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import numpy as np |
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import matplotlib.pyplot as plt |
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from PIL import Image |
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from io import BytesIO |
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from sklearn.linear_model import Ridge |
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from sklearn.gaussian_process.kernels import ExpSineSquared |
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from sklearn.kernel_ridge import KernelRidge |
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import gradio as gr |
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import random |
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def generate_data(n_samples: int) -> tuple: |
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rng = np.random.RandomState(random.randint(0, 1000)) |
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data = np.linspace(0, 30, num=n_samples).reshape(-1, 1) |
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target = np.sin(data).ravel() |
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training_sample_indices = rng.choice( |
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np.arange(0, int(0.4 * n_samples)), size=int(0.2 * n_samples), replace=False |
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) |
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training_data = data[training_sample_indices] |
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training_noisy_target = ( |
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target[training_sample_indices] + 0.5 * rng.randn(len(training_sample_indices)) |
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) |
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return data, target, training_data, training_noisy_target |
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def plot_ridge_and_kernel(n_samples: int) -> plt.figure: |
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data, target, training_data, training_noisy_target = generate_data(n_samples) |
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ridge = Ridge().fit(training_data, training_noisy_target) |
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kernel_ridge = KernelRidge(kernel=ExpSineSquared()) |
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kernel_ridge.fit(training_data, training_noisy_target) |
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fig, ax = plt.subplots(figsize=(8, 4)) |
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ridge_predictions = ridge.predict(data) |
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kernel_ridge_predictions = kernel_ridge.predict(data) |
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ax.plot(data, target, label="True signal", linewidth=2) |
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ax.scatter( |
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training_data, |
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training_noisy_target, |
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color="black", |
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label="Noisy measurements", |
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) |
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ax.plot(data, ridge_predictions, label="Ridge regression") |
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ax.plot( |
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data, |
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kernel_ridge_predictions, |
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label="Kernel ridge", |
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linewidth=2, |
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linestyle="dashdot", |
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) |
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ax.fill_between( |
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data.ravel(), |
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ridge_predictions, |
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kernel_ridge_predictions, |
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color="lightgrey", |
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alpha=0.4, |
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) |
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ax.legend() |
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ax.set_xlabel("data") |
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ax.set_ylabel("target") |
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_ = ax.set_title("Ridge vs Kernel Ridge with the area between highlighted") |
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return fig |
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def gradio_plot(n_samples: int) -> Image.Image: |
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fig = plot_ridge_and_kernel(n_samples) |
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buf = BytesIO() |
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fig.savefig(buf, format="png") |
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buf.seek(0) |
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im = Image.open(buf) |
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return im |
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inputs = [ |
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gr.inputs.Slider(minimum=100, maximum=5000, step=100, label="n_samples", default=1000), |
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] |
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title = "Comparison of kernel ridge and Gaussian process regression" |
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description = "Kernel ridge regression and Gaussian process regression both use the kernel trick to fit data. While kernel ridge regression aims to find a single target function minimizing the loss (mean squared error), Gaussian process regression takes a probabilistic approach, defining a Gaussian posterior distribution over target functions using Bayes' theorem. Essentially, kernel ridge regression seeks one best function, while Gaussian process regression considers a range of probable functions based on prior probabilities and observed data. \n \n link to the official doc https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_compare_gpr_krr.html#sphx-glr-auto-examples-gaussian-process-plot-compare-gpr-krr-py" |
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iface = gr.Interface(fn=gradio_plot, inputs=inputs, outputs="image", title = title , description = description) |
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iface.launch() |
