Importance Sampling

import torch
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
# Retina display
%config InlineBackend.figure_format = 'retina'
import warnings
warnings.filterwarnings('ignore')

from tueplots import bundles
plt.rcParams.update(bundles.beamer_moml())


# Also add despine to the bundle using rcParams
plt.rcParams['axes.spines.right'] = False
plt.rcParams['axes.spines.top'] = False

# Increase font size to match Beamer template
plt.rcParams['font.size'] = 16
# Make background transparent
plt.rcParams['figure.facecolor'] = 'none'

mu1 = 0
sigma1 = 0.25

mu2 = 0.5
sigma2 = 0.5

x_range = torch.linspace(-6, 6, 1000)
pdf1 = torch.exp(-0.5 * ((x_range - mu1) / sigma1)**2) / \
    (sigma1 * (2 * torch.tensor(np.pi).sqrt()))
pdf2 = torch.exp(-0.5 * ((x_range - mu2) / sigma2)**2) / \
    (sigma2 * (2 * torch.tensor(np.pi).sqrt()))
ratio_pdf = pdf1 / pdf2

plt.plot(x_range, pdf1.numpy(), label='p(x)')
plt.plot(x_range, pdf2.numpy(), label='q(x)')
plt.plot(x_range, ratio_pdf.numpy(), label='w(x)')
plt.xlim(-2, 2)
plt.title('Weight function w(x)')
plt.xlabel('X')
plt.ylabel('w(x)')
plt.legend()
plt.grid()
# plt.savefig('figures/sampling/importance_sampling_weight_function.pdf', dpi=300, transparent=True)

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findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed