
---
title: "Introduction to PIE -- A Partially Interpretable Model with Black-box Refinement"
author: "Tong Wang, Jingyi Yang, Yunyi Li and Boxiang Wang"
date: "2025-01-20"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to PIE -- A Partially Interpretable Model with Black-box Refinement}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# Introduction to `PIE`

The `PIE` package implements Partially Interpretable Estimators (PIE), a framework that jointly train an interpretable model and a black-box model to achieve high predictive performance as well as partial model transparency.

## Installation

To install the development version from GitHub, run the following:

```r
# Install the R package from CRAN
install.packages("PIE")
```

## Getting Started

This section demonstrates how to generate synthetic data for transfer learning and apply the ART framework using different models.

### Generate Data

The function `data_process()` allows you to process dataset into the format that fits with PIE model, including cross-validation dataset (such as training, validation and testing) and group indicators for group lasso. 

```r
library(PIE)
# Load the training data
data("winequality")
# Which columns are numerical?
num_col <- 1:11
# Which columns are categorical?
cat_col <- 12
# Which column is the response?
y_col <- ncol(winequality)
# Data Processing
dat <- data_process(X = as.matrix(winequality[, -y_col]), 
  y = winequality[, y_col], 
  num_col = num_col, cat_col = cat_col, y_col = y_col)
```

## Fitting PIE

Once the data is prepared, you can use the `PIE_fit()` function to train PIE model. In this example, we fit only with 5 iterations using group lasso and XGBoost models.

```r
# Fit a PIE model
fold <- 1
fit <- PIE_fit(
  X = dat$spl_train_X[[fold]],
  y = dat$train_y[[fold]],
  lasso_group = dat$lasso_group,
  X_orig = dat$orig_train_X[[fold]],
  lambda1 = 0.01, lambda2 = 0.01, iter = 5, eta = 0.05, nrounds = 200
)
```

## Predicting PIE

Once your PIE model is trained, you can use the `PIE_predict()` function to predict on test data. 

```r
# Prediction
pred <- predict(fit, 
  X = dat$spl_validation_X[[fold]],
  X_orig = dat$orig_validation_X[[fold]])
```
## Evaluate PIE
You can evaluate your PIE model's performance with `RPE()`, which has formula $RPE=\frac{\sum_i(y_i-\hat{y_i})^2}{\sum_i(y_i-\bar{y})^2}$, where $\bar{y} = \frac{1}{n}\sum_i^n y_i$.

```r
# Validation
val_rrmse_test <- RPE(pred$total, dat$validation_y[[fold]])
```



