Package 'TraceAssist'

ADMM algorithm for weighted classification

Description

Implement an ADMM algorithm to optimize the weigthed classificiation loss.

Usage

ADMM(X,ybar,Weight,Covariate=NULL,r,srow,scol,lambda=0,rho.ini=1)

Arguments

X	A list of matrix-valued predictors.
ybar	A vector of shifted response variables.
Weight	Classification weight.
Covariate	Additional covariates including intercept. Covariate = NULL indicates no covariates.
r	The rank of coefficient matrix to be fitted.
srow	The number of zero rows in coefficient matrix.
scol	The number of zero columns in coefficient matrix.
lambda	Lagrangian multiplier. Default is zero.
rho.ini	Initial step size. Default is 1.

Value

The returned object is a list of components.

intercept - The estimated intercept of the classifier.

P_row - The left-singular vectors of the coefficient matrix.

P_col - The right-singular vectors of the coefficient matrix.

obj - Trajectory of weighted classification loss values over iterations.

iter - The number of iterations.

fitted - A vector of fitted reponse from estimated classifier.

B - The estimated coefficient matrix of the classifier.

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 matrix predictors  ##########
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
for(i in 1:10){
 y = c(y,sign(sum(X[[i]]*B)+rnorm(1,sd = 0.1)))
}

#### classification with equal weights #########
res = ADMM(X,y,rep(1,10),r = 1,srow = 0,scol = 0)

### Misclassification rate on training data ######
mean(sign(res$fitted)-y)

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Convolutional Neural Network (CNN) with two hidden layers

Description

Implement a CNN with two hidden layers and ReLU activation.

Usage

CNN(X,y,X_new,plot.figure = FALSE)

Arguments

X	A list of matrix-valued predictors.
y	Binary response variable.
X_new	A list of new matrices in the test data.
plot.figure	Option for plotting trajectory of accuracy over epochs.

Value

The returned object is a list of components.

prob - The predicted probabilities for the test data.

class - The estimated binary response for the test data.

history - The trajectory of classification accuracy over epochs.

acc - The classification accuracy on test data.

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Logistic probability model via penalized maximum likelihood

Description

Fit a logistic probability model based on Lasso penalty

Usage

Lasso(xvec,y,xnew,lambda)

Arguments

xvec	An input matrix. Each row is a vectorized predictor.
y	Binary response variable.
xnew	New predictors in the test data. Organized as a matrix with each row being a data point.
lambda	The regularization penalty.

Value

The returned object is a list of components.

B_est - The estimated coefficient vector of linear predictor.

prob - The predicted probabilities for the test data.

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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))

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