gmus {hdme}

Generalized Matrix Uncertainty Selector

Description

Generalized Matrix Uncertainty Selector

Usage

gmus(W, y, lambda = NULL, delta = NULL, family = "gaussian", weights = NULL)

Arguments

W

Design matrix, measured with error. Must be a numeric matrix.

y

Vector of responses.

lambda

Regularization parameter.

delta

Additional regularization parameter, bounding the measurement error.

family

"gaussian" for linear regression, "binomial" for logistic regression or "poisson" for Poisson regression. Defaults go "gaussian".

weights

A vector of weights for each row of X.

Value

An object of class "gmus".

References

Rosenbaum M, Tsybakov AB (2010). “Sparse recovery under matrix uncertainty.” Ann. Statist., 38(5), 2620–2651.

Sorensen O, Hellton KH, Frigessi A, Thoresen M (2018). “Covariate Selection in High-Dimensional Generalized Linear Models With Measurement Error.” Journal of Computational and Graphical Statistics, 27(4), 739-749. doi:10.1080/10618600.2018.1425626, https://doi.org/10.1080/10618600.2018.1425626.

Examples

# Example with linear regression
set.seed(1)
n <- 100 # Number of samples
p <- 50 # Number of covariates
# True (latent) variables
X <- matrix(rnorm(n * p), nrow = n)
# Measurement matrix (this is the one we observe)
W <- X + matrix(rnorm(n*p, sd = 1), nrow = n, ncol = p)
# Coefficient vector
beta <- c(seq(from = 0.1, to = 1, length.out = 5), rep(0, p-5))
# Response
y <- X %*% beta + rnorm(n, sd = 1)
# Run the MU Selector
fit1 <- gmus(W, y)
# Draw an elbow plot to select delta
plot(fit1)
coef(fit1)

# Now, according to the "elbow rule", choose
# the final delta where the curve has an "elbow".
# In this case, the elbow is at about delta = 0.08,
# so we use this to compute the final estimate:
fit2 <- gmus(W, y, delta = 0.08)
# Plot the coefficients
plot(fit2)
coef(fit2)
coef(fit2, all = TRUE)