add a very minimal example separate from code

examples/minimal_classifier.py

@@ -0,0 +1,91 @@
+"""
+A minimal classifier example
+"""
+
+import jax
+import matplotlib.pyplot as plt
+import numpy as np
+from flax import linen as nn
+from optax import adam, apply_updates, sigmoid_binary_cross_entropy
+from scipy.stats import multivariate_normal
+from sklearn.model_selection import train_test_split
+
+np.random.seed(2024)
+dim = 10
+n_sample = 10000
+
+
+m1 = np.random.randn(dim)
+m2 = np.random.randn(dim)
+
+M_0 = multivariate_normal(mean=m1, cov=np.eye(dim))
+M_1 = multivariate_normal(mean=m2, cov=np.eye(dim))
+
+X = np.concatenate((M_0.rvs(n_sample), M_1.rvs(n_sample)))
+y = np.concatenate((np.zeros(n_sample), np.ones(n_sample)))
+
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.01)
+
+
+###############################################################################
+# Neural Network code
+# imports needed
+# import jax
+# from flax import linen as nn
+# from optax import adam, apply_updates, sigmoid_binary_cross_entropy
+
+rng = jax.random.PRNGKey(0)
+
+
+class Network(nn.Module):
+    @nn.compact
+    def __call__(self, x):
+        x = nn.Dense(200)(x)
+        x = nn.relu(x)
+        for _ in range(2):
+            x = nn.Dense(100)(x)
+            x = nn.relu(x)
+        x = nn.Dense(1)(x)
+        return x
+
+
+learning_rate = 1e-2
+# epochs = steps * batch_size / n_sample
+batch_size = 512
+steps = 1000
+
+network_params = Network().init(rng, X_train[0])
+optimizer = adam(learning_rate=learning_rate)
+state = optimizer.init(network_params)
+
+
+def loss_fn(params, batch, labels):
+    logits = Network().apply(params, batch)
+    return sigmoid_binary_cross_entropy(logits.squeeze(), labels).mean()
+
+
+for i in range(steps):
+    rng, step_rng = jax.random.split(rng)
+    idx = jax.random.choice(step_rng, X_train.shape[0], shape=(batch_size,))
+    loss, grad = jax.value_and_grad(jax.jit(loss_fn))(
+        network_params, X_train[idx], y_train[idx]
+    )
+    updates, state = optimizer.update(grad, state)
+    network_params = apply_updates(network_params, updates)
+    if i % 100 == 0:
+        print(f"Step {i}, Loss: {loss}")
+
+
+def predict(x):
+    return Network().apply(network_params, x)
+
+
+#########################################################################
+# Check the outputs
+
+network_log_k = predict(X_test).squeeze()
+true_k = M_1.logpdf(X_test) - M_0.logpdf(X_test)
+
+
+plt.scatter(network_log_k, true_k)
+plt.show()