Polinomial regressiya va regularizatsiya

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

np.random.seed(42)

x = np.linspace(0, 10, 100)
y = 0.5 * x ** 2 - 3 * x + 8 + np.random.normal(0, 3, 100)

X = x.reshape(-1, 1)

chiziqli = LinearRegression().fit(X, y)
print(f"Chiziqli model R2: {chiziqli.score(X, y):.3f}")

from sklearn.preprocessing import PolynomialFeatures

kengaytiruvchi = PolynomialFeatures(degree=2, include_bias=False)
X_kengaygan = kengaytiruvchi.fit_transform(X)

print("Asl shakl:      ", X.shape)
print("Kengaygan shakl:", X_kengaygan.shape)
print(kengaytiruvchi.get_feature_names_out())

polinomial = LinearRegression().fit(X_kengaygan, y)
print(f"Polinomial model R2: {polinomial.score(X_kengaygan, y):.3f}")

X_ikki = np.random.rand(100, 2)
kengaytiruvchi = PolynomialFeatures(degree=2, include_bias=False)
X_yangi = kengaytiruvchi.fit_transform(X_ikki)

print(kengaytiruvchi.get_feature_names_out())

from sklearn.model_selection import train_test_split
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

X_oqitish, X_sinov, y_oqitish, y_sinov = train_test_split(
    X, y, test_size=0.3, random_state=42
)

print("Daraja   O'qitish R2    Sinov R2")

for daraja in [1, 2, 3, 5, 10, 15, 20]:
    model = make_pipeline(
        PolynomialFeatures(daraja),
        LinearRegression(),
    )
    model.fit(X_oqitish, y_oqitish)

    r2_oqitish = model.score(X_oqitish, y_oqitish)
    r2_sinov   = model.score(X_sinov, y_sinov)

    print(f"{daraja:>7} {r2_oqitish:>13.3f} {r2_sinov:>11.3f}")

model_20 = make_pipeline(PolynomialFeatures(20), LinearRegression())
model_20.fit(X_oqitish, y_oqitish)

koeffitsiyentlar = model_20.named_steps["linearregression"].coef_
print(f"Eng katta koeffitsiyent: {np.abs(koeffitsiyentlar).max():.2e}")

Oddiy MSE:        xato
Ridge (L2):       xato + alfa · Σ w²
Lasso (L1):       xato + alfa · Σ |w|

from sklearn.linear_model import Ridge

for alfa in [0, 0.01, 1, 100]:
    model = make_pipeline(
        PolynomialFeatures(15),
        StandardScaler(),
        Ridge(alpha=alfa),
    )
    model.fit(X_oqitish, y_oqitish)

    print(f"alfa={alfa:6.2f}  "
          f"o'qitish={model.score(X_oqitish, y_oqitish):.3f}  "
          f"sinov={model.score(X_sinov, y_sinov):.3f}")

from sklearn.linear_model import Lasso

# Ko'p keraksiz belgi bo'lgan ma'lumot
np.random.seed(42)
n = 200
X_kop = np.random.randn(n, 30)
# Faqat birinchi 3 ta belgi haqiqatan muhim
y_kop = 5 * X_kop[:, 0] - 3 * X_kop[:, 1] + 2 * X_kop[:, 2] + np.random.randn(n) * 0.5

lasso = Lasso(alpha=0.1).fit(X_kop, y_kop)

nolmas = np.sum(lasso.coef_ != 0)
print(f"Jami belgilar:        {X_kop.shape[1]}")
print(f"Model ishlatgan:      {nolmas}")
print(f"Eng katta 5 ta vazn:  {np.round(np.sort(np.abs(lasso.coef_))[-5:], 2)}")

from sklearn.linear_model import ElasticNet

model = ElasticNet(alpha=0.1, l1_ratio=0.5)
model.fit(X_oqitish, y_oqitish)

from sklearn.linear_model import RidgeCV, LassoCV

alfalar = np.logspace(-3, 3, 50)

ridge_cv = RidgeCV(alphas=alfalar, cv=5).fit(X_oqitish, y_oqitish)
print(f"Eng yaxshi alfa: {ridge_cv.alpha_:.4f}")
print(f"Sinov R2:        {ridge_cv.score(X_sinov, y_sinov):.3f}")

from sklearn.datasets import make_regression

X_test, y_test = make_regression(
    n_samples=300, n_features=50, n_informative=10,
    noise=15, random_state=42,
)

X_o, X_s, y_o, y_s = train_test_split(X_test, y_test, test_size=0.3, random_state=42)

modellar = {
    "Chiziqli":   LinearRegression(),
    "Ridge":      Ridge(alpha=1.0),
    "Lasso":      Lasso(alpha=1.0),
    "ElasticNet": ElasticNet(alpha=1.0, l1_ratio=0.5),
}

for nom, model in modellar.items():
    quvur = make_pipeline(StandardScaler(), model)
    quvur.fit(X_o, y_o)

    nolmas = np.sum(quvur[-1].coef_ != 0)
    print(f"{nom:12s}  sinov R2={quvur.score(X_s, y_s):.3f}  "
          f"ishlatilgan belgilar={nolmas}")