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app.py
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import gradio as gr
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import time
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy.linalg import toeplitz, cholesky
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from sklearn.covariance import LedoitWolf, OAS
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np.random.seed(0)
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def plot_mse():
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# plot MSE
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plt.clf()
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plt.subplot(2, 1, 1)
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plt.errorbar(
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slider_samples_range,
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lw_mse.mean(1),
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yerr=lw_mse.std(1),
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label="Ledoit-Wolf",
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color="navy",
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lw=2,
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)
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plt.errorbar(
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slider_samples_range,
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oa_mse.mean(1),
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yerr=oa_mse.std(1),
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label="OAS",
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color="darkorange",
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lw=2,
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)
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plt.ylabel("Squared error")
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plt.legend(loc="upper right")
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plt.title("Comparison of covariance estimators")
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plt.xlim(5, 31)
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return plt
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def plot_shrinkage():
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# plot shrinkage coefficient
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plt.subplot(2, 1, 2)
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plt.errorbar(
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slider_samples_range,
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lw_shrinkage.mean(1),
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yerr=lw_shrinkage.std(1),
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label="Ledoit-Wolf",
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color="navy",
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lw=2,
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)
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plt.errorbar(
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slider_samples_range,
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oa_shrinkage.mean(1),
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yerr=oa_shrinkage.std(1),
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label="OAS",
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color="darkorange",
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lw=2,
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)
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plt.xlabel("n_samples")
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plt.ylabel("Shrinkage")
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plt.legend(loc="lower right")
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plt.ylim(plt.ylim()[0], 1.0 + (plt.ylim()[1] - plt.ylim()[0]) / 10.0)
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plt.xlim(5, 31)
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# plt.show()
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return plt
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title = "Ledoit-Wolf vs OAS estimation"
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# def greet(name):
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# return "Hello " + name + "!"
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with gr.Blocks(title=title, theme=gr.themes.Default(font=[gr.themes.GoogleFont("Inconsolata"), "Arial", "sans-serif"])) as demo:
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gr.Markdown(f"# {title}")
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gr.Markdown(
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"""
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The usual covariance maximum likelihood estimate can be regularized using shrinkage. Ledoit and Wolf proposed a close formula to compute the asymptotically optimal shrinkage parameter (minimizing a MSE criterion), yielding the Ledoit-Wolf covariance estimate.
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Chen et al. proposed an improvement of the Ledoit-Wolf shrinkage parameter, the OAS coefficient, whose convergence is significantly better under the assumption that the data are Gaussian.
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This example, inspired from Chen’s publication [1], shows a comparison of the estimated MSE of the LW and OAS methods, using Gaussian distributed data.
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[1] “Shrinkage Algorithms for MMSE Covariance Estimation” Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.
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""")
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n_features = 100
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min_slider_samples_range = gr.Slider(6, 31, value=6, step=1, label="min_samples_range", info="Choose between 6 and 31")
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max_slider_samples_range = gr.Slider(6, 31, value=31, step=1, label="max_samples_range", info="Choose between 6 and 31")
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r = 0.1
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real_cov = toeplitz(r ** np.arange(n_features))
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coloring_matrix = cholesky(real_cov)
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gr.Markdown(" **[Demo is based on sklearn docs](https://scikit-learn.org/stable/auto_examples/covariance/plot_lw_vs_oas.html)**")
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# name = "hardy"
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# greet_btn = gr.Button("Greet")
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# output = gr.Textbox(label="Output Box")
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# greet_btn.click(fn=greet, inputs=name, outputs=output)
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gr.Label(value="Comparison of Covariance Estimators")
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# generate_plots()
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# print("slider_samples_range:",slider_samples_range)
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slider_samples_range =np.arange(min_slider_samples_range,max_slider_samples_range,1)
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n_features = 100
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repeat = 100
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lw_mse = np.zeros((slider_samples_range.size, repeat))
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oa_mse = np.zeros((slider_samples_range.size, repeat))
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lw_shrinkage = np.zeros((slider_samples_range.size, repeat))
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oa_shrinkage = np.zeros((slider_samples_range.size, repeat))
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for i, n_samples in enumerate(slider_samples_range):
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for j in range(repeat):
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X = np.dot(np.random.normal(size=(n_samples, n_features)), coloring_matrix.T)
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lw = LedoitWolf(store_precision=False, assume_centered=True)
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lw.fit(X)
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lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
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lw_shrinkage[i, j] = lw.shrinkage_
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oa = OAS(store_precision=False, assume_centered=True)
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oa.fit(X)
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oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
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oa_shrinkage[i, j] = oa.shrinkage_
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#if min_slider_samples_range:
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min_slider_samples_range.change(plot_mse, outputs= gr.Plot() )
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max_slider_samples_range.change(plot_shrinkage, outputs= gr.Plot() )
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#elif max_slider_samples_range:
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# elif changed == False:
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# min_slider_samples_range.change(generate_plots, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
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# max_slider_samples_range.change(generate_plots, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
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# changed = True
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# else:
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# pass
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demo.launch()
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