Models: Neural Networks

In this tutorial, we will demonstrate how to use neural networks for two common tasks in deep learning (DL): regression for structured data and image classification. We will use two datasets for this purpose: the Boston Housing dataset for regression and the CIFAR-10 dataset for image classification. It is highly recommended that you use Python for this part since R does not have a very good support for DL. However, we will provide the R code for the regression part to show how you can use the keras3 package to build and train neural networks in R.

Introduction

Neural networks are powerful machine learning models inspired by the human brain. Two popular frameworks for building them are:

• PyTorch: A flexible deep learning framework popular in research, offering an intuitive “define-by-run” approach.
• Keras (with TensorFlow backend): A high-level API that makes it easy to construct and train deep learning models. Keras 3 is actively maintained and supports multiple backends (TensorFlow, PyTorch, JAX). Note that raw TensorFlow has limited support on some platforms (e.g., Apple Silicon).

In both frameworks, the basic workflow for building a neural network is:

1. Define the model architecture: Create a model and add layers to it. We can add as many layers as needed where the type of each layer can also be specified (e.g., dense, convolutional) and any necessary parameters for each layer (e.g., number of nodes, activation function).

2. Compile/configure the model: Specify the loss function, optimizer, and any additional metrics you want to track during training.

3. Train the model: Pass in your training data and any necessary hyperparameters (e.g., batch size, number of epochs). A validation set can also be specified to monitor the model’s performance during training. Additionally, there are techniques such as early stopping, which stops the training if the model’s performance on the validation set does not improve after a certain number of epochs.

4. Evaluate the model: After training, evaluate the model’s performance on a test set.

5. Use the model to make predictions: Use the trained model to make predictions on new data. This stage is also known as “inference” in DL.

Setup

Python (PyTorch)

import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import TensorDataset, DataLoader
print(f"PyTorch version: {torch.__version__}")

PyTorch version: 2.10.0+cpu

Python (TensorFlow)

import numpy as np
import keras
from keras import layers
print(f"Keras version: {keras.__version__}")

Keras version: 3.12.1

R

# keras3 should already be installed via renv::restore()
# If not, run: install.packages("keras3"); keras3::install_keras(backend = "tensorflow")
library(keras3)

Regression for Structured Data

Boston Housing Dataset

The Boston Housing dataset is a well-known dataset used for regression tasks. It contains 506 instances and 13 features, including the median value of owner-occupied homes in $1000s. We will use this dataset to demonstrate how to perform regression on the sales price.

Python (PyTorch)

from keras.datasets import boston_housing

(train_x_np, train_y_np), (test_x_np, test_y_np) = boston_housing.load_data()
print(f"Train: {train_x_np.shape}, Test: {test_x_np.shape}")

Train: (404, 13), Test: (102, 13)

Python (TensorFlow)

from keras.datasets import boston_housing

(train_x, train_y), (test_x, test_y) = boston_housing.load_data()
print(f"Train: {train_x.shape}, Test: {test_x.shape}")

Train: (404, 13), Test: (102, 13)

R

houses <- keras3::dataset_boston_housing()

train_x <- houses$train$x
train_y <- houses$train$y
test_x <- houses$test$x
test_y <- houses$test$y

Data Preparation

We need to normalize the data. This is especially relevant for neural networks to stabilize the computation of the gradients and consequently improve the training process.

Python (PyTorch)

means_np = train_x_np.mean(axis=0)
stds_np = train_x_np.std(axis=0)

train_x_np = (train_x_np - means_np) / stds_np
test_x_np = (test_x_np - means_np) / stds_np

# Convert to PyTorch tensors
train_x_t = torch.tensor(train_x_np, dtype=torch.float32)
train_y_t = torch.tensor(train_y_np, dtype=torch.float32).unsqueeze(1)
test_x_t = torch.tensor(test_x_np, dtype=torch.float32)
test_y_t = torch.tensor(test_y_np, dtype=torch.float32).unsqueeze(1)

Python (TensorFlow)

means = train_x.mean(axis=0)
stds = train_x.std(axis=0)

train_x = (train_x - means) / stds
test_x = (test_x - means) / stds

R

means <- apply(train_x, 2, mean)
sds <- apply(train_x, 2, sd)

train_x <- scale(train_x, means, sds)
test_x <- scale(test_x, means, sds)

Model Definition

We will use a simple neural network with two hidden layers to perform regression.

TipLearning about some of the hyperparameters

You have many options for different hyperparameters; however, one lab session barely scratches the surface of DL and its hyperparameters. There are a couple of points that we need to specify here:

1. You can use any activation function in the middle layers, from a simple linear regression (linear) to more common ones such as hyperbolic tangent or tanh (often suitable for tabular data) to more sophisticated ones such as rectified linear unit or relu (better suited to high dimensional data). What is imperative is that in the last dense layer, the number of units and the activation function determine the kind of task (e.g., classification, regression, etc.) you’re trying to accomplish. If you’re doing a regression, the last dense layer has to have 1 unit and a linear activation function. If you’re doing a binary classification (logistic regression), you still use 1 dense unit but must apply the sigmoid activation function. If you’re doing multi-class classification, then the number of dense units must equal the number of classes, and the activation function is softmax (which is a generalization of sigmoid for multiple classes). Google also provides a nice visual that explains the difference between the classification models. If you remove the >0.5 rule (i.e., sigmoid), you essentially get a linear regression for that layer.

2. It is imperative that, depending on the task, you use the correct type of loss function. For instance, you can use mean squared error (mse) for regression and categorical cross-entropy for multi-class classification.

As mentioned, during the ML course, we cannot cover the details of DL. If you want to understand these hyperparameters better and explore additional ones, some excellent resources include Stanford’s CS231n: Deep Learning for Computer Vision and the PyTorch tutorials.

Python (PyTorch)

_ = torch.manual_seed(123)

# Define the model
model_reg_pt = nn.Sequential(
    nn.Linear(train_x_t.shape[1], 64),
    nn.ReLU(),
    nn.Linear(64, 64),
    nn.ReLU(),
    nn.Linear(64, 1)
)

# Define loss function and optimizer
criterion = nn.MSELoss()
optimizer_pt = optim.Adam(model_reg_pt.parameters())

Python (TensorFlow)

keras.utils.set_random_seed(123)

# Define the model
model_reg = keras.Sequential([
    layers.Dense(64, activation='relu', input_shape=(train_x.shape[1],)),
    layers.Dense(64, activation='relu'),
    layers.Dense(1, activation='linear')
])

# Compile the model
model_reg.compile(optimizer='adam', loss='mean_squared_error', metrics=['mean_absolute_error'])
model_reg.summary()

Model: "sequential"
┌─────────────────────────────────┬────────────────────────┬───────────────┐
│ Layer (type)                    │ Output Shape           │       Param # │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense (Dense)                   │ (None, 64)             │           896 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_1 (Dense)                 │ (None, 64)             │         4,160 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_2 (Dense)                 │ (None, 1)              │            65 │
└─────────────────────────────────┴────────────────────────┴───────────────┘
 Total params: 5,121 (20.00 KB)
 Trainable params: 5,121 (20.00 KB)
 Non-trainable params: 0 (0.00 B)

R

keras3::set_random_seed(123)

model_reg <- keras_model_sequential(input_shape = ncol(train_x)) |>
  layer_dense(units = 64, activation = "relu") |>
  layer_dense(units = 64, activation = "relu") |>
  layer_dense(units = 1, activation = "linear")

model_reg |> compile(
  optimizer = "adam",
  loss = "mean_squared_error",
  metrics = c("mean_absolute_error")
)

Model Training

Python (PyTorch)

import matplotlib.pyplot as plt

# Create data loaders
train_dataset = TensorDataset(train_x_t, train_y_t)
train_loader = DataLoader(train_dataset, batch_size=32, shuffle=True)

# Training loop
loss_history = []
_ = model_reg_pt.train()
for epoch in range(10):  # 300 for best results
    epoch_loss = 0
    for batch_x, batch_y in train_loader:
        optimizer_pt.zero_grad()
        pred = model_reg_pt(batch_x)
        loss = criterion(pred, batch_y)
        loss.backward()
        optimizer_pt.step()
        epoch_loss += loss.item()
    avg_loss = epoch_loss / len(train_loader)
    loss_history.append(avg_loss)
    if (epoch + 1) % 5 == 0:
        print(f"Epoch {epoch+1}, Loss: {avg_loss:.4f}")

plt.plot(loss_history);
plt.xlabel("Epoch");
plt.ylabel("Loss (MSE)");
plt.title("Training Loss");
plt.show()

Epoch 5, Loss: 257.8388
Epoch 10, Loss: 36.2100

Python (TensorFlow)

import matplotlib.pyplot as plt

history = model_reg.fit(
    train_x, train_y,
    epochs=10,  # 300 to get the best results
    batch_size=32,
    validation_split=0.2,
    callbacks=[keras.callbacks.EarlyStopping(patience=30, restore_best_weights=True)],
    verbose=1
)

plt.plot(history.history['loss'], label='Train');
plt.plot(history.history['val_loss'], label='Validation');
plt.xlabel("Epoch");
plt.ylabel("Loss (MSE)");
plt.title("Training Loss");
plt.legend();
plt.show()

Epoch 1/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m3s[0m 363ms/step - loss: 566.7098 - mean_absolute_error: 21.7820
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 11ms/step - loss: 548.3987 - mean_absolute_error: 21.5741 - val_loss: 586.5386 - val_mean_absolute_error: 22.5123
Epoch 2/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 16ms/step - loss: 517.0693 - mean_absolute_error: 20.7190
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 501.7396 - mean_absolute_error: 20.5227 - val_loss: 534.2108 - val_mean_absolute_error: 21.3861
Epoch 3/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 16ms/step - loss: 465.5650 - mean_absolute_error: 19.5448
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 5ms/step - loss: 448.2894 - mean_absolute_error: 19.2557 - val_loss: 468.3222 - val_mean_absolute_error: 19.8879
Epoch 4/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 18ms/step - loss: 401.8004 - mean_absolute_error: 18.0079
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 379.8379 - mean_absolute_error: 17.5461 - val_loss: 383.2387 - val_mean_absolute_error: 17.8069
Epoch 5/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 17ms/step - loss: 321.5128 - mean_absolute_error: 15.8981
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 294.5597 - mean_absolute_error: 15.2094 - val_loss: 283.1658 - val_mean_absolute_error: 14.9977
Epoch 6/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 15ms/step - loss: 227.8317 - mean_absolute_error: 13.1221
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 201.2679 - mean_absolute_error: 12.1951 - val_loss: 183.1437 - val_mean_absolute_error: 11.4459
Epoch 7/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 16ms/step - loss: 135.8779 - mean_absolute_error: 9.7947
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 119.6998 - mean_absolute_error: 8.9462 - val_loss: 107.9070 - val_mean_absolute_error: 8.1430
Epoch 8/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 15ms/step - loss: 68.3341 - mean_absolute_error: 6.7204
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 70.8525 - mean_absolute_error: 6.5915 - val_loss: 71.4134 - val_mean_absolute_error: 6.4259
Epoch 9/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 17ms/step - loss: 36.8598 - mean_absolute_error: 5.2102
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 52.5437 - mean_absolute_error: 5.4284 - val_loss: 57.1445 - val_mean_absolute_error: 5.6849
Epoch 10/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 16ms/step - loss: 25.8261 - mean_absolute_error: 4.2970
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 43.6421 - mean_absolute_error: 4.7666 - val_loss: 47.6434 - val_mean_absolute_error: 5.1693

R

history <- model_reg |> fit(
  train_x, train_y,
  epochs = 10,  # 300 to get the best results
  batch_size = 32,
  validation_split = 0.2,
  callbacks = callback_early_stopping(patience = 30, restore_best_weights = TRUE),
  verbose = 1
)

plot(history)

Epoch 1/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m3s[0m 331ms/step - loss: 566.7198 - mean_absolute_error: 21.7822
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 12ms/step - loss: 548.4251 - mean_absolute_error: 21.5747 - val_loss: 586.6022 - val_mean_absolute_error: 22.5136
Epoch 2/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 20ms/step - loss: 517.1339 - mean_absolute_error: 20.7204
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 5ms/step - loss: 501.8156 - mean_absolute_error: 20.5244 - val_loss: 534.3273 - val_mean_absolute_error: 21.3886
Epoch 3/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 28ms/step - loss: 465.6811 - mean_absolute_error: 19.5475
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 448.4161 - mean_absolute_error: 19.2588 - val_loss: 468.4966 - val_mean_absolute_error: 19.8920
Epoch 4/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 25ms/step - loss: 401.9715 - mean_absolute_error: 18.0122
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 6ms/step - loss: 380.0186 - mean_absolute_error: 17.5507 - val_loss: 383.4724 - val_mean_absolute_error: 17.8128
Epoch 5/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 29ms/step - loss: 321.7372 - mean_absolute_error: 15.9045
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 294.7874 - mean_absolute_error: 15.2162 - val_loss: 283.4386 - val_mean_absolute_error: 15.0061
Epoch 6/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m1s[0m 102ms/step - loss: 228.0873 - mean_absolute_error: 13.1302
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 201.5058 - mean_absolute_error: 12.2035 - val_loss: 183.3969 - val_mean_absolute_error: 11.4563
Epoch 7/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 29ms/step - loss: 136.1075 - mean_absolute_error: 9.8040
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 119.8846 - mean_absolute_error: 8.9541 - val_loss: 108.0732 - val_mean_absolute_error: 8.1505
Epoch 8/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 27ms/step - loss: 68.4765 - mean_absolute_error: 6.7264
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 70.9415 - mean_absolute_error: 6.5963 - val_loss: 71.4844 - val_mean_absolute_error: 6.4290
Epoch 9/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m0s[0m 80ms/step - loss: 36.9140 - mean_absolute_error: 5.2137
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 52.5765 - mean_absolute_error: 5.4308 - val_loss: 57.1857 - val_mean_absolute_error: 5.6866
Epoch 10/10

[1m 1/11[0m [32m━[0m[37m━━━━━━━━━━━━━━━━━━━[0m [1m1s[0m 103ms/step - loss: 25.8527 - mean_absolute_error: 4.2993
[1m11/11[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 7ms/step - loss: 43.6699 - mean_absolute_error: 4.7684 - val_loss: 47.6769 - val_mean_absolute_error: 5.1710

Model Evaluation

Python (PyTorch)

_ = model_reg_pt.eval()
with torch.no_grad():
    preds = model_reg_pt(test_x_t)
    test_mae = torch.mean(torch.abs(preds - test_y_t)).item()
    test_mse = criterion(preds, test_y_t).item()
print(f"Test MSE: {test_mse:.4f}, Test MAE: {test_mae:.4f}")

Test MSE: 39.6828, Test MAE: 4.8964

Python (TensorFlow)

nn_results = model_reg.evaluate(test_x, test_y)
print(f"Test Loss (MSE): {nn_results[0]:.4f}, Test MAE: {nn_results[1]:.4f}")

[1m1/4[0m [32m━━━━━[0m[37m━━━━━━━━━━━━━━━[0m [1m0s[0m 15ms/step - loss: 41.2739 - mean_absolute_error: 4.8162
[1m4/4[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 4ms/step - loss: 44.3121 - mean_absolute_error: 5.1213 
Test Loss (MSE): 44.3121, Test MAE: 5.1213

R

nn_results <- model_reg |> evaluate(test_x, test_y)
nn_results

4/4 - 0s - 5ms/step - loss: 44.3387 - mean_absolute_error: 5.1227
$loss
[1] 44.33867

$mean_absolute_error
[1] 5.122735

To put these results in context, we can compare it with a simple linear regression in R:

df_tr <- data.frame(train_y, train_x)
lm_mod <- lm(train_y ~ ., data = df_tr)
lm_preds <- as.vector(predict(lm_mod, newdata=data.frame(test_x)))

caret::MAE(obs = test_y, pred = lm_preds)

[1] 3.464186

We see that the neural network does significantly better than a regression model. We can also compare it with the trees seen in the CART series.

library(rpart)
set.seed(123)
tree_model <- rpart(train_y ~ ., data=df_tr)
tree_preds <- predict(tree_model,newdata = data.frame(test_x))

caret::MAE(obs = test_y, pred = tree_preds)

[1] 3.246767

The neural network also outperforms CART (if you run NN for 300 epochs). This is due to multiple reasons, including a higher complexity of the neural network (more parameters), using a validation set, and so on. You will learn about ensemble methods (bagging and boosting) in the upcoming lectures. Ensemble methods are the true champions for structured data and usually outperform neural networks for structured/low-dimensional data.

Image Classification

CIFAR-10 Dataset

The CIFAR-10 dataset is a well-known dataset used for image classification tasks. It contains 50,000 training images and 10,000 testing images of size 32x32 pixels, each belonging to one of ten classes. We will use this dataset to demonstrate how to perform image classification.

Python (PyTorch)

import torchvision
import torchvision.transforms as transforms

transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))])
trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)
testset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform)
train_loader_img = DataLoader(trainset, batch_size=64, shuffle=True)
test_loader_img = DataLoader(testset, batch_size=64, shuffle=False)

# Display some sample images
classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck')
fig, axes = plt.subplots(2, 5, figsize=(10, 4))
for i, ax in enumerate(axes.flat):
    img = testset[i][0].permute(1, 2, 0) * 0.5 + 0.5  # unnormalize
    ax.imshow(img);
    ax.set_title(classes[testset[i][1]]);
    ax.axis('off');
plt.suptitle("Sample CIFAR-10 Images");
plt.tight_layout();
plt.show()

_ = torch.manual_seed(123)

model_cnn_pt = nn.Sequential(
    nn.Conv2d(3, 32, 3, padding=0), nn.ReLU(), nn.MaxPool2d(2),
    nn.Conv2d(32, 64, 5, padding=0), nn.ReLU(), nn.MaxPool2d(3),
    nn.Conv2d(64, 64, 3, padding=0), nn.ReLU(),
    nn.Flatten(),
    nn.Linear(64, 64), nn.ReLU(),
    nn.Linear(64, 10)
)

criterion_cnn = nn.CrossEntropyLoss()
optimizer_cnn = optim.Adam(model_cnn_pt.parameters())

for epoch in range(10):
    _ = model_cnn_pt.train()
    running_loss, correct_train, total_train = 0, 0, 0
    for images, labels in train_loader_img:
        optimizer_cnn.zero_grad()
        outputs = model_cnn_pt(images)
        loss = criterion_cnn(outputs, labels)
        loss.backward()
        optimizer_cnn.step()
        running_loss += loss.item()
        _, predicted = torch.max(outputs, 1)
        total_train += labels.size(0)
        correct_train += (predicted == labels).sum().item()
    train_acc = correct_train / total_train
    avg_loss = running_loss / len(train_loader_img)
    print(f"Epoch {epoch+1}, Loss: {avg_loss:.4f}, Accuracy: {train_acc:.4f}")

# Evaluate
correct, total = 0, 0
_ = model_cnn_pt.eval()
with torch.no_grad():
    for images, labels in test_loader_img:
        outputs = model_cnn_pt(images)
        _, predicted = torch.max(outputs, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()
print(f"Test Accuracy: {correct/total:.4f}")

# Show predictions on sample images
_ = model_cnn_pt.eval()
fig, axes = plt.subplots(2, 5, figsize=(10, 4))
with torch.no_grad():
    for i, ax in enumerate(axes.flat):
        img = testset[i][0].unsqueeze(0)
        pred = model_cnn_pt(img).argmax(1).item()
        true_label = testset[i][1]
        img_show = testset[i][0].permute(1, 2, 0) * 0.5 + 0.5
        ax.imshow(img_show);
        color = 'green' if pred == true_label else 'red'
        ax.set_title(f"{classes[pred]}", color=color);
        ax.set_xlabel(f"({classes[true_label]})", fontsize=8);
        ax.set_xticks([]); ax.set_yticks([]);
plt.suptitle("Predictions (true label in parentheses)");
plt.tight_layout();
plt.show()

Epoch 1, Loss: 1.5595, Accuracy: 0.4207
Epoch 2, Loss: 1.1944, Accuracy: 0.5734
Epoch 3, Loss: 1.0373, Accuracy: 0.6344
Epoch 4, Loss: 0.9373, Accuracy: 0.6696
Epoch 5, Loss: 0.8591, Accuracy: 0.7001
Epoch 6, Loss: 0.8064, Accuracy: 0.7193
Epoch 7, Loss: 0.7582, Accuracy: 0.7370
Epoch 8, Loss: 0.7143, Accuracy: 0.7522
Epoch 9, Loss: 0.6763, Accuracy: 0.7628
Epoch 10, Loss: 0.6430, Accuracy: 0.7754
Test Accuracy: 0.7028

Python (TensorFlow)

(train_images, train_labels), (test_images, test_labels) = keras.datasets.cifar10.load_data()

# Normalize
train_images = train_images / 255.0
test_images = test_images / 255.0

classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']

# Display some sample images
fig, axes = plt.subplots(2, 5, figsize=(10, 4))
for i, ax in enumerate(axes.flat):
    ax.imshow(test_images[i]);
    ax.set_title(classes[test_labels[i][0]]);
    ax.axis('off');
plt.suptitle("Sample CIFAR-10 Images");
plt.tight_layout();
plt.show()

# One-hot encode labels
train_labels_cat = keras.utils.to_categorical(train_labels, 10)
test_labels_cat = keras.utils.to_categorical(test_labels, 10)

keras.utils.set_random_seed(123)

model_cnn = keras.Sequential([
    layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)),
    layers.MaxPooling2D((2, 2)),
    layers.Conv2D(64, (5, 5), activation='relu'),
    layers.MaxPooling2D((3, 3)),
    layers.Conv2D(64, (3, 3), activation='relu'),
    layers.Flatten(),
    layers.Dense(64, activation='relu'),
    layers.Dense(10, activation='softmax')
])

model_cnn.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])

model_cnn.fit(train_images, train_labels_cat, epochs=10, batch_size=64,
              validation_data=(test_images, test_labels_cat))
model_cnn.evaluate(test_images, test_labels_cat)

# Show predictions on sample images
predictions = model_cnn.predict(test_images[:10])
fig, axes = plt.subplots(2, 5, figsize=(10, 4))
for i, ax in enumerate(axes.flat):
    ax.imshow(test_images[i]);
    pred = predictions[i].argmax()
    true_label = test_labels[i][0]
    color = 'green' if pred == true_label else 'red'
    ax.set_title(f"{classes[pred]}", color=color);
    ax.set_xlabel(f"({classes[true_label]})", fontsize=8);
    ax.set_xticks([]); ax.set_yticks([]);
plt.suptitle("Predictions (true label in parentheses)");
plt.tight_layout();
plt.show()

Epoch 1/10

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Epoch 2/10

[1m  1/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m20s[0m 26ms/step - accuracy: 0.5312 - loss: 1.3719
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Epoch 3/10

[1m  1/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m19s[0m 25ms/step - accuracy: 0.6875 - loss: 1.0634
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[1m 25/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m3s[0m 4ms/step - accuracy: 0.5812 - loss: 1.1939
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Epoch 4/10

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Epoch 5/10

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Epoch 6/10

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Epoch 7/10

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Epoch 8/10

[1m  1/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m20s[0m 26ms/step - accuracy: 0.7969 - loss: 0.7215
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Epoch 9/10

[1m  1/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m18s[0m 24ms/step - accuracy: 0.7812 - loss: 0.7284
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[1m 24/782[0m [37m━━━━━━━━━━━━━━━━━━━━[0m [1m3s[0m 4ms/step - accuracy: 0.7297 - loss: 0.8568
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Epoch 10/10

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<keras.src.callbacks.history.History object at 0x000001E89C351330>

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[0.9579431414604187, 0.6678000092506409]

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R

cifar10 <- dataset_cifar10()

train_images <- cifar10$train$x / 255
test_images <- cifar10$test$x / 255
train_labels_raw <- cifar10$train$y
test_labels_raw <- cifar10$test$y
train_labels <- to_categorical(train_labels_raw, 10)
test_labels <- to_categorical(test_labels_raw, 10)

classes <- c("plane", "car", "bird", "cat", "deer", "dog", "frog", "horse", "ship", "truck")

# Display some sample images
par(mfrow = c(2, 5), mar = c(1, 0.5, 2, 0.5))
for (i in 1:10) {
  img <- test_images[i, , , ]
  img <- aperm(img, c(2, 1, 3))  # transpose for correct orientation
  plot(as.raster(img))
  title(main = classes[test_labels_raw[i] + 1], cex.main = 1)
}

set_random_seed(123)

model_cnn <- keras_model_sequential(input_shape = c(32, 32, 3)) |>
  layer_conv_2d(filters = 32, kernel_size = c(3, 3), activation = "relu") |>
  layer_max_pooling_2d(pool_size = c(2, 2)) |>
  layer_conv_2d(filters = 64, kernel_size = c(5, 5), activation = "relu") |>
  layer_max_pooling_2d(pool_size = c(3, 3)) |>
  layer_conv_2d(filters = 64, kernel_size = c(3, 3), activation = "relu") |>
  layer_flatten() |>
  layer_dense(units = 64, activation = "relu") |>
  layer_dense(units = 10, activation = "softmax")

model_cnn |> compile(
  loss = "categorical_crossentropy",
  optimizer = optimizer_adam(),
  metrics = c("accuracy")
)

model_cnn |> fit(train_images, train_labels, epochs = 10, batch_size = 64,
                 validation_data = list(test_images, test_labels))
model_cnn |> evaluate(test_images, test_labels)

# Show predictions on sample images
predictions <- model_cnn |> predict(test_images[1:10, , , , drop = FALSE])
par(mfrow = c(2, 5), mar = c(2, 0.5, 2, 0.5))
for (i in 1:10) {
  img <- test_images[i, , , ]
  img <- aperm(img, c(2, 1, 3))
  pred <- which.max(predictions[i, ])
  true_label <- test_labels_raw[i] + 1
  plot(as.raster(img))
  color <- if (pred == true_label) "darkgreen" else "red"
  title(main = classes[pred], col.main = color, cex.main = 1)
  mtext(paste0("(", classes[true_label], ")"), side = 1, cex = 0.7)
}

Epoch 1/10
782/782 - 5s - 6ms/step - accuracy: 0.4010 - loss: 1.6185 - val_accuracy: 0.4926 - val_loss: 1.4559
Epoch 2/10
782/782 - 5s - 6ms/step - accuracy: 0.5383 - loss: 1.2860 - val_accuracy: 0.5818 - val_loss: 1.1779
Epoch 3/10
782/782 - 4s - 6ms/step - accuracy: 0.5935 - loss: 1.1456 - val_accuracy: 0.6075 - val_loss: 1.1105
Epoch 4/10
782/782 - 4s - 5ms/step - accuracy: 0.6257 - loss: 1.0598 - val_accuracy: 0.6350 - val_loss: 1.0409
Epoch 5/10
782/782 - 4s - 5ms/step - accuracy: 0.6495 - loss: 0.9953 - val_accuracy: 0.6442 - val_loss: 1.0054
Epoch 6/10
782/782 - 4s - 6ms/step - accuracy: 0.6684 - loss: 0.9439 - val_accuracy: 0.6434 - val_loss: 1.0087
Epoch 7/10
782/782 - 4s - 5ms/step - accuracy: 0.6865 - loss: 0.8963 - val_accuracy: 0.6585 - val_loss: 0.9752
Epoch 8/10
782/782 - 4s - 6ms/step - accuracy: 0.7023 - loss: 0.8522 - val_accuracy: 0.6647 - val_loss: 0.9679
Epoch 9/10
782/782 - 4s - 5ms/step - accuracy: 0.7156 - loss: 0.8162 - val_accuracy: 0.6671 - val_loss: 0.9647
Epoch 10/10
782/782 - 4s - 5ms/step - accuracy: 0.7272 - loss: 0.7830 - val_accuracy: 0.6678 - val_loss: 0.9579
313/313 - 1s - 2ms/step - accuracy: 0.6678 - loss: 0.9579
$accuracy
[1] 0.6678

$loss
[1] 0.9579431

1/1 - 0s - 54ms/step

You may notice that we did not obtain extremely high accuracy, but this is okay for multiple reasons:

1. We only trained the model for a few epochs and stopped the training very early. You’re welcome to let it run for more epochs.
2. We’re dealing with at least ten classes; this is a rather complicated problem.
3. In DL, you can define many different architectures and hyperparameters, and since we did not play around with these values, this could also explain the lower performance.

Your turn: NNs applied to the nursing data

Use NNs to fit nursing data, with the cost variable once again set as the prediction outcome. Compare the performance against the tree-based methods. Which type of machine learning model would you go for and why? (think in terms of interpretability and performance)

References

• Keras 3 documentation
• PyTorch documentation
• PyTorch tutorials
• Stanford CS231n: Deep Learning for Computer Vision
• Google ML guide: activation functions for classifier neural networks