探究不同阶数对4种线性回归影响

import numpy as np
from sklearn.linear_model import LinearRegression, RidgeCV, LassoCV, ElasticNetCV
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.exceptions import ConvergenceWarning
import matplotlib as mpl
import matplotlib.pyplot as plt
import warnings
def xss(y, y_hat):
    y = y.ravel()
    y_hat = y_hat.ravel()
    # Version 1
    tss = ((y - np.average(y)) ** 2).sum()
    rss = ((y_hat - y) ** 2).sum()
    ess = ((y_hat - np.average(y)) ** 2).sum()
    r2 = 1 - rss / tss
    # print 'RSS:', rss, '\t ESS:', ess
    # print 'TSS:', tss, 'RSS + ESS = ', rss + ess

    # Version 2
    # tss = np.var(y)
    # rss = np.average((y_hat - y) ** 2)
    # r2 = 1 - rss / tss
    corr_coef = np.corrcoef(y, y_hat)[0, 1]
    tss_list.append(tss)
    rss_list.append(rss)
    ess_list.append(ess)
    ess_rss_list.append(rss + ess)
    return r2, corr_coef
if __name__ == "__main__":
    warnings.filterwarnings(action='ignore', category=ConvergenceWarning)
    np.random.seed(0)
    np.set_printoptions(linewidth=300, suppress=True)
    N = 9
    x = np.linspace(0, 6, N) + np.random.randn(N)
    x = np.sort(x)
    y = x**2 - 4*x - 3 + np.random.randn(N)
    x.shape = -1, 1
    y.shape = -1, 1

    models = [Pipeline([
        ('poly', PolynomialFeatures()),
        ('linear', LinearRegression(fit_intercept=False))]),
        Pipeline([
            ('poly', PolynomialFeatures()),
            ('linear', RidgeCV(alphas=np.logspace(-3, 2, 10), fit_intercept=False))]),
        Pipeline([
            ('poly', PolynomialFeatures()),
            ('linear', LassoCV(alphas=np.logspace(-3, 2, 10), fit_intercept=False))]),
        Pipeline([
            ('poly', PolynomialFeatures()),
            ('linear', ElasticNetCV(alphas=np.logspace(-3, 2, 10), l1_ratio=[.1, .5, .7, .9, .95, .99, 1],
                                    fit_intercept=False))])
    ]
    mpl.rcParams['font.sans-serif'] = ['simHei']
    mpl.rcParams['axes.unicode_minus'] = False

    plt.figure(figsize=(15, 10), facecolor='w')
    d_pool = np.arange(1, N, 1)  # 阶
    m = d_pool.size
    clrs = []  # 颜色
    for c in np.linspace(16711680, 255, m, dtype=int):
        clrs.append('#%06x' % c)
    line_width = np.linspace(5, 2, m) * 0.7
    titles = '线性回归', 'Ridge回归', 'LASSO', 'ElasticNet'
    tss_list = []
    rss_list = []
    ess_list = []
    ess_rss_list = []
    for t in range(4):
        model = models[t]
        plt.subplot(2, 2, t+1)
        plt.plot(x, y, 'ro', markersize=7, zorder=N, mec='k')
        for i, d in enumerate(d_pool):
            model.set_params(poly__degree=d)
            model.fit(x, y.ravel())
            lin = model.get_params('linear')['linear']
            output = '%s：%d阶，系数为：' % (titles[t], d)
            if hasattr(lin, 'alpha_'):
                idx = output.find('系数')
                output = output[:idx] + ('alpha=%.6f，' % lin.alpha_) + output[idx:]
            if hasattr(lin, 'l1_ratio_'):   # 根据交叉验证结果，从输入l1_ratio(list)中选择的最优l1_ratio_(float)
                idx = output.find('系数')
                output = output[:idx] + ('l1_ratio=%.6f，' % lin.l1_ratio_) + output[idx:]
            print(output, lin.coef_.ravel())
            x_hat = np.linspace(x.min(), x.max(), num=100)
            x_hat.shape = -1, 1
            y_hat = model.predict(x_hat)
            s = model.score(x, y)
            r2, corr_coef = xss(y, model.predict(x))
            # print 'R2和相关系数：', r2, corr_coef
            # print 'R2：', s, '\n'
            z = N - 1 if (d == 2) else 0
            label = '%d阶，$R^2$=%.3f' % (d, s)
            if hasattr(lin, 'l1_ratio_'):
                label += '，L1 ratio=%.2f' % lin.l1_ratio_
            plt.plot(x_hat, y_hat, color=clrs[i], lw=line_width[i], alpha=0.75, label=label, zorder=z)
        plt.legend(loc='upper left')
        plt.grid(True)
        plt.title(titles[t], fontsize=18)
        plt.xlabel('X', fontsize=16)
        plt.ylabel('Y', fontsize=16)
    plt.tight_layout(1, rect=(0, 0, 1, 0.95))
    plt.suptitle('多项式曲线拟合比较', fontsize=22)
    plt.show()

    y_max = max(max(tss_list), max(ess_rss_list)) * 1.05
    plt.figure(figsize=(9, 7), facecolor='w')
    t = np.arange(len(tss_list))
    plt.plot(t, tss_list, 'ro-', lw=2, label='TSS(Total Sum of Squares)', mec='k')
    plt.plot(t, ess_list, 'mo-', lw=1, label='ESS(Explained Sum of Squares)', mec='k')
    plt.plot(t, rss_list, 'bo-', lw=1, label='RSS(Residual Sum of Squares)', mec='k')
    plt.plot(t, ess_rss_list, 'go-', lw=2, label='ESS+RSS', mec='k')
    plt.ylim((0, y_max))
    plt.legend(loc='center right')
    plt.xlabel('实验：线性回归/Ridge/LASSO/Elastic Net', fontsize=15)
    plt.ylabel('XSS值', fontsize=15)
    plt.title('总平方和TSS=？', fontsize=18)
    plt.grid(True)
    plt.show()