Create app.py

app.py

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+import gradio as gr
+import time
+import numpy as np
+import matplotlib.pyplot as plt
+
+from scipy.linalg import toeplitz, cholesky
+from sklearn.covariance import LedoitWolf, OAS
+
+np.random.seed(0)
+
+
+
+
+def plot_mse(min_slider_samples_range,max_slider_samples_range):
+     # plot MSE
+     print("inside plot_mse")
+     plt.subplot(2, 1, 1)
+     plt.errorbar(
+          slider_samples_range,
+          lw_mse.mean(1),
+          yerr=lw_mse.std(1),
+          label="Ledoit-Wolf",
+          color="navy",
+          lw=2,
+    )
+     plt.errorbar(
+          slider_samples_range,
+          oa_mse.mean(1),
+          yerr=oa_mse.std(1),
+          label="OAS",
+          color="darkorange",
+          lw=2,
+    )
+     plt.ylabel("Squared error")
+     plt.legend(loc="upper right")
+     plt.title("Comparison of covariance estimators")
+     plt.xlim(5, 31)
+     print("outside plot_mse")
+     return plt  
+
+
+def plot_shrinkage(min_slider_samples_range,max_slider_samples_range):
+    # plot shrinkage coefficient
+    print("inside plot_shrink")
+    plt.subplot(2, 1, 2)
+    plt.errorbar(
+      slider_samples_range,
+      lw_shrinkage.mean(1),
+      yerr=lw_shrinkage.std(1),
+      label="Ledoit-Wolf",
+      color="navy",
+      lw=2,
+      )
+    plt.errorbar(
+      slider_samples_range,
+      oa_shrinkage.mean(1),
+      yerr=oa_shrinkage.std(1),
+      label="OAS",
+      color="darkorange",
+      lw=2,
+      )
+    plt.xlabel("n_samples")
+    plt.ylabel("Shrinkage")
+    plt.legend(loc="lower right")
+    plt.ylim(plt.ylim()[0], 1.0 + (plt.ylim()[1] - plt.ylim()[0]) / 10.0)
+    plt.xlim(5, 31)
+    print("outside plot_shrink")
+    # plt.show()
+    return plt
+
+
+
+
+
+
+title = "Ledoit-Wolf vs OAS estimation"
+
+
+with gr.Blocks(title=title, theme=gr.themes.Default(font=[gr.themes.GoogleFont("Inconsolata"), "Arial", "sans-serif"])) as demo:
+    gr.Markdown(f"# {title}")
+
+    gr.Markdown(
+    """
+    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.
+
+    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.
+
+    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.
+
+    [1] “Shrinkage Algorithms for MMSE Covariance Estimation” Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.
+    """)
+
+    n_features = 100
+
+
+
+
+
+
+    
+    min_slider_samples_range = gr.Slider(6, 31, value=6, step=1, label="min_samples_range", info="Choose between 6 and 31")
+    max_slider_samples_range = gr.Slider(6, 31, value=31, step=1, label="max_samples_range", info="Choose between 6 and 31")
+
+    print("min_slider_samples_range=",min_slider_samples_range.value)
+    print("max_slider_samples_range=",max_slider_samples_range.value)
+    
+
+    low = min_slider_samples_range.value
+    high = max_slider_samples_range.value
+    ###### initialisation code
+    slider_samples_range =np.arange(low, high,1)
+    n_features = 100
+    repeat = 100
+    lw_mse = np.zeros((slider_samples_range.size, repeat))
+    
+    oa_mse = np.zeros((slider_samples_range.size, repeat))
+    
+    lw_shrinkage = np.zeros((slider_samples_range.size, repeat))
+    
+    oa_shrinkage = np.zeros((slider_samples_range.size, repeat))
+    
+
+
+
+    r = 0.1
+
+    real_cov = toeplitz(r ** np.arange(n_features))
+    coloring_matrix = cholesky(real_cov)
+
+    for i, n_samples in enumerate(slider_samples_range):
+        for j in range(repeat):
+            X = np.dot(np.random.normal(size=(n_samples, n_features)), coloring_matrix.T)
+
+            lw = LedoitWolf(store_precision=False, assume_centered=True)
+            lw.fit(X)
+            lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
+            lw_shrinkage[i, j] = lw.shrinkage_
+
+            oa = OAS(store_precision=False, assume_centered=True)
+            oa.fit(X)
+            oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
+            oa_shrinkage[i, j] = oa.shrinkage_ 
+
+
+    gr.Markdown(" **[Demo is based on sklearn docs](https://scikit-learn.org/stable/auto_examples/covariance/plot_lw_vs_oas.html)**")
+
+    gr.Label(value="Comparison of Covariance Estimators")
+
+
+    min_slider_samples_range.change(plot_mse, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
+    max_slider_samples_range.change(plot_shrinkage, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
+
+
+
+demo.launch()