机器学习-高斯密度估计（最大似然、Bayes）

秒速五厘米 2023-06-09 11:29 16阅读 0赞

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程序代码matlab版
    
    % script file example1.m to compute exponential of a set of numbers
    clear; clc;
    %%
    PI = 3.1415926;
    P_Male = 0.6; P_Female = 0.4;
    MALE_SIZE = 600000; FEMALE_SIZE = 400000; TEST_SIZE = 100000; %Sample Size
    Miu_Male_R = [170, 65]; Miu_Female_R = [160 55]; %Miu
    Diata_Male_R = [5 5]; Diata_Female_R = [5 5]; %Diata
    Male_Data = [Miu_Male_R(1) + Diata_Male_R(1) * randn(MALE_SIZE, 1), Miu_Male_R(2) + Diata_Male_R(2) * randn(MALE_SIZE, 1)];...
    Female_Data = [Miu_Female_R(1) + Diata_Female_R(1) * randn(FEMALE_SIZE, 1), Miu_Female_R(2) + Diata_Female_R(2) * randn(FEMALE_SIZE, 1)];
    Test_Data = [Miu_Male_R(1) + Diata_Male_R(1) * randn(TEST_SIZE, 1), Miu_Male_R(2) + Diata_Male_R(2) * randn(TEST_SIZE, 1);...
    Miu_Female_R(1) + Diata_Female_R(1) * randn(TEST_SIZE, 1), Miu_Female_R(2) + Diata_Female_R(2) * randn(TEST_SIZE, 1)];
    Test_Label = [ones(TEST_SIZE, 1); zeros(TEST_SIZE, 1)];
    Miu_Male_E = mean (Male_Data); Diata_Male_E =cov (Male_Data);
    Miu_Female_E = mean (Female_Data); Diata_Female_E = cov (Female_Data);
    
    for Tmp = 1 : 2*TEST_SIZE
    Px_Male = 1 / ((2*PI)^1.5 * sqrt(det(Diata_Male_E))) ...
    * exp (-0.5 * (Test_Data(Tmp, :) - Miu_Male_E) ...
    * inv (Diata_Male_E) * (Test_Data(Tmp, :) - Miu_Male_E)');
    g_Male = Px_Male * P_Male; 
    Px_Female = 1 / ((2*PI)^1.5 * sqrt(det(Diata_Female_E))) ...
    * exp (-0.5 * (Test_Data(Tmp, :) - Miu_Female_E) ...
    * inv (Diata_Female_E) * (Test_Data(Tmp, :) - Miu_Female_E)');
    g_Female = Px_Female * P_Female; 
    Decision(Tmp) = (g_Male > g_Female);
    end
    Accuracy = sum (Decision' == Test_Label) / (2*TEST_SIZE)

#代码python版
    import numpy as np
    PI = 3.1415926
    P_Male = 0.6; P_Female = 0.4;
    MALE_SIZE = 600000; FEMALE_SIZE = 400000; TEST_SIZE = 100000
    Miu_Male_R = [170, 65]; Miu_Female_R = [160, 55]
    Diata_Male_R = [5 ,5]; Diata_Female_R = [5 ,5]
    #男生数据样本
    Male_Data = [Miu_Male_R[0] + Diata_Male_R[0] *np.random.randn(MALE_SIZE, 1),
                 Miu_Male_R[1] + Diata_Male_R[1] * np.random.randn(MALE_SIZE, 1)];
    #女生数据样本
    Female_Data = [Miu_Female_R[0] + Diata_Female_R[0] * np.random.randn(FEMALE_SIZE, 1),Miu_Female_R[1] + Diata_Female_R[1] * np.random.randn(FEMALE_SIZE, 1)];
    #测试数据
    Test_M_Data = [Miu_Male_R[0] + Diata_Male_R[0] * np.random.randn(TEST_SIZE, 1),Miu_Male_R[1] + Diata_Male_R[1] * np.random.randn(TEST_SIZE, 1)]
    Test_M_Data=np.hstack((Test_M_Data[0],Test_M_Data[1]))
    #男测试数据格式处理
    Test_F_Data=[Miu_Female_R[0] + Diata_Female_R[0] * np.random.randn(TEST_SIZE, 1), Miu_Female_R[1] + Diata_Female_R[1] * np.random.randn(TEST_SIZE, 1)]
    Test_F_Data=np.hstack((Test_F_Data[0],Test_F_Data[1]))#女测试数据格式处理
    Test_Data=np.vstack((Test_M_Data,Test_F_Data))#测试数据格式处理
    #样本数据的期望和协方差
    Miu_Male_E = [np.mean (Male_Data[0]),np.mean(Male_Data[1])]
    Diata_Male_E = np.cov (Male_Data[0].T,Male_Data[1].T);
    Miu_Female_E = [np.mean (Female_Data[0]),np.mean(Female_Data[1])];
    Diata_Female_E = np.cov (Female_Data[0].T,Female_Data[1].T);
    #定义集合存储对比结果
    Decision=[]
    #f循环测试数据进行计算
    for Tmp in range(0,2*TEST_SIZE):
       #代入公式计算是男生的概率
       Px_Male = 1 / ((2 * PI)**1.5 *np.sqrt(np.linalg.det(Diata_Male_E)))
       c=(Test_Data[Tmp] - Miu_Male_E)
       Px_Male = Px_Male*np.exp(-0.5 * (Test_Data[Tmp] - Miu_Male_E)
                                .dot(np.linalg.inv(Diata_Male_E))
                                .dot(np.vstack((c[0],c[1]))))
       g_Male = Px_Male * P_Male
       # 代入公式计算是女生的概率
       Px_Female = 1 / ((2 * PI) ** 1.5 * np.sqrt(np.linalg.det(Diata_Female_E)))
       c1 = (Test_Data[Tmp] - Miu_Female_E)
       Px_Female = Px_Female * np.exp(-0.5 * (Test_Data[Tmp] - Miu_Female_E)
                                  .dot(np.linalg.inv(Diata_Female_E))
                                  .dot(np.vstack((c[0], c[1]))))
       g_Female = Px_Female * P_Female
       #对比结果放入集合 True-1,False-0
       Decision.insert(Tmp,(g_Male > g_Female)[0])
    #男用1代表，女用0代表
    Test_Label = [np.ones(TEST_SIZE),np.zeros(TEST_SIZE)]
    Test_Label=np.hstack((Test_Label[0],Test_Label[1]))#格式处理
    #计算
    Accuracy = np.sum (Decision== Test_Label) / (2*TEST_SIZE)
    print(Accuracy)

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\#三维图像代码python版，调整不同参数值呈现不同图像。

#三维图像代码python版
    import numpy as np
    from scipy import stats
    import matplotlib as mpl
    import matplotlib.pyplot as plt
    from matplotlib import cm
    from mpl_toolkits.mplot3d import Axes3D
    if __name__ == '__main__':
        #编码和字体设置
        mpl.rcParams['axes.unicode_minus'] = False
        mpl.rcParams['font.sans-serif'] = 'SimHei'
        MALE_SIZE = 60000; FEMALE_SIZE = 40000
        TEST_SIZE = 100000; Miu_Male_R = [170, 65]
                Miu_Female_R = [160, 55]
        Diata_Male_R = [5, 5];Diata_Female_R = [5, 5]
        # 男/女生数据
        Male_Data = [Miu_Male_R[0] + Diata_Male_R[0] * np.random.randn(MALE_SIZE, 1), Miu_Male_R[1] + Diata_Male_R[1] * np.random.randn(MALE_SIZE, 1)]
        Female_Data = [Miu_Female_R[0] + Diata_Female_R[0] * np.random.randn(FEMALE_SIZE, 1), Miu_Female_R[1] + Diata_Female_R[1] * np.random.randn(FEMALE_SIZE, 1)]
        #μ和 协方差
        Miu_Male_E = [np.mean(Male_Data[0]), np.mean(Male_Data[1])]
        Diata_Male_E = np.cov(Male_Data[0].T, Male_Data[1].T)
        Miu_Female_E = [np.mean(Female_Data[0]), np.mean(Female_Data[1])]
        Diata_Female_E = np.cov(Female_Data[0].T, Female_Data[1].T)
        #男生图像数据
        M_density=np.sqrt(MALE_SIZE)*1j;
        M_x1, M_x2 = np.mgrid[150:180:M_density,40:90:M_density]
        M_x = np.stack((M_x1, M_x2), axis=2)
        # 参数μ和cov/Miu_Male_E和Diata_Male_E
        M_norm = stats.multivariate_normal(Miu_Male_R, [[5, 0], [0,5]])
        M_y = M_norm.pdf(M_x)
        # 女生图像数据
        F_density = np.sqrt(MALE_SIZE) * 1j;
        F_x1, F_x2 = np.mgrid[150:180:F_density,40:90:F_density]
        #F_x1, F_x2 = np.mgrid[140:180:616j, 50:60:616j]
        F_x = np.stack((F_x1, F_x2), axis=2)
        F_norm = stats.multivariate_normal(Miu_Female_R, [[5, 0], [0,5]])
        F_y = F_norm.pdf(F_x)
        #画图
        fig = plt.figure(facecolor='w')
        ax = plt.subplot( projection='3d')
        ax.plot_surface(M_x1, M_x2, M_y,  rstride=1, cstride=1,cmap=cm.Accent,  alpha=0.9, lw=0.9)
        ax.plot_surface(F_x1, F_x2, F_y,  rstride=1, cstride=1,cmap='rainbow',  alpha=0.9, lw=0.9)
        ax.set_xlabel('X身高')
        ax.set_ylabel('Y体重')
        ax.set_zlabel('Z')
        plt.suptitle('三维图', fontsize=18)
        plt.show()

\#二维散点图代码python版，调整不同参数值呈现不同图像。

#二维散点图代码python版
    import numpy as np
    import matplotlib.pyplot as plt
    #%matplotlib inline
    
    plt.figure()
    plt.axis([140,190,40,90])
    plt.gca().set_aspect(1)
    X = np.random.multivariate_normal(mean=[170,65], cov=[[5, 0], [0,5]], size = 600000)
    X1 = np.random.multivariate_normal(mean=[160,55], cov=[[5, 0], [0,5]], size = 400000)
    plt.scatter(X[:,0], X[:,1])
    plt.scatter(X1[:,0], X1[:,1])
    plt.show()

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