simpleMLP is an implementation of a multilayer perceptron, a type of feedforward, fully connected neural network. It features 2 ReLU hidden layers and supports hyperparameter tuning for learning rate, batch size, epochs, and hidden units for both layers.

simpleMLP also allows you to directly load the MNIST database of handwritten digits to quickly start training models.

Neural networks are a popular type of machine learning model used for object recognition, natural language processing, and more. It uses a composition of vector valued functions called the layers of the network and are composed of individual units, also known as neurons. Inputs are fed through the first layer, or the input layer, and travel through one or more hidden layers before ending at the output layer. Each layer uses a linear or nonlinear activation function on the input before outputting it to the next layer. By using many layers of vector functions, neural networks can generalize to approximate an arbitrary function f*.

A multilayer perceptron is a type of neural network in which inputs pass only in the direction of input to output without feeding back into itself and each layer is fully connected to its following layer. This means that every unit in one layer connects to every unit in the next layer. This implementation includes two hidden layers which both use the Rectified Linear Unit (ReLU) function, a popular nonlinear activation function. It implements the backpropagation algorithm which trains the network by computing gradients of its functions to minimize a specified cost function. We use cross entropy loss as our cost function to determine the performance of the model.

This model supports hyperparameter tuning. It is worth trying different combinations of hyperparameters to observe how they affect overfitting and underfitting. For more information, the following resources might be helpful:

- Ian Goodfellow, Yoshua Bengio, & Aaron Courville (2016). Deep Learning. MIT Press.
- Coursera Machine Learning

You can install the released version of simpleMLP from CRAN with:

And the development version from GitHub with:

The training data must be a design matrix (i.e. each row is an observation) and the targets must be a matrix of one-hot encodings.

To load the MNIST database, run the following:

```
library(simpleMLP)
mnist <- load_mnist()
train_data <- mnist[1]
train_target <- mnist[2]
validate_data <- mnist[3]
validate_target <- mnist[4]
test_data <- mnist[5]
test_target <- mnist[6]
```

After loading the dataset, the model can be trained like so:

```
# Initialize the network model. The data has dimension 784, there are
# 10 classes, and we choose 100 and 50 hidden units for the first and second
# hidden layers.
mlp_model <- init_nn(784, 100, 50, 10)
# Now we train the model. We decide on the following hyperparameters. Overall,
# the hyperparameters should be tuned as to avoid overfitting. We also plot the
# test cross entropy and accuracy to see how it changes over time.
alpha <- 0.01
epochs <- 1
batch_size <- 64
plot_acc <- TRUE
mlp_model <- train_nn(train_data, train_target, validate_data, validate_target,
mlp_model, alpha, epochs, batch_size, plot_acc)
# To see how well the model performs, we evaluate it on the test data.
evaluate(test_data, test_target, mlp_model)
```

Using the given hyperparameters, a final test accuracy of `0.955723`

was achieved, with the accuracy plot shown below.