gibbs_gauss_demo.ipynb

Kernel: Python [conda env:py3713]

# Illustration of gibbs sampling for 2-dim Gaussian
# Author: Gerardo Durán-Martín
# Translated from gibbsGaussDemo.m


import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal, norm

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml
import os

os.environ["LATEXIFY"] = ""
os.environ["FIG_DIR"] = "figures"

pml.latexify(width_scale_factor=2)

μ = np.zeros(2)
Σ = np.array([[1, 0.99], [0.99, 1]])
mvn = multivariate_normal(μ, Σ)

# Plot one contour of the multivariate normal
X = np.mgrid[-3:3:0.01, -3:3:0.01]
density = np.apply_along_axis(mvn.pdf, 0, X)

# Gibbs-Sampling path
blue_seq = (
    np.array(
        [
            [-1 / 2, -1],
            [-1 / 2, 0],
            [1, 0],
            [1, 1],
            [-1 / 2, 1],
            [-1 / 2, 1 / 2],
            [1.5, 1 / 2],
            [1.5, 1.5],
        ]
    )
    / 3
)

# Compute marginal parameters x0|x1
x0_range = np.arange(-2, 2, 0.01)
x0_obs = 0.7
Σ0_cond = Σ[0, 0] - Σ[0, 1] * Σ[1, 0] / Σ[1, 1]
μ0_cond = μ[0] + Σ[0, 1] * (x0_obs - μ[1]) / Σ[1, 1]

plt.plot(*blue_seq.T)
plt.contour(*X, density, levels=[0.07], colors="tab:red")
plt.xlim(-3, 3)
plt.ylim(-3, 3)
plt.scatter(0, 0, marker="x", c="tab:red", s=300)
plt.text(0, 1.7, "L", size=11)
plt.text(1.2, -2, "l", size=11)
plt.annotate("", xy=(-2.5, 1.5), xytext=(2.5, 1.5), arrowprops=dict(arrowstyle="<->"))
plt.annotate("", xy=(0.5, -2), xytext=(1, -2), arrowprops=dict(arrowstyle="<->"))
# Scaled down and shifted marginal gaussian
plt.plot(x0_range, norm(μ0_cond, np.sqrt(Σ0_cond)).pdf(x0_range) * 0.3 - 3, c="tab:green")
plt.tight_layout()
pml.savefig("gmm_singularity.pdf")
plt.show()

/home/patel_karm/sendbox/probml-utils/probml_utils/plotting.py:71: UserWarning: renaming figures/gmm_singularity.pdf to figures/gmm_singularity_latexified.pdf because LATEXIFY is True
  f"renaming {fname_full} to {fname}{extention} because LATEXIFY is {LATEXIFY}",

saving image to figures/gmm_singularity_latexified.pdf
Figure size: [3.  1.5]