回归算法实例二：线性回归、Lasso回归、Ridge回归、ElasticNet的多项式过拟合比较

深藏阁楼爱情的钟 2023-07-13 08:23 78阅读 0赞

import numpy as np
    import matplotlib as mpl
    import matplotlib.pyplot as plt
    import pandas as pd
    import warnings
    import sklearn
    from sklearn.linear_model import LinearRegression, LassoCV, RidgeCV, ElasticNetCV
    from sklearn.preprocessing import PolynomialFeatures		# 数据预处理，标准化
    from sklearn.pipeline import Pipeline
    from sklearn.linear_model.coordinate_descent import ConvergenceWarning
    
    # 设置字符集，防止中文乱码
    mpl.rcParams['font.sans-serif']=[u'simHei']
    mpl.rcParams['axes.unicode_minus']=False
    # 拦截异常
    warnings.filterwarnings(action = 'ignore', category=ConvergenceWarning)
    
    # 创建模拟数据
    np.random.seed(100)
    # 显示方式设置，每行的字符数用于插入换行符，是否使用科学计数法
    np.set_printoptions(linewidth=1000, suppress=True)
    N = 10
    x = np.linspace(0, 6, N) + np.random.randn(N)
    y = 1.8*x**3 + x**2 - 14*x - 7 + np.random.randn(N)
    # 将其设置为矩阵
    x.shape = -1, 1
    y.shape = -1, 1
    
    # RidgeCV和Ridge的区别是：前者可以进行交叉验证
    models = [
        Pipeline([
                ('Poly', PolynomialFeatures(include_bias=False)),
                ('Linear', LinearRegression(fit_intercept=False))
            ]),
        Pipeline([
                ('Poly', PolynomialFeatures(include_bias=False)),
                ('Linear', RidgeCV(alphas=np.logspace(-3,2,50), fit_intercept=False))
            ]),
        Pipeline([
                ('Poly', PolynomialFeatures(include_bias=False)),
                ('Linear', LassoCV(alphas=np.logspace(0,1,10), fit_intercept=False))
            ]),
        Pipeline([
                ('Poly', PolynomialFeatures(include_bias=False)),
                ('Linear', ElasticNetCV(alphas=np.logspace(0,1,10), l1_ratio=[.1, .5, .7, .9, .95, 1], fit_intercept=False))
            ])
    ]
    
    # 线性模型过拟合图形识别
    plt.figure(facecolor='w')
    degree = np.arange(1,N,4) # 阶
    dm = degree.size
    # 颜色
    colors = []
    for c in np.linspace(16711680, 255, dm):
        colors.append('#%06x' % int(c))
    
    model = models[0]
    for i,d in enumerate(degree):
        plt.subplot(int(np.ceil(dm/2.0)),2,i+1)
        plt.plot(x, y, 'ro', ms=10, zorder=N)
    
        # 设置阶数
        model.set_params(Poly__degree=d)
        # 模型训练
        model.fit(x, y.ravel())
        
        lin = model.get_params('Linear')['Linear']
        output = u'%d阶，系数为：' % (d)
        print (output, lin.coef_.ravel())
        
        # 产生模拟数据
        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)
        
        z = N - 1 if (d == 2) else 0
        label = u'%d阶, 正确率=%.3f' % (d,s)
        plt.plot(x_hat, y_hat, color=colors[i], lw=2, alpha=0.75, label=label, zorder=z)
        
        plt.legend(loc = 'upper left')
        plt.grid(True)
        plt.xlabel('X', fontsize=16)
        plt.ylabel('Y', fontsize=16)
    
    plt.tight_layout(1, rect=(0,0,1,0.95))
    plt.suptitle(u'线性回归过拟合显示', fontsize=22)
    plt.show()

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70][]

# 线性回归、Lasso回归、Ridge回归、ElasticNet比较
    plt.figure(facecolor='w')
    # 多项式阶数
    degree = np.arange(1,N, 2)
    dm = degree.size
    # 颜色
    colors = []
    for c in np.linspace(16711680, 255, dm):
        colors.append('#%06x' % int(c))
    titles = [u'线性回归', u'Ridge回归', u'Lasso回归', u'ElasticNet']
    
    for t in range(4):
        # 模型具体的pipeline
        model = models[t]
        plt.subplot(2,2,t+1)
        plt.plot(x, y, 'ro', ms=10, zorder=N)
    
        for i,d in enumerate(degree):
            # 设置阶数（多项式）
            model.set_params(Poly__degree=d)
            # 模型训练
            model.fit(x, y.ravel())
    
            # 获取得到具体的算法模型
            lin = model.get_params('Linear')['Linear']
            # 打印数据
            output = u'%s:%d阶，系数为：' % (titles[t],d)
            print (output, lin.coef_.ravel())
    
            # 产生模拟数据
            x_hat = np.linspace(x.min(), x.max(), num=100)
            x_hat.shape = -1,1
            # 数据预测
            y_hat = model.predict(x_hat)
            # 计算准确率
            s = model.score(x, y)
    
            z = N - 1 if (d == 2) else 0
            label = u'%d阶, 正确率=%.3f' % (d,s)
            plt.plot(x_hat, y_hat, color=colors[i], lw=2, alpha=0.75, label=label, zorder=z)
        
        plt.legend(loc = 'upper left')
        plt.grid(True)
        plt.title(titles[t])
        plt.xlabel('X', fontsize=16)
        plt.ylabel('Y', fontsize=16)
    plt.tight_layout(1, rect=(0,0,1,0.95))
    plt.suptitle(u'各种不同线性回归过拟合显示', fontsize=22)
    plt.show()

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70 1][]  
![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70 2][]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20200311122853994.PNG?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20200311123447120.PNG?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/2020031112353298.PNG?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2dvbmd4aWZhY2FpX2JlbGlldmU=,size_16,color_FFFFFF,t_70