lassoPathProstate.ipynb

Kernel: Unknown Kernel

# Figure 11.12 (b)
# Plot the full L1 regularization path for the prostate data set


from scipy.io import loadmat

try:
    from sklearn import linear_model
except ModuleNotFoundError:
    %pip install -qq scikit-learn
    from sklearn import linear_model
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import requests
from io import BytesIO

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

# Load prostate cancer data
url = "https://github.com/probml/probml-data/blob/main/data/prostate/prostateStnd.mat?raw=true"
response = requests.get(url)
rawdata = BytesIO(response.content)
data = loadmat(rawdata)

names = list(map(lambda x: x[0], data["names"][0]))
X, y = data["X"], data["y"]

# Finding coefficients for lasso path

_, _, coefs = linear_model.lars_path(X, y.flatten(), method="lasso")

tau = np.sum(np.abs(coefs.T), axis=1)

# Figure 11.12 (b)
# Profile of lasso coeficients for prostate cancer example

fig, ax = plt.subplots()
xs = tau
ys = coefs.T
plt.xlabel(r"$\tau$")
ax.xaxis.set_major_locator(ticker.MultipleLocator(0.5))
plt.plot(xs, ys, marker="o")
plt.legend(names)
pml.savefig("L1.pdf")
plt.show()