---
title: "The supervised `s2net`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{The supervised `s2net`}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = FALSE,
  results = "hold",
  comment = " ",
  warning = FALSE,
  message = FALSE
)
```

`s2net` can be used as a supervised method (without unlabeled data) and it is equivalent to elastic net. 

## Data

The `auto_mpg` dataset is available when `s2net` is installed. 

```{r}
library(s2net)
data("auto_mpg")

# Preprocess the data using the s2Data function
train = s2Data(auto_mpg$P1$xL, auto_mpg$P1$yL, preprocess = TRUE)
```

## Ordinary least squares

To fit an OLS model, we will use the `lm` function (without intercept).

```{r}
lm.fit = lm( y~ 0 + ., data = data.frame(train$xL, y = train$yL))
```

To obtain the estimations from `s2net` we use

```{r}
obj = s2netR(train, s2Params(0))
# We set all the hyper-parameters to 0
```

We can compare the training objectives of both algorithms, as well as the estimations.

```{r}
library(Metrics)
# Training error
ypred = predict.lm(lm.fit, data.frame(train$xL))
print("OLS error:")
mse(ypred, train$yL)

ypred = predict(obj, train$xL)
print("s2net error:")
mse(ypred, train$yL)

#Estimations
data.frame(mle = lm.fit$coefficients, s2net = obj$beta)
```

## Lasso

```{r}
library(glmnet)

lasso.fit = glmnet(train$xL, train$yL, family = "gaussian", 
                           alpha = 1, lambda = 0.01, intercept = F)
ypred = predict(lasso.fit, train$xL)
print("Lasso error:")
mse(ypred, train$yL)

obj = s2netR(train, s2Params(lambda1 = 0.01))
ypred = predict(obj, train$xL)
print("s2net error")
mse(ypred, train$yL)

print("Coefficients")
data.frame(lasso = as.numeric(lasso.fit$beta), s2net = obj$beta)
```

## Elastic net

```{r}
enet.fit = glmnet(train$xL, train$yL, family = "gaussian", 
                          alpha = 0.3333, lambda = 0.03, intercept = F)
ypred = predict(enet.fit, train$xL)
print("glmnet error")
mse(ypred, train$yL)

obj = s2netR(train, s2Params(lambda1 = 0.01, lambda2 = 0.01))
ypred = predict(obj, train$xL)
print("s2net error")
mse(ypred, train$yL)

print("Coefficients")
data.frame(enet = as.matrix(enet.fit$beta), s2net = obj$beta)
```