Pushing the docs for revision for branch: master, commit 45949ab4ebe346bd1b12e0a51b0747cd132d0861

Author: skoptci

_downloads/1c9bc01d15cf0a1e95b499b64cae5679/bayesian-optimization.ipynb

@@ -26,7 +26,7 @@
       },
       "outputs": [],
       "source": [
-        "print(__doc__)\n\nimport numpy as np\nnp.random.seed(1234)\nimport matplotlib.pyplot as plt"
+        "print(__doc__)\n\nimport numpy as np\nnp.random.seed(237)\nimport matplotlib.pyplot as plt"
       ]
     },
     {
@@ -80,7 +80,7 @@
       },
       "outputs": [],
       "source": [
-        "from skopt import gp_minimize\n\nres = gp_minimize(f,                  # the function to minimize\n                  [(-2.0, 2.0)],      # the bounds on each dimension of x\n                  acq_func=\"EI\",      # the acquisition function\n                  n_calls=15,         # the number of evaluations of f\n                  n_random_starts=5,  # the number of random initialization points\n                  noise=0.1**2,       # the noise level (optional)\n                  random_state=123)   # the random seed"
+        "from skopt import gp_minimize\n\nres = gp_minimize(f,                  # the function to minimize\n                  [(-2.0, 2.0)],      # the bounds on each dimension of x\n                  acq_func=\"EI\",      # the acquisition function\n                  n_calls=15,         # the number of evaluations of f\n                  n_random_starts=5,  # the number of random initialization points\n                  noise=0.1**2,       # the noise level (optional)\n                  random_state=1234)   # the random seed"
       ]
     },
     {

_downloads/5514e237431a52400fbf5075b0d92256/optimizer-with-different-base-estimator.py

@@ -0,0 +1,169 @@
+"""
+==============================================
+Use different base estimators for optimization
+==============================================
+
+Sigurd Carlen, September 2019.
+Reformatted by Holger Nahrstaedt 2020
+
+.. currentmodule:: skopt
+
+
+To use different base_estimator or create a regressor with different parameters,
+we can create a regressor object and set it as kernel.
+
+"""
+print(__doc__)
+
+import numpy as np
+np.random.seed(1234)
+import matplotlib.pyplot as plt
+
+
+#############################################################################
+# Toy example
+# -----------
+#
+# Let assume the following noisy function :math:`f`:
+
+noise_level = 0.1
+
+# Our 1D toy problem, this is the function we are trying to
+# minimize
+
+def objective(x, noise_level=noise_level):
+    return np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2))\
+           + np.random.randn() * noise_level
+
+#############################################################################
+
+from skopt import Optimizer
+opt_gp = Optimizer([(-2.0, 2.0)], base_estimator="GP", n_initial_points=5,
+                acq_optimizer="sampling", random_state=42)
+
+#############################################################################
+
+x = np.linspace(-2, 2, 400).reshape(-1, 1)
+fx = np.array([objective(x_i, noise_level=0.0) for x_i in x])
+
+#############################################################################
+
+from skopt.acquisition import gaussian_ei
+
+def plot_optimizer(res, next_x, x, fx, n_iter, max_iters=5):
+    x_gp = res.space.transform(x.tolist())
+    gp = res.models[-1]
+    curr_x_iters = res.x_iters
+    curr_func_vals = res.func_vals
+
+    # Plot true function.
+    ax = plt.subplot(max_iters, 2, 2 * n_iter + 1)
+    plt.plot(x, fx, "r--", label="True (unknown)")
+    plt.fill(np.concatenate([x, x[::-1]]),
+             np.concatenate([fx - 1.9600 * noise_level,
+                             fx[::-1] + 1.9600 * noise_level]),
+             alpha=.2, fc="r", ec="None")
+    if n_iter < max_iters - 1:
+        ax.get_xaxis().set_ticklabels([])
+    # Plot GP(x) + contours
+    y_pred, sigma = gp.predict(x_gp, return_std=True)
+    plt.plot(x, y_pred, "g--", label=r"$\mu_{GP}(x)$")
+    plt.fill(np.concatenate([x, x[::-1]]),
+             np.concatenate([y_pred - 1.9600 * sigma,
+                             (y_pred + 1.9600 * sigma)[::-1]]),
+             alpha=.2, fc="g", ec="None")
+
+    # Plot sampled points
+    plt.plot(curr_x_iters, curr_func_vals,
+             "r.", markersize=8, label="Observations")
+    plt.title(r"x* = %.4f, f(x*) = %.4f" % (res.x[0], res.fun))
+    # Adjust plot layout
+    plt.grid()
+
+    if n_iter == 0:
+        plt.legend(loc="best", prop={'size': 6}, numpoints=1)
+
+    if n_iter != 4:
+        plt.tick_params(axis='x', which='both', bottom='off',
+                        top='off', labelbottom='off')
+
+    # Plot EI(x)
+    ax = plt.subplot(max_iters, 2, 2 * n_iter + 2)
+    acq = gaussian_ei(x_gp, gp, y_opt=np.min(curr_func_vals))
+    plt.plot(x, acq, "b", label="EI(x)")
+    plt.fill_between(x.ravel(), -2.0, acq.ravel(), alpha=0.3, color='blue')
+
+    if n_iter < max_iters - 1:
+        ax.get_xaxis().set_ticklabels([])
+
+    next_acq = gaussian_ei(res.space.transform([next_x]), gp,
+                           y_opt=np.min(curr_func_vals))
+    plt.plot(next_x, next_acq, "bo", markersize=6, label="Next query point")
+
+    # Adjust plot layout
+    plt.ylim(0, 0.07)
+    plt.grid()
+    if n_iter == 0:
+        plt.legend(loc="best", prop={'size': 6}, numpoints=1)
+
+    if n_iter != 4:
+        plt.tick_params(axis='x', which='both', bottom='off',
+                        top='off', labelbottom='off')
+
+#############################################################################
+# GP kernel
+# ---------
+
+fig = plt.figure()
+fig.suptitle("Standard GP kernel")
+for i in range(10):
+    next_x = opt_gp.ask()
+    f_val = objective(next_x)
+    res = opt_gp.tell(next_x, f_val)
+    if i >= 5:
+        plot_optimizer(res, opt_gp._next_x, x, fx, n_iter=i-5, max_iters=5)
+plt.tight_layout(rect=[0, 0.03, 1, 0.95])
+plt.plot()
+
+#############################################################################
+# Test different kernels
+# ----------------------
+
+from skopt.learning import GaussianProcessRegressor
+from skopt.learning.gaussian_process.kernels import ConstantKernel, Matern
+# Gaussian process with Matérn kernel as surrogate model
+
+from sklearn.gaussian_process.kernels import (RBF, Matern, RationalQuadratic,
+                                              ExpSineSquared, DotProduct,
+                                              ConstantKernel)
+
+
+kernels = [1.0 * RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0)),
+           1.0 * RationalQuadratic(length_scale=1.0, alpha=0.1),
+           1.0 * ExpSineSquared(length_scale=1.0, periodicity=3.0,
+                                length_scale_bounds=(0.1, 10.0),
+                                periodicity_bounds=(1.0, 10.0)),
+           ConstantKernel(0.1, (0.01, 10.0))
+               * (DotProduct(sigma_0=1.0, sigma_0_bounds=(0.1, 10.0)) ** 2),
+           1.0 * Matern(length_scale=1.0, length_scale_bounds=(1e-1, 10.0),
+                        nu=2.5)]
+
+#############################################################################
+
+for kernel in kernels:
+    gpr = GaussianProcessRegressor(kernel=kernel, alpha=noise_level ** 2,
+                                   normalize_y=True, noise="gaussian",
+                                   n_restarts_optimizer=2
+                                   )
+    opt = Optimizer([(-2.0, 2.0)], base_estimator=gpr, n_initial_points=5,
+                    acq_optimizer="sampling", random_state=42)
+    fig = plt.figure()
+    fig.suptitle(repr(kernel))
+    for i in range(10):
+        next_x = opt.ask()
+        f_val = objective(next_x)
+        res = opt.tell(next_x, f_val)
+        if i >= 5:
+            plot_optimizer(res, opt._next_x, x, fx, n_iter=i - 5, max_iters=5)
+    plt.tight_layout(rect=[0, 0.03, 1, 0.95])
+    plt.show()