Package 'rDecode'

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)

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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)

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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

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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.

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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.

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