Bayesian optimization example added

Author: cosmic-cortex

examples/bayesian_optimization.py

@@ -0,0 +1,54 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.gaussian_process import GaussianProcessRegressor
+from sklearn.gaussian_process.kernels import Matern
+from modAL.models import BayesianOptimizer
+from modAL.acquisition import PI, EI, UCB, max_PI, max_EI, max_UCB
+
+
+# generating the data
+X = np.linspace(0, 20, 1000).reshape(-1, 1)
+y = np.sin(X)/2 - ((10 - X)**2)/50 + 2
+
+# assembling initial training set
+X_initial, y_initial = X[150].reshape(1, -1), y[150].reshape(1, -1)
+
+# defining the kernel for the Gaussian process
+kernel = Matern(length_scale=1.0)
+
+# initializing the optimizer
+optimizer = BayesianOptimizer(
+    estimator=GaussianProcessRegressor(kernel=kernel),
+    X_training=X_initial, y_training=y_initial,
+    query_strategy=max_EI
+)
+
+# plotting the initial estimation
+with plt.style.context('seaborn-white'):
+    plt.figure(figsize=(30, 6))
+    for n_query in range(5):
+        # plot current prediction
+        plt.subplot(2, 5, n_query + 1)
+        plt.title('Query no. %d' %(n_query + 1))
+        if n_query == 0:
+            plt.ylabel('Predictions')
+        plt.ylim([-1.5, 3])
+        pred, std = optimizer.predict(X.reshape(-1, 1), return_std=True)
+        utility = EI(optimizer, X)
+        plt.plot(X, pred)
+        plt.fill_between(X.reshape(-1, ), pred.reshape(-1, ) - std, pred.reshape(-1, ) + std, alpha=0.2)
+        plt.plot(X, y, c='k', linewidth=3)
+        # plotting acquired values
+        plt.scatter(optimizer.X_training[-1], optimizer.y_training[-1], c='w', s=40, zorder=20)
+        plt.scatter(optimizer.X_training, optimizer.y_training, c='k', s=80, zorder=1)
+
+        plt.subplot(2, 5, 5 + n_query + 1)
+        if n_query == 0:
+            plt.ylabel('Expected improvement')
+        plt.plot(X, 5*utility, c='r')
+        plt.ylim([-0.1, 1])
+
+        # query
+        query_idx, query_inst = optimizer.query(X)
+        optimizer.teach(X[query_idx].reshape(1, -1), y[query_idx].reshape(1, -1))
+    plt.show()