# missoNet: Missingness in Multi-Task Regression with Network Estimation

`missoNet` is a novel approach to fitting penalized multi-task regression models, which are used to estimate the coefficients of predictor variables for multiple correlated tasks or response variables. The package achieves this by simultaneously estimating the regression coefficients and the conditional response network structure given all predictors, using penalized maximum likelihood in an undirected conditional Gaussian graphical model. In contrast to most penalized multi-task regression methods, such as conditional graphical lasso, `missoNet` is capable of obtaining estimates even when the response data is corrupted by missing values. The method is based on convex optimization, which provides both theoretical and computational benefits, and returns solutions that are comparable to the estimates obtained without any missing values.

The package provides an integrated set of core routines including 1) data simulation; 2) model fitting and cross-validation; 3) visualization of results; 4) predictions in new data. The function arguments are specified in the same style as those of `glmnet`, making it easy for experienced users to get started.

## Installation

To install the package `missoNet` from CRAN, type the following command in the R console:

``install.packages("missoNet")``

Or install the development version of `missoNet` from GitHub:

``````if(!require("devtools")) {
install.packages("devtools")
}
devtools::install_github("yixiao-zeng/missoNet", build_vignettes = TRUE)``````

## An example for getting started

An example of how to use the package:

``````# Simulate a dataset with response values missing completely at random (MCAR),
# the overall missing rate is around 10%.
sim.dat <- generateData(n = 300, p = 50, q = 20, rho = 0.1, missing.type = "MCAR")
tr <- 1:240  # training set indices
tst <- 241:300  # test set indices
X.tr <- sim.dat\$X[tr, ]  # predictor matrix
Y.tr <- sim.dat\$Z[tr, ]  # corrupted response matrix

# Perform a five-fold cross-validation on the training set.
cvfit <- cv.missoNet(X = X.tr, Y = Y.tr, kfold = 5)

# Alternatively, compute the cross-validation folds in parallel.
cl <- parallel::makeCluster(min(parallel::detectCores()-1, 3))
cvfit <- cv.missoNet(X = X.tr, Y = Y.tr, kfold = 5,
parallel = TRUE, cl = cl)
parallel::stopCluster(cl)

# Plot the standardized mean cross-validated errors in a heatmap.
plot(cvfit)

# Extract the estimates at "lambda.min" that gives the minimum cross-validated error.
Beta_hat <- cvfit\$est.min\$Beta
Theta_hat <- cvfit\$est.min\$Theta

# Make predictions of response values on the test set.
newy <- predict(cvfit, newx = sim.dat\$X[tst, ], s = "lambda.min")``````

``vignette("missoNet")``