polynomical regression.md

Polynomial Regression

import numpy as np
import sklearn
from sklearn.preprocessing import PolynomialFeatures

m = 100
X = 6 * np.random.rand(m, 1) - 3
y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)

poly_features = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly_features.fit_transform(X)
print(X[0])
print(X_poly[0])

[0.94765133]
[0.94765133 0.89804305]

from sklearn.linear_model import LinearRegression
lin_reg = LinearRegression()
lin_reg.fit(X_poly, y)
lin_reg.intercept_, lin_reg.coef_

(array([1.92496392]), array([[0.99715908, 0.50733236]]))

from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt

def plot_learning_curves(model, X, y):
    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2)
    train_errors, val_errors = [], []
    for m in range(1, len(X_train)):
        model.fit(X_train[:m], y_train[:m])
        y_train_predict = model.predict(X_train[:m])
        y_val_predict = model.predict(X_val)
        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))
        val_errors.append(mean_squared_error(y_val, y_val_predict))
    plt.plot(np.sqrt(train_errors), "r-+", linewidth=2, label="train")
    plt.plot(np.sqrt(val_errors), "b-", linewidth=3, label="val")

lin_reg = LinearRegression()
plot_learning_curves(lin_reg, X, y)

10 degree polynomial

from sklearn.pipeline import Pipeline
polynomial_regression = Pipeline([
("poly_features", PolynomialFeatures(degree=10, include_bias=False)),
("lin_reg", LinearRegression()),
])

plot_learning_curves(polynomial_regression, X, y)