Spaces:
Sleeping
Sleeping
File size: 4,939 Bytes
815161b cbda4c5 815161b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 |
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():
# plot MSE
plt.clf()
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)
return plt
def plot_shrinkage():
# plot shrinkage coefficient
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)
# plt.show()
return plt
title = "Ledoit-Wolf vs OAS estimation"
# def greet(name):
# return "Hello " + name + "!"
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")
r = 0.1
real_cov = toeplitz(r ** np.arange(n_features))
coloring_matrix = cholesky(real_cov)
gr.Markdown(" **[Demo is based on sklearn docs](https://scikit-learn.org/stable/auto_examples/covariance/plot_lw_vs_oas.html)**")
# name = "hardy"
# greet_btn = gr.Button("Greet")
# output = gr.Textbox(label="Output Box")
# greet_btn.click(fn=greet, inputs=name, outputs=output)
gr.Label(value="Comparison of Covariance Estimators")
# generate_plots()
# print("slider_samples_range:",slider_samples_range)
slider_samples_range =np.arange(min_slider_samples_range,max_slider_samples_range,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))
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_
#if min_slider_samples_range:
min_slider_samples_range.change(plot_mse, outputs= gr.Plot() )
max_slider_samples_range.change(plot_shrinkage, outputs= gr.Plot() )
#elif max_slider_samples_range:
# elif changed == False:
# min_slider_samples_range.change(generate_plots, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
# max_slider_samples_range.change(generate_plots, inputs=[min_slider_samples_range,max_slider_samples_range], outputs= gr.Plot() )
# changed = True
# else:
# pass
demo.launch() |