linreg_contours_sse_plot.ipynb

Kernel: Unknown Kernel

# Plot error surface for linear regression model.
# Based on https://github.com/probml/pmtk3/blob/master/demos/contoursSSEdemo.m


import numpy as np
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

from mpl_toolkits.mplot3d import axes3d, Axes3D

np.random.seed(0)

N = 21
x = np.linspace(0.0, 20, N)
X0 = x.reshape(N, 1)
X = np.c_[np.ones((N, 1)), X0]
w = np.array([-1.5, 1 / 9.0])
y = w[0] * x + w[1] * np.square(x)
y = y + np.random.normal(0, 1, N) * 2

w = np.linalg.lstsq(X, y, rcond=None)[0]
W0, W1 = np.meshgrid(np.linspace(-8, 0, 100), np.linspace(-0.5, 1.5, 100))

SS = np.array([sum((w0 * X[:, 0] + w1 * X[:, 1] - y) ** 2) for w0, w1 in zip(np.ravel(W0), np.ravel(W1))])
SS = SS.reshape(W0.shape)

plt.figure()
plt.contourf(W0, W1, SS)
pml.savefig("linregHeatmapSSE.pdf")
plt.colorbar()
plt.show()

fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
surf = ax.plot_surface(W0, W1, SS)
pml.savefig("linregSurfSSE.pdf")
plt.show()

fig, ax = plt.subplots()
CS = plt.contour(W0, W1, SS, levels=np.linspace(0, 2000, 10), cmap="jet")
plt.plot(w[0], w[1], "x")
pml.savefig("linregContoursSSE.pdf")
plt.show()