t(runif(2,-1,1))

######### Generate response variables ###########################
y = NULL;signal = NULL
for(i in 1:10){
 signal = c(signal,sum(X[[i]]*B))
 y = c(y,sum(X[[i]]*B)+rnorm(1,sd = 0.1))
}


######### Run ASSIST ############################################
res =TraceAssist(X,y,r = 1,sparse_r = 0,sparse_c = 0,min = min(y),max = max(y))
mean(abs(res$fitted-signal))


######### Generate new matrices in the test data ################
X_new = list()
for(i in 1:10){
  X_new[[i]] = matrix(runif(4,-1,1),nrow = 2,ncol = 2)
}

######### Generate response variables from X_new ################
y_new = NULL
for(i in 1:10){
  y_new = c(y_new,sum(X_new[[i]]*B))
}

######### Run ASSIST #############################################
res =TraceAssist(X,y,X_new,r = 1,sparse_r = 0,sparse_c = 0,min = min(y),max = max(y))
mean(abs(res$fitted-y_new))