---
title: "bnns"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{bnns}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## Overview

The `bnns` package provides an efficient and user-friendly implementation of **Bayesian Neural Networks (BNNs)** for regression, binary classification, and multiclass classification problems. By integrating Bayesian inference, `bnns` allows for uncertainty quantification in predictions and robust parameter estimation.

This vignette covers:
1. Installing and loading the package
2. Preparing data
3. Fitting a BNN model
4. Summarizing the model
5. Making predictions
6. Model evaluation
7. Customizing prior

## 1. Installation

To install the package, use the following commands:

```{r}
# Install from CRAN (if available)
#  install.packages("bnns")

# Or install the development version from GitHub
# devtools::install_github("swarnendu-stat/bnns")
```

Load the package in your R session:

```{r}
library(bnns)
```

## 2. Preparing the Data

The `bnns` package expects data in the form of matrices for predictors and a vector for responses.

Here’s an example of generating synthetic data:

```{r}
# Generate training data
set.seed(123)
df <- data.frame(x1 = runif(10), x2 = runif(10), y = rnorm(10))
```

For binary or multiclass classification:

```{r}
# Binary classification response
df$y_bin <- sample(0:1, 10, replace = TRUE)

# Multiclass classification response
df$y_cat <- factor(sample(letters[1:3], 10, replace = TRUE)) # 3 classes
```

## 3. Fitting a Bayesian Neural Network Model

Fit a Bayesian Neural Network using the `bnns()` function. Specify the network architecture using arguments like the number of layers (`L`), nodes per layer (`nodes`), and activation functions (`act_fn`).

### Regression Example

```{r message=FALSE, warning=FALSE, echo = TRUE, results = 'hide', eval = FALSE}
model_reg <- bnns(
  y ~ -1 + x1 + x2,
  data = df,
  L = 1, # Number of hidden layers
  nodes = 2, # Nodes per layer
  act_fn = 3, # Activation functions: 3 = ReLU
  out_act_fn = 1, # Output activation function: 1 = Identity (for regression)
  iter = 1e1,  # Very low number of iteration is shown, increase to at least 1e3 for meaningful inference
  warmup = 5,  # Very low number of warmup is shown, increase to at least 2e2 for meaningful inference
  chains = 1
)
```

### Binary Classification Example

```{r message=FALSE, warning=FALSE, echo = TRUE, results = 'hide', eval = FALSE}
model_bin <- bnns(
  y_bin ~ -1 + x1 + x2,
  data = df,
  L = 1,
  nodes = c(16),
  act_fn = c(2),
  out_act_fn = 2, # Output activation: 2 = Logistic sigmoid
  iter = 2e2,
  warmup = 1e2,
  chains = 1
)
```

### Multiclass Classification Example

```{r message=FALSE, warning=FALSE, echo = TRUE, results = 'hide', eval = FALSE}
model_cat <- bnns(
  y_cat ~ -1 + x1 + x2,
  data = df,
  L = 3,
  nodes = c(32, 16, 8),
  act_fn = c(3, 2, 2),
  out_act_fn = 3, # Output activation: 3 = Softmax
  iter = 2e2,
  warmup = 1e2,
  chains = 1
)
```

## 4. Summarizing the Model

Use the `summary()` function to view details of the fitted model, including the network architecture, posterior distributions, and predictive performance.

```{r eval = FALSE}
summary(model_reg)
```

```{r eval=FALSE}
summary(model_bin)
summary(model_cat)
```

## 5. Making Predictions

The `predict()` function generates predictions for new data. The format of predictions depends on the output activation function.

```{r eval = FALSE}
# New data
test_x <- matrix(runif(10), nrow = 5, ncol = 2) |>
  data.frame() |>
  `colnames<-`(c("x1", "x2"))

# Regression predictions
pred_reg <- predict(model_reg, test_x)
```

```{r eval = FALSE}
# Binary classification predictions
pred_bin <- predict(model_bin, test_x)

# Multiclass classification predictions
pred_cat <- predict(model_cat, test_x)
```

## 6. Evaluating the Model

The `bnns` package includes utility functions like `measure_cont`, `measure_bin`, and `measure_cat` for evaluating model performance.

### Regression Evaluation

```{r eval = FALSE}
# True responses
test_y <- rnorm(5)

# Evaluate predictions
metrics_reg <- measure_cont(obs = test_y, pred = pred_reg)
print(metrics_reg)
```

### Binary Classification Evaluation

```{r eval = FALSE}
# True responses
test_y_bin <- sample(c(rep(0, 2), rep(1, 3)), 5)

# Evaluate predictions
metrics_bin <- measure_bin(obs = test_y_bin, pred = pred_bin)
```

### Multiclass Classification Evaluation

```{r eval = FALSE}
# True responses
test_y_cat <- factor(sample(letters[1:3], 5, replace = TRUE))

# Evaluate predictions
metrics_cat <- measure_cat(obs = test_y_cat, pred = pred_cat)
```

## 7. Customized Prior

Customized priors can be used for weights as well as the `sigma` parameter (for regression).  Here we show an example use of a `Cauchy` prior for weights in multi-classification case.

```{r message=FALSE, warning=FALSE, echo = TRUE, results = 'hide', eval = FALSE}
model_cat_cauchy <- bnns(
  y_cat ~ -1 + x1 + x2,
  data = df,
  L = 3,
  nodes = c(32, 16, 8),
  act_fn = c(3, 2, 2),
  out_act_fn = 3, # Output activation: 3 = Softmax
  iter = 2e2,
  warmup = 1e2,
  chains = 1,
  prior_weights = list(dist = "cauchy", params = list(mu = 0, sigma = 2.5))
)
```

```{r eval = FALSE}
# Evaluate predictions
metrics_cat_cauchy <- measure_cat(obs = test_y_cat, pred = predict(model_cat_cauchy, test_x))
```

## 8. Notes on Bayesian Neural Networks

- Bayesian inference allows for use of prior knowledge about the weights.
- It allows for uncertainty quantification in predictions.
- Always check convergence diagnostics such as R-hat values.
- Use informative priors when possible to stabilize the model.

## References

For more details, consult the source code on [GitHub](https://github.com/swarnendu-stat/bnns).
