generativeVsDiscrim.ipynb

Kernel: Unknown Kernel

import numpy as np
from numpy.random import laplace
from scipy.stats import multivariate_normal
import matplotlib.pyplot as plt

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

domain = np.arange(0, 1.001, 0.001)


def f1(x):
    return multivariate_normal.pdf(x, 0.7, 0.09**2)


def f2(x):
    return 0.6 * multivariate_normal.pdf(x, 0.1, 0.09**2) + 0.4 * multivariate_normal.pdf(x, 0.4, 0.09**2)


plt.plot(domain, f1(domain), "r-", linewidth=2)
plt.plot(domain, f2(domain), "k-", linewidth=2)
plt.xlabel("x")
plt.ylabel("class conditional densities")
plt.annotate("p(x|y=1)", (0.196, 2), fontsize=14)
plt.annotate("p(x|y=2)", (0.8, 4), fontsize=14)
pml.savefig("genVsDiscrimClassCond.pdf")
plt.show()

domain = np.arange(0, 1.001, 0.001)


def f1(x):
    return 1 / (1 + np.exp((27 * x - 15)))


def f2(x):
    return 1 / (1 + np.exp((-27 * x + 15)))


plt.plot(domain, f1(domain), "-r", linewidth=2)
plt.plot(domain, f2(domain), "-k", linewidth=2)
plt.plot([0.556, 0.556], [0, 1.2], "-g")
plt.annotate("p(y=1|x)", (0.14, 1.1), fontsize=14)
plt.annotate("p(y=2|x)", (0.8, 1.1), fontsize=14)
pml.savefig("genVsDiscrimPost.pdf")
plt.show()


domain = np.arange(0.001, 10.001, 0.001)


def NB(x):
    return np.power(x, -0.5)


def LR(x):
    return np.divide(7, np.power(x, 0.8)) - 2


plt.axis([-0.1, 10, -1, 10])

plt.plot(domain, NB(domain), "--r")
plt.plot(domain, LR(domain), "-b")
plt.xlabel("size of training set")
plt.ylabel("test error")
plt.xticks([])
plt.yticks([])
plt.annotate("NB", (0.5, 1.5), fontsize=20, color="red")
plt.annotate("LR", (1.8, 3.5), fontsize=20, color="blue")
pml.savefig("genVsDiscrimTestError.pdf")
plt.show()