pareto_dist_plot.ipynb

Kernel: prob_ml

Pareto distribution

import jax.numpy as jnp
import seaborn as sns
import matplotlib.pyplot as plt
from jax.scipy.stats import pareto

try:
    from probml_utils import savefig, latexify
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    from probml_utils import savefig, latexify

latexify(width_scale_factor=2, fig_height=1.5)

def pareto_distribution(params, x, styles):
    labels = [f"m={m}, k={int(k)}" for m, k in params]

    plt.figure()
    for i, param in enumerate(params):
        m, k = param
        probabilities = pareto.pdf(x, k, scale=m)
        plt.plot(x, probabilities, styles[i], label=labels[i])

    sns.despine()
    plt.xlabel("x")
    plt.ylabel(r"$p(x \vert m, k)$")
    plt.title("Pareto Distribution")
    plt.legend(fontsize=8)
    plt.axis((0.0, 0.5, 0, 20))

    savefig("paretoPdf.pdf")
    plt.show()

def log_pareto_distribution(params, x, styles):

    plt.figure()
    for i, param in enumerate(params):
        m, k = param
        probabilities = pareto.pdf(x, k, scale=m)
        plt.loglog(x, probabilities, styles[i])

    sns.despine()
    plt.xlim(0.05, 1)
    plt.xlabel(r"$\log (x)$")
    plt.ylabel(r"$\log p(x \vert m, k)$")
    plt.title("Log Pareto Distribution")

    savefig("paretoLogPdf.pdf")
    plt.show()

params = [(0.1, 1), (0.1, 2), (0.2, 1), (0.2, 2)]  # List of pair of parameters m and k
styles = ["b-", "r:", "k-.", "g--"]  # style of graph line corresponds to a parameter pair

x = jnp.linspace(0, 1, 1000)

pareto_distribution(params, x, styles)
log_pareto_distribution(params, x, styles)

saving image to /home/tensorboy/Desktop/paretoPdf.pdf
Figure size: [3.  1.5]

/home/tensorboy/dev/env/lib/python3.8/site-packages/probml_utils/plotting.py:69: UserWarning: renaming /home/tensorboy/Desktop/paretoPdf.pdf to /home/tensorboy/Desktop/paretoPdf_latexified.pdf because LATEXIFY is True
  warnings.warn(
/tmp/ipykernel_19031/3048080196.py:18: UserWarning: Matplotlib is currently using ps, which is a non-GUI backend, so cannot show the figure.
  plt.show()

saving image to /home/tensorboy/Desktop/paretoLogPdf.pdf
Figure size: [3.  1.5]

/home/tensorboy/dev/env/lib/python3.8/site-packages/probml_utils/plotting.py:69: UserWarning: renaming /home/tensorboy/Desktop/paretoLogPdf.pdf to /home/tensorboy/Desktop/paretoLogPdf_latexified.pdf because LATEXIFY is True
  warnings.warn(
/tmp/ipykernel_19031/3659129367.py:16: UserWarning: Matplotlib is currently using ps, which is a non-GUI backend, so cannot show the figure.
  plt.show()

Interactive demo

from ipywidgets import interact


@interact(m=(0, 1.0), k=(1, 5.0))
def generate_interactinve_pareto(m, k):
    x = jnp.linspace(0, 1, 1000)

    plt.figure()
    probabilities = pareto.pdf(x, k, scale=m)
    plt.plot(x, probabilities)

    plt.xlim(0.05, 1)
    sns.despine()
    plt.xlabel("x")
    plt.ylabel(r"$p(x \vert m, k)$")
    plt.title("Pareto Distribution")
    plt.show()

interactive(children=(FloatSlider(value=0.5, description='m', max=1.0), FloatSlider(value=3.0, description='k'…

from ipywidgets import interact


@interact(m=(0, 1.0), k=(1, 5.0))
def generate_interactinve_pareto_log(m, k):
    x = jnp.linspace(0, 1, 1000)

    plt.figure()
    probabilities = pareto.pdf(x, k, scale=m)
    plt.loglog(x, probabilities)

    plt.xlim(0.05, 1)
    sns.despine()
    plt.xlabel("\log(x)")
    plt.ylabel(r"$\log p(x \vert m, k)$")

    plt.title("Log Pareto Distribution")
    plt.show()

interactive(children=(FloatSlider(value=0.5, description='m', max=1.0), FloatSlider(value=3.0, description='k'…