Note
Go to the end to download the full example code.
Simple Neural Network#
This example solves a simple binary classification problem using a basic neural network with 2 layers.
The classification problem is generated by the make_moons dataset generator from scikit–learn.
import matplotlib.pyplot as plt
from utils.plotting import plot_decision_boundary
from tqdm.auto import tqdm
import torch as pt
import torch.nn as nn
from torch.utils.data import TensorDataset, DataLoader
from sklearn.model_selection import train_test_split
from skwdro.torch import robustify
Problem setup#
from sklearn.datasets import make_moons
n = 256 + 64
X, y = make_moons(n_samples=n,
noise=0.05,
random_state=42)
Visualize the data#
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdYlBu) # type: ignore
plt.show()
Preprocessing#
# Split the data into train and test sets
X_train, X_test, y_train, y_test = train_test_split(
X,
y,
train_size=256,
test_size=64,
random_state=42
)
device = "cuda" if pt.cuda.is_available() else "cpu"
# Set a seed for torch to avoid too widely different results
pt.manual_seed(42)
# Turn data into tensors
full_batch_x = pt.from_numpy(X_train).to(device)
full_batch_y = pt.from_numpy(y_train).unsqueeze(-1).to(full_batch_x)
dataset = DataLoader(
TensorDataset(
full_batch_x,
full_batch_y
),
batch_size=64
)
batch_x_test = pt.from_numpy(X_train).to(device)
batch_y_test = pt.from_numpy(y_train).unsqueeze(-1).to(batch_x_test)
Two-layers model#
class SimpleNN(nn.Module):
def __init__(self, in_features, out_features, hidden_units):
super().__init__()
# Two hidden layers and logit output
self.linear_relu_stack = nn.Sequential(
nn.Linear(in_features, hidden_units),
nn.ReLU(),
nn.Linear(hidden_units, hidden_units),
nn.ReLU(),
nn.Linear(hidden_units, out_features),
)
def forward(self, x):
logits = self.linear_relu_stack(x)
return logits
loss_fn = nn.BCEWithLogitsLoss(reduction='none')
# Define a sample batch for initialization
sample_batch_x, sample_batch_y = next(iter(dataset))
Set the models up#
First build the ERM model solving:
\[\min_\theta \frac{1}{N}\sum_{i=1}^NL_\theta(\xi_i)\]
erm_model = SimpleNN(
in_features=2,
out_features=1,
hidden_units=10
).to(full_batch_x)
print(erm_model)
# ERM loss, with the same interfaces as the robust one
erm_loss = robustify(
loss_fn,
erm_model,
pt.tensor(0.),
sample_batch_x, sample_batch_y
) # Replaces the loss of the model by the dual WDRO loss
SimpleNN(
(linear_relu_stack): Sequential(
(0): Linear(in_features=2, out_features=10, bias=True)
(1): ReLU()
(2): Linear(in_features=10, out_features=10, bias=True)
(3): ReLU()
(4): Linear(in_features=10, out_features=1, bias=True)
)
)
Then the robust model solving
\[\min_{\theta, \lambda\ge 0} \rho\lambda+\frac{1}{N}\sum_{i=1}^N\texttt{LogSumExp}_\varepsilon \{L_\theta(\cdot)-\lambda\|\cdot-\xi_i\|_2^2\}\]
robust_model = SimpleNN(
in_features=2,
out_features=1,
hidden_units=100
).to(full_batch_x)
print(robust_model)
# Robust loss
robust_loss = robustify(
loss_fn,
robust_model,
pt.tensor(1e-3),
sample_batch_x, sample_batch_y,
cost_spec="t-NLC-2-2",
n_samples=16
) # Replaces the loss of the model by the dual WDRO loss
SimpleNN(
(linear_relu_stack): Sequential(
(0): Linear(in_features=2, out_features=100, bias=True)
(1): ReLU()
(2): Linear(in_features=100, out_features=100, bias=True)
(3): ReLU()
(4): Linear(in_features=100, out_features=1, bias=True)
)
)
Training loop#
def train(model, epochs = 300, lr = 5e-3):
optimizer = pt.optim.AdamW(params=model.parameters(), lr=lr)
# optimizer = pt.optim.AdamW(params=robust_loss.parameters())
# Training loop
epoch_iterator = tqdm(range(epochs), position=0, desc='Epochs', leave=True)
losses = []
for _ in epoch_iterator:
avg_testloss = 0.
for batch_x, batch_y in tqdm(dataset, position=1, desc='Sample', leave=False):
# ## Training
model.train()
optimizer.zero_grad()
# loss = loss_fn(model(batch_x.squeeze()), batch_y)
loss = model(batch_x, batch_y, reset_sampler=True)
loss.backward()
optimizer.step()
# ## Testing
model.eval()
with pt.no_grad():
# Forward pass
model.erm_mode = True
test_logits = model.primal_loss.transform(batch_x_test)
test_pred = pt.round(pt.sigmoid(test_logits))
# Compute the loss
avg_testloss += loss_fn(test_logits, batch_y_test).mean().item()
model.erm_mode = False
epoch_iterator.set_postfix(
{'acc': f"{(test_pred == batch_y_test).float().mean().item()*100}%"}
)
losses.append(avg_testloss / len(dataset))
# Print
epoch_iterator.set_postfix({'loss': avg_testloss / len(dataset)})
return losses
Learn the ERM model#
erm_losses = train(erm_loss)
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Epochs: 100%|██████████| 300/300 [00:02<00:00, 127.82it/s, loss=0.000264]
Learn the SkWDRO model#
dro_losses = train(robust_loss)
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Visuals#
First, the ERM:
# Plot decision boundaries for training and test sets
plt.figure(figsize=(12, 6))
plt.subplot(2, 2, 1)
plt.title("Train")
plot_decision_boundary(erm_model, full_batch_x, full_batch_y)
plt.subplot(2, 2, 2)
plt.title("Test")
plot_decision_boundary(erm_model, batch_x_test, batch_y_test)
plt.subplot(2, 1, 2)
plt.title("Test loss through epochs")
plt.plot(erm_losses)
plt.yscale('log')
plt.show()
Then the DRO model:
# Plot decision boundaries for training and test sets
plt.figure(figsize=(12, 6))
plt.subplot(2, 2, 1)
plt.title("Train")
plot_decision_boundary(robust_model, full_batch_x, full_batch_y)
plt.subplot(2, 2, 2)
plt.title("Test")
plot_decision_boundary(robust_model, batch_x_test, batch_y_test)
plt.subplot(2, 1, 2)
plt.title("Test loss through epochs")
plt.plot(dro_losses)
plt.yscale('log')
plt.show()
Total running time of the script: (0 minutes 9.836 seconds)