low variance high bias

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
from sklearn.model_selection import learning_curve
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import Ridge

# Generate a synthetic dataset
X, y = make_regression(n_samples=100, n_features=1, noise=20, random_state=42)

# Define the model complexities (degrees of polynomial features)
degrees = [1, 4, 15]

# Plot the learning curves for different model complexities
for degree in degrees:
    model = make_pipeline(PolynomialFeatures(degree), Ridge(alpha=0.1))
    train_sizes, train_scores, valid_scores = learning_curve(model, X, y, cv=5)
    
    plt.plot(train_sizes, np.mean(train_scores, axis=1), label=f'Degree {degree} (training)')
    plt.plot(train_sizes, np.mean(valid_scores, axis=1), label=f'Degree {degree} (validation)')

plt.xlabel('Training set size')
plt.ylabel('Score')
plt.legend(loc='best')
plt.show()