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| 1 | +# /// script |
| 2 | +# requires-python = ">=3.12" |
| 3 | +# dependencies = [ |
| 4 | +# "marimo", |
| 5 | +# "matplotlib==3.10.3", |
| 6 | +# "numpy==2.2.6", |
| 7 | +# "scikit-learn==1.6.1", |
| 8 | +# "scipy==1.15.3", |
| 9 | +# ] |
| 10 | +# /// |
| 11 | + |
| 12 | +import marimo |
| 13 | + |
| 14 | +__generated_with = "0.13.7" |
| 15 | +app = marimo.App(width="medium") |
| 16 | + |
| 17 | + |
| 18 | +@app.cell |
| 19 | +def _(): |
| 20 | + import numpy as np |
| 21 | + import matplotlib.pyplot as plt |
| 22 | + from sklearn.gaussian_process import GaussianProcessRegressor |
| 23 | + from sklearn.gaussian_process.kernels import Matern, WhiteKernel, ConstantKernel as C |
| 24 | + |
| 25 | + def black_box_function(x): |
| 26 | + return - (np.sin(3*x) + 0.5 * x) |
| 27 | + return ( |
| 28 | + C, |
| 29 | + GaussianProcessRegressor, |
| 30 | + Matern, |
| 31 | + WhiteKernel, |
| 32 | + black_box_function, |
| 33 | + np, |
| 34 | + plt, |
| 35 | + ) |
| 36 | + |
| 37 | + |
| 38 | +@app.cell |
| 39 | +def _(black_box_function, np, plt): |
| 40 | + X = np.linspace(0, 5.5, 1000).reshape(-1, 1) |
| 41 | + y = black_box_function(X) |
| 42 | + plt.plot(X, y) |
| 43 | + plt.title("Black-box function") |
| 44 | + plt.xlabel("x") |
| 45 | + plt.ylabel("f(x)") |
| 46 | + plt.show() |
| 47 | + return X, y |
| 48 | + |
| 49 | + |
| 50 | +@app.cell |
| 51 | +def _(black_box_function, np): |
| 52 | + X_grid = np.linspace(0, 2, 100).reshape(-1, 1) |
| 53 | + y_grid = black_box_function(X_grid) |
| 54 | + x_best = X_grid[np.argmax(y_grid)] |
| 55 | + return |
| 56 | + |
| 57 | + |
| 58 | +@app.cell |
| 59 | +def _(black_box_function, np): |
| 60 | + # Initial sample points (simulate prior evaluations) |
| 61 | + X_sample = np.array([[1.0], [3.0], [5.5]]) |
| 62 | + y_sample = black_box_function(X_sample) |
| 63 | + return X_sample, y_sample |
| 64 | + |
| 65 | + |
| 66 | +@app.cell |
| 67 | +def _(C, GaussianProcessRegressor, Matern, WhiteKernel, X_sample, y_sample): |
| 68 | + # Define the kernel |
| 69 | + kernel = C(1.0) * Matern(length_scale=1.0, nu=2.5) + WhiteKernel(noise_level=1e-5, noise_level_bounds=(1e-10, 1e1)) |
| 70 | + |
| 71 | + # Create and fit the Gaussian Process model |
| 72 | + gpr = GaussianProcessRegressor(kernel=kernel, alpha=0.0) |
| 73 | + gpr.fit(X_sample, y_sample) |
| 74 | + return (gpr,) |
| 75 | + |
| 76 | + |
| 77 | +@app.cell |
| 78 | +def _(X, X_sample, gpr, plt, y, y_sample): |
| 79 | + # Predict across the domain |
| 80 | + mu, std = gpr.predict(X, return_std=True) |
| 81 | + |
| 82 | + # Plot the result |
| 83 | + plt.figure(figsize=(10, 5)) |
| 84 | + plt.plot(X, y, 'k--', label="True function") |
| 85 | + plt.plot(X, mu, 'b-', label="GPR mean") |
| 86 | + plt.fill_between(X.ravel(), mu - std, mu + std, alpha=0.3, label="Uncertainty") |
| 87 | + plt.scatter(X_sample, y_sample, c='red', label="Samples") |
| 88 | + plt.legend() |
| 89 | + plt.title("Gaussian Process Fit") |
| 90 | + plt.xlabel("x") |
| 91 | + plt.ylabel("f(x)") |
| 92 | + plt.show() |
| 93 | + return |
| 94 | + |
| 95 | + |
| 96 | +@app.cell |
| 97 | +def _(np): |
| 98 | + from scipy.stats import norm |
| 99 | + |
| 100 | + def expected_improvement(X, X_sample, y_sample, model, xi=0.01): |
| 101 | + mu, std = model.predict(X, return_std=True) |
| 102 | + mu_sample_opt = np.min(y_sample) |
| 103 | + |
| 104 | + with np.errstate(divide='warn'): |
| 105 | + imp = mu_sample_opt - mu - xi # because we are minimizing |
| 106 | + Z = imp / std |
| 107 | + ei = imp * norm.cdf(Z) + std * norm.pdf(Z) |
| 108 | + ei[std == 0.0] = 0.0 |
| 109 | + |
| 110 | + return ei |
| 111 | + |
| 112 | + return (expected_improvement,) |
| 113 | + |
| 114 | + |
| 115 | +@app.cell |
| 116 | +def _(X, X_sample, expected_improvement, gpr, np, plt, y_sample): |
| 117 | + ei = expected_improvement(X, X_sample, y_sample, gpr) |
| 118 | + |
| 119 | + plt.figure(figsize=(10, 4)) |
| 120 | + plt.plot(X, ei, label="Expected Improvement") |
| 121 | + plt.axvline(X[np.argmax(ei)], color='r', linestyle='--', label="Next sample point") |
| 122 | + plt.title("Acquisition Function (Expected Improvement)") |
| 123 | + plt.xlabel("x") |
| 124 | + plt.ylabel("EI(x)") |
| 125 | + plt.legend() |
| 126 | + plt.show() |
| 127 | + |
| 128 | + return |
| 129 | + |
| 130 | + |
| 131 | +@app.cell |
| 132 | +def _(X, black_box_function, expected_improvement, gpr, np): |
| 133 | + def bayesian_optimization(n_iter=10): |
| 134 | + # Initial data |
| 135 | + X_sample = np.array([[1.0], [2.5], [4.0]]) |
| 136 | + y_sample = black_box_function(X_sample) |
| 137 | + |
| 138 | + for i in range(n_iter): |
| 139 | + gpr.fit(X_sample, y_sample) |
| 140 | + ei = expected_improvement(X, X_sample, y_sample, gpr) |
| 141 | + x_next = X[np.argmax(ei)].reshape(-1, 1) |
| 142 | + |
| 143 | + # Evaluate the function at the new point |
| 144 | + y_next = black_box_function(x_next) |
| 145 | + |
| 146 | + # Add the new sample to our dataset |
| 147 | + X_sample = np.vstack((X_sample, x_next)) |
| 148 | + y_sample = np.append(y_sample, y_next) |
| 149 | + return X_sample, y_sample |
| 150 | + |
| 151 | + return (bayesian_optimization,) |
| 152 | + |
| 153 | + |
| 154 | +@app.cell |
| 155 | +def _(bayesian_optimization): |
| 156 | + X_opt, y_opt = bayesian_optimization(n_iter=10) |
| 157 | + |
| 158 | + return X_opt, y_opt |
| 159 | + |
| 160 | + |
| 161 | +@app.cell |
| 162 | +def _(X, X_opt, black_box_function, plt, y_opt): |
| 163 | + # Plot final sampled points |
| 164 | + plt.plot(X, black_box_function(X), 'k--', label="True function") |
| 165 | + plt.scatter(X_opt, y_opt, c='red', label="Sampled Points") |
| 166 | + plt.title("Bayesian Optimization with Gaussian Process") |
| 167 | + plt.xlabel("x") |
| 168 | + plt.ylabel("f(x)") |
| 169 | + plt.legend() |
| 170 | + plt.show() |
| 171 | + |
| 172 | + return |
| 173 | + |
| 174 | + |
| 175 | +@app.cell |
| 176 | +def _(): |
| 177 | + return |
| 178 | + |
| 179 | + |
| 180 | +if __name__ == "__main__": |
| 181 | + app.run() |
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