ridgePathProstate.ipynb

Kernel: Unknown Kernel

# Plot the full L2 regularization path for the prostate data set


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

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 requests
from io import BytesIO
from scipy.io import loadmat

# Load prostate cancer data
#!wget https://github.com/probml/probml-data/blob/main/data/prostateStnd.mat?raw=true -O prostateStnd.mat

# matlab data is created by this
# https://github.com/probml/pmtk3/blob/master/data/prostate/prostateDataMake.m

# data = loadmat('prostateStnd.mat')

url = "https://raw.githubusercontent.com/probml/probml-data/main/data/prostateStnd.mat"
response = requests.get(url)
# rawdata = response.text
rawdata = BytesIO(response.content)
data = loadmat(rawdata)


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

# Ridge regression

n_alpha = 30
alphas = np.logspace(5, 0, n_alpha)

coefs = map(lambda a: linear_model.Ridge(a).fit(X, y).coef_.flatten(), alphas)
coefs = np.array(list(coefs))

# Ridge regression with cross validation

best_model = linear_model.RidgeCV(alphas)
b = best_model.fit(X, y)

# Figure 11.12 (a)
# Profile of ridge coeficients for prostate cancer example
# Vertical line is values chosen by cross validation

fig, ax = plt.subplots()
plt.plot(coefs, marker="o")
plt.axvline(x=np.where(alphas == best_model.alpha_), c="r")
plt.legend(names)
pml.savefig("prostate_data.pdf")
plt.show()