Regressione non lineare (parte 1): soluzioni esercizi

sols.py

# ESERCIZIO 1

# 1a
lrm = LinearRegression()
summer_X_train = summer_train[["temp"]]
summer_y_train = summer_train["demand"]
lrm.fit(summer_X_train, summer_y_train)

# 1b
print_eval(summer_X_train, summer_y_train, lrm)

# 1c
summer_X_val = summer_val[["temp"]]
summer_y_val = summer_val["demand"]
print_eval(summer_X_val, summer_y_val, lrm)

# 1d
plot_model_on_data(summer_X_train, summer_y_train, lrm)

# 1e
plot_model_on_data(summer_X_val, summer_y_val, lrm)


# ESERCIZIO 2

# 2a
X_train_d3 = np.hstack([X_train, X_train ** 2, X_train ** 3])

# 2b
X_val_d3 = np.hstack([X_val, X_val ** 2, X_val ** 3])

# 2c
prm = LinearRegression()
prm.fit(X_train_d3, y_train)

# 2d
print_eval(X_train_d3, y_train, prm)
print_eval(X_val_d3, y_val, prm)


# ESERCIZIO 3

# 3a
prm = Pipeline([
    ("poly", PolynomialFeatures(degree=3, include_bias=False)),
    ("linreg", LinearRegression())
])

# 3b
prm.fit(X_train, y_train)

# 3c
print_eval(X_train, y_train, prm)

# 3d
plot_model_on_data(X_val, y_val, prm)


# ESERCIZIO 4

# 4a
prm = Pipeline([
    ("poly",   PolynomialFeatures(degree=15, include_bias=False)),
    ("linreg", LinearRegression())
])
prm.fit(X_train, y_train)
print_eval(X_val, y_val, prm)

# 4b
prm = Pipeline([
    ("poly",   PolynomialFeatures(degree=15, include_bias=False)),
    ("scale",  StandardScaler()),
    ("linreg", LinearRegression())
])
prm.fit(X_train, y_train)
print_eval(X_val, y_val, prm)


# ESERCIZIO 5

# 5a
def test_regression(degree, alpha):
    rrm = Pipeline([
        ("poly", PolynomialFeatures(degree=degree, include_bias=False)),
        ("scale", StandardScaler()),
        ("ridge", Ridge(alpha=alpha))
    ])
    rrm.fit(X_train, y_train)
    return rrm.score(X_val, y_val)

# 5b
res_degree = np.arange(3, 31)
res_no_reg = np.array([test_regression(d, 0.01) for d in res_degree])

# 5c
res_with_reg = np.array([test_regression(d, 10) for d in res_degree])

# 5d
plt.plot(res_degree, res_no_reg, "ro-")
plt.plot(res_degree, res_with_reg, "bo-")
plt.grid()
plt.xlabel("Grado regr. polinomiale")
plt.ylabel("Score R²")
# aggiungiamo una legenda al grafico
plt.legend(["α = 0.01", "α = 10"], loc="lower right");


# ESERCIZIO 6

# 6a
nlrm = Pipeline([
    ("scale",  StandardScaler()),
    ("linreg", LinearRegression())
])

# 6b
nlrm.fit(X_train, y_train)

# 6c
print_eval(X_val, y_val, nlrm)

# 6d
pd.Series(nlrm.named_steps["linreg"].coef_, X_train.columns)


# ESERCIZIO 7

for n, (train_indices, val_indices) in enumerate(kf.split(X, y)):
    X_train = X.iloc[train_indices]
    y_train = y.iloc[train_indices]
    X_val = X.iloc[val_indices]
    y_val = y.iloc[val_indices]
    lrm = LinearRegression()
    lrm.fit(X_train, y_train)
    print("FOLD {}:".format(n))
    print_eval(X_val, y_val, lrm)


# ESERCIZIO 8

# 8a
model = Pipeline([
    ("poly", PolynomialFeatures(degree=2, include_bias=False)),
    ("scale", StandardScaler()),
    ("ridge", Ridge(alpha=1))
])

# 8b
cv_result = cross_validate(model, X, y, cv=kf)

# 8c
cv_result["test_score"].mean(), cv_result["test_score"].std()
# la media è più alta e la deviazione standard più bassa