---
title: "Introduction to gglasso"
author: "Yi Yang"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to gglasso}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---


## Install the package

```{r, eval=FALSE}
# on CRAN
install.packages("gglasso")

# dev version on GitHub
pacman::p_load_gh('emeryyi/gglasso')
```


## Least squares regression
```{r}
library(gglasso)

# load bardet data set
data(bardet)

group1 <- rep(1:20, each = 5)

fit_ls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "ls")

plot(fit_ls)

coef(fit_ls)[1:5,90:100]
```

## Cross-Validation

```{r}
cvfit_ls <- cv.gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "ls")

plot(cvfit_ls)
coef(cvfit_ls, s = "lambda.min")
```




## Weight Least squares regression

We can also perform weighted least-squares regression by specifying `loss='wls'`, and providing a $n \times n$ weight matrix in the `weights` argument, where $n$ is the number of observations. Note that cross-validation is **NOT IMPLEMENTED** for `loss='wls'`.

```{r}
# generate weight matrix
times <- seq_along(bardet$y)
rho <- 0.5
sigma <- 1
H <- abs(outer(times, times, "-"))
V <- sigma * rho^H
p <- nrow(V)
V[cbind(1:p, 1:p)] <- V[cbind(1:p, 1:p)] * sigma

# reduce eps to speed up convergence for vignette build
fit_wls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "wls", 
                   weight = V, eps = 1e-4)

plot(fit_wls)

coef(fit_wls)[1:5,90:100]
```