Type: Package
Title: Descent-Based Calibrated Optimal Direct Estimation
Version: 0.1.0
Author: Chi Seng Pun, Matthew Zakharia Hadimaja
Maintainer: Chi Seng Pun <cspun@ntu.edu.sg>
Description: Algorithms for solving a self-calibrated l1-regularized quadratic programming problem without parameter tuning. The algorithm, called DECODE, can handle high-dimensional data without cross-validation. It is found useful in high dimensional portfolio selection (see Pun (2018) https://ssrn.com/abstract=3179569) and large precision matrix estimation and sparse linear discriminant analysis (see Pun and Hadimaja (2019) https://ssrn.com/abstract=3422590).
License: GPL-2
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.0.0
Depends: R (≥ 2.10)
Imports: stats
NeedsCompilation: no
Packaged: 2019-12-13 15:54:26 UTC; cspun
Repository: CRAN
Date/Publication: 2019-12-18 14:20:05 UTC

Descent-based Calibrated Optimal Direct Estimation

Description

Implement DECODE for sigma and beta to estimate \Sigma^{-1}\beta where sigma is an estimator of \Sigma and beta is an estimator of \beta.

Usage

decode(sigma, beta, lambda0, decode.tol = 1e-06, decode.maxit = 100,
  trace = FALSE, solver = c("apg", "homotopy"), solver.tol = 1e-08,
  solver.maxit = 10000, return.sigma = FALSE, return.beta = FALSE,
  return.param = FALSE)

Arguments

sigma

p \times p positive semidefinite symmetric matrix. sigma will be perturbed if needed.

beta

p-length vector.

lambda0

number between 0 and 1.

decode.tol

error tolerance for DECODE.

decode.maxit

maximum iterations for DECODE

trace

logical. If TRUE, will return \eta, \theta, and \lambda found during each iteration of DECODE

solver

solver for \ell_1-RQP problem inside DECODE.

solver.tol

tolerance for solver.

solver.maxit

maximum iterations for solver (only for APG).

return.sigma

logical. If TRUE the sigma entered is returned.

return.beta

logical. If TRUE the beta entered is returned.

return.param

logical. If TRUE the parameters used are returned.

Value

An object of class decode containing:

eta

DECODE of \Sigma^{-1}\beta.

theta

final \theta of the DECODE.

lambda

final \lambda of the DECODE.

sigma.mult

multiplier applied on sigma to ensure convergence.

total.iter

number of iterations until convergence.

call

the matched call.

method

the solver used, if requested.

lambda0

the lambda0 entered, if requested.

decode.tol

the decode.tol used, if requested.

decode.maxit

the decode.maxit used, if requested.

trace

the trace used, if requested.

solver.tol

the solver.tol used, if requested.

solver.maxit

the solver.maxit used, if requested.

eta.trace

matrix of \eta used in each iteration, if requested.

theta.trace

vector of \theta used in each iteration, if requested.

lambda.trace

vector of \lambda used in each iteration, if requested.

References

Pun, C. S. (2018). A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection. Hadimaja, M. Z., & Pun, C. S. (2018). A Self-Calibrated Regularized Direct Estimation for Graphical Selection and Discriminant Analysis.

Examples

# estimate A^(-1) b with a certain lambda0
X <- matrix(rnorm(100), 10, 10)
A <- t(X) %*% X
b <- rnorm(10)
object <- decode(A, b, lambda0 = 0.8)

object
summary(object)

coef(object)

Implement DECODE for simple LDA

Description

Implement DECODE for simple LDA. The LDA assumes both classes have equal prior probabilities. This implementation is used in Hadimaja and Pun (2018).

Usage

decodeLDA(X, y, lambda0 = NULL, ...)

Arguments

X

n\times p data matrix.

y

binary n-length vector containing the class of each observation.

lambda0

number between 0 and 1. If NULL, will use \sqrt{2 \log{p}/n}.

...

additional arguments to be passed to general decode function.

Value

An object of class decodeLDA containing:

eta

DECODE of \Omega\delta

X

training data used

y

training label used

and various outputs from decode function.

References

Hadimaja, M. Z., & Pun, C. S. (2018). A Self-Calibrated Regularized Direct Estimation for Graphical Selection and Discriminant Analysis.

Examples

# for efficiency, we will only use 500 variables

# load the training data (Lung cancer data, cleaned)
data(lung.train) # 145 x 1578
X.train <- lung.train[,1:500]
y.train <- lung.train[,1578]

# build the DECODE
object <- decodeLDA(X.train, y.train)

object
summary(object)
coef(object)

# test on test data
data(lung.test)
X.test <- lung.test[,1:500]
y.test <- lung.test[,1578]
y.pred <- predict(object, X.test)
table(y.pred, y.test)

Implement DECODE for simple precision matrix estimation

Description

Implement DECODE to estimate a precision matrix of X. This implementation is used in Hadimaja and Pun (2018).

Usage

decodePM(X, lambda0 = NULL, ...)

Arguments

X

n\times p data matrix.

lambda0

number between 0 and 1. If NULL, will use \sqrt{2 \log{p}/n}.

...

additional arguments to be passed to general decode function.

Value

An object of class decodePM containing:

Omega

DECODE of \Omega.

lambda0

the lambda0 used.

X

data used.

theta

final \theta for each column.

lambda

final \lambda for each column.

total.iter

number of iterations until convergence for each column.

References

Hadimaja, M. Z., & Pun, C. S. (2018). A Self-Calibrated Regularized Direct Estimation for Graphical Selection and Discriminant Analysis.

Examples

# estimate the precision matrix of iris data
object <- decodePM(iris[,1:4], lambda0 = 0.01)

object
summary(object)

object$Omega

Lung cancer test data set from Gordon et al. (2002)

Description

Preprocessed lung cancer test data of 1577 genes from 36 patients with lung cancer. There are 30 patients with adenocarcinoma (AD) and 6 patients with malignant pleural mesothelioma (MPM). The original data was used in Gordon et al. (2002), with this preprocessed version used in Pun and Hadimaja (2018).

Usage

data(lung.test)

Format

A data frame with 36 observations on 1577 variables.

Source

http://dx.doi.org/10.17632/ynp2tst2hh.4#file-673c9416-39ed-446d-9be9-37ac74353029

References

Gordon, G. J., Jensen, R. V., Hsiao, L. L., Gullans, S. R., Blumenstock, J. E., Ramaswamy, S., ... & Bueno, R. (2002). Translation of microarray data into clinically relevant cancer diagnostic tests using gene expression ratios in lung cancer and mesothelioma. Cancer research, 62(17), 4963-4967.

Lung cancer training data set from Gordon et al. (2002)

Description

Preprocessed lung cancer training data of 1577 genes from 145 patients with lung cancer. There are 120 patients with adenocarcinoma (AD) and 25 patients with malignant pleural mesothelioma (MPM). The original data was used in Gordon et al. (2002), with this preprocessed version used in Pun and Hadimaja (2018).

Usage

data(lung.train)

Format

A data frame with 145 observations on 1577 variables.

Source

http://dx.doi.org/10.17632/ynp2tst2hh.4#file-673c9416-39ed-446d-9be9-37ac74353029

References

Gordon, G. J., Jensen, R. V., Hsiao, L. L., Gullans, S. R., Blumenstock, J. E., Ramaswamy, S., ... & Bueno, R. (2002). Translation of microarray data into clinically relevant cancer diagnostic tests using gene expression ratios in lung cancer and mesothelioma. Cancer research, 62(17), 4963-4967.