sklearn线性回归模型

import numpy as npimport matplotlib.pyplot as pltfrom sklearn import linear_modeldef get_data():    #506行,14列，最后一列为label，前面13列为参数    data_original = np.loadtxt('housing.data')      scale_data = scale_n(data_original)    np.random.shuffle(scale_data)    #在位置0，插入一列1，axis=1代表列，代表b    data = np.insert(scale_data, 0, 1, axis=1)     train_X = data[:400, :-1] #前400行为训练数据    train_y = data[:400, -1]    train_y.shape = (train_y.shape[0],1)    test_X = data[400:, :-1]    test_y = data[400:, -1]    test_y.shape = (test_y.shape[0],1)    # test测试数据没有返回    return train_X,train_y,test_X,test_ydef scale_n(x):    return (x-x.mean(axis=0))/x.std(axis=0)if __name__=="__main__":    train_X,train_y,test_X,test_y = get_data()        l_model = linear_model.Ridge(alpha = 1000)     # 参数是正则化系数            l_model.fit(train_X,train_y)        predict_train_y = l_model.predict(train_X)    predict_train_y.shape = (predict_train_y.shape[0],1)    error = (predict_train_y-train_y)    rms_train = np.sqrt(np.mean(error**2, axis=0))                predict_test_y = l_model.predict(test_X)    predict_test_y.shape = (predict_test_y.shape[0],1)    error = (predict_test_y-test_y)    rms_test = np.sqrt(np.mean(error**2, axis=0))        print (rms_train, rms_test)        plt.figure(figsize=(10, 8))    plt.scatter(np.arange(test_y.size), sorted(test_y), c='b', edgecolor='None', alpha=0.5, label='actual')    plt.scatter(np.arange(test_y.size), sorted(predict_test_y), c='g', edgecolor='None', alpha=0.5, label='predicted')    plt.legend(loc='upper left')    plt.ylabel('House price ($1000s)')    plt.xlabel('House #')    plt.show()

 sklearn模型调用民工三连：

l_model = linear_model.Ridge(alpha = 1000)     # 模型装载        l_model.fit(train_X,train_y)                   # 模型训练    predict_train_y = l_model.predict(train_X)     # 模型预测

手动线性回归模型

数据获取

房价数据，506行,14列，最后一列为label，前面13列为参数

假如我们需要平方特征，只要修改get_data()中的data_original即可，在13列后添加平方项或者立方项等，由于我们不知道具体添加多少特征的组合更好，神经网络自动提取组合特征的功能就被很好的凸显出来了

import numpy as npimport matplotlib.pyplot as pltdef get_data():    #506行,14列，最后一列为label，前面13列为参数    data_original = np.loadtxt('housing.data')      # 读取数据    scale_data = scale_n(data_original)             # 归一化处理    np.random.shuffle(scale_data)                   # 打乱顺序    #在位置0，插入一列1，axis=1代表列，代表b    data = np.insert(scale_data, 0, 1, axis=1)      # 数组插入函数    train_X = data[:400, :-1]                       #前400行为训练数据    train_y = data[:400, -1]    train_y.shape = (train_y.shape[0],1)    test_X = data[400:, :-1]    test_y = data[400:, -1]    test_y.shape = (test_y.shape[0],1)    # test测试数据没有返回    return train_X,train_y,test_X,test_y

其中：

np.loadtxt('housing.data')     # 读取数据# 本函数读取数据后自动转化为ndarray数组，可以自行设定分隔符delimiter=","np.insert(scale_data, 0, 1, axis=1)      # 数组插入函数# 在数组中插入指定的行列，numpy.insert(arr, obj, values, axis=None）# 和其他数组一样，axis不设定的话会把数组定为一维后插入，axis=0的话行扩展，axis=1的话列扩展

预处理

中心归零，标准差归一

def scale_n(x):    """    减去平均值，除以标准差    """    x = (x - np.mean(x,axis=0))/np.std(x,axis=0)    return x

线性回归类

class LinearModel():    def __init__(self,learn_rate=0.06,lamda=0.01,threhold=0.0000005):        """        初始化一些参数        """        self.learn_rate = learn_rate  # 学习率        self.lamda = lamda            # 正则化系数        self.threhold = threhold      # 迭代阈值        def get_cost_grad(self,theta,X,y):        """        计算代价cost和梯度grad        """        y_pre = X.dot(theta)        cost = (y_pre-y).T.dot(y_pre-y) + self.lamda*theta.T.dot(theta)        grad = (2.0*X.T.dot(y_pre-y) + 2.0*self.lamda*theta)/X.shape[0]               # 实际上是1个batch的梯度的累加值        return cost, grad            def grad_check(self,X,y):        """        梯度检查： 函数计算梯度 == L(theta+delta)-L(theta-delta) / 2delta        """        m,n = X.shape        delta = 10**(-4)        sum_error = 0        for i in range(100):            theta = np.random.random((n,1))            j = np.random.randint(1,n)            theta1,theta2 = theta.copy(),theta.copy()            theta1[j] += delta            theta2[j] -= delta            cost1, grad1 = self.get_cost_grad(theta1, X, y)            cost2, grad2 = self.get_cost_grad(theta2, X, y)            cost,  grad  = self.get_cost_grad(theta , X, y)            sum_error += np.abs(grad[j] - (cost1-cost2)/(delta*2))        print(sum_error/300.0)    def train(self,X,y):        """        初始化theta        训练后，将theta保存到实例变量里        """        m,n = X.shape        theta = np.random.random((n,1))        prev_cost = None        for loop in range(1000):            cost,grad = self.get_cost_grad(theta,X,y)            theta -= self.learn_rate*grad            if prev_cost:                if prev_cost - cost < self.threhold:                    break            prev_cost = cost        self.theta = theta        # print(theta,loop,cost)    def predict(self,X):        """        预测程序        """        return X.dot(self.theta)

 主函数

if __name__ == "__main__":    train_X,train_y,test_X,test_y = get_data()    linear_model = LinearModel()    linear_model.grad_check(train_X,train_y)    linear_model.train(train_X,train_y)    predict_train_y = linear_model.predict(train_X)    error = (predict_train_y - train_y)    rms_train = np.sqrt(np.mean(error ** 2,axis=0))    predict_test_y = linear_model.predict(test_X)    error = (predict_test_y - test_y)    rms_test = np.sqrt(np.mean(error ** 2,axis=0))    #    print(rms_train,rms_test)    # [ 0.54031084] [ 0.60065021]    plt.figure(figsize=(10,8))    plt.scatter(np.arange(test_y.size),sorted(test_y),c='b',edgecolor='None',alpha=0.5,label='actual')    plt.scatter(np.arange(test_y.size),sorted(predict_test_y),c='g',edgecolor='None',alpha=0.5,label='predicted')    plt.legend(loc='upper left')    plt.ylabel('House price ($1000s)')    plt.xlabel('House #')    plt.show()

 

Logistic回归

数据获取&预处理

logistic回归输出值在0~1之间，所以数据预处理分两部分，前13列仍然是均值归零标准差归一，label列采取(x-x.min(axis=0))/(x.max(axis=0)-x.min(axis=0))的方式

import numpy as npimport matplotlib.pyplot as pltimport mathdef get_data(N=400):    #506行,14列，最后一列为label，前面13列为参数    data_original = np.loadtxt('housing.data')      scale_data = np.zeros(data_original.shape)    scale_data[:,:13] = scale_n(data_original[:,:13])    scale_data[:,-1] = scale_max(data_original[:,-1])    np.random.shuffle(scale_data)    #在位置0，插入一列1，axis=1代表列，代表b    data = np.insert(scale_data, 0, 1, axis=1)     train_X = data[:N, :-1] #前400行为训练数据    train_y = data[:N, -1]    train_y.shape = (train_y.shape[0],1)    test_X = data[N:, :-1]    test_y = data[N:, -1]    test_y.shape = (test_y.shape[0],1)    # test测试数据没有返回    return train_X,train_y,test_X,test_ydef scale_n(x):    return (x-x.mean(axis=0))/x.std(axis=0)def scale_max(x):    print (x.min(axis=0))    print (x.max(axis=0))    print (x.mean(axis=0))    print (x.std(axis=0))    return (x-x.min(axis=0))/(x.max(axis=0)-x.min(axis=0))

 Logistic回归类

 公式参考，

实际代码，

class LogisticModel(object):    def __init__(self,lamda=0.01, alpha=0.6,threhold=0.0000005):        self.alpha = alpha        self.threhold = threhold        self.lamda = lamda            def sigmoid(self,x):        return 1.0/(1+np.exp(-x))            def get_cost_grad(self,theta,X,y):        m, n = X.shape        y_dash = self.sigmoid(X.dot(theta))        error = np.sum((y * np.log(y_dash) + (1-y) * np.log(1-y_dash)),axis=1)        cost = -np.sum(error, axis=0)+self.lamda*theta.T.dot(theta)        grad = X.T.dot(y_dash-y)+2.0*self.lamda*theta                            return cost,grad/m                    def grad_check(self,X,y):        epsilon = 10**-4        m, n = X.shape                   sum_error=0                for i in range(300):            theta = np.random.random((n, 1))            j = np.random.randint(1,n)            theta1=theta.copy()            theta2=theta.copy()            theta1[j]+=epsilon            theta2[j]-=epsilon            cost1,grad1 = self.get_cost_grad(theta1,X,y)            cost2,grad2 = self.get_cost_grad(theta2,X,y)            cost3,grad3 = self.get_cost_grad(theta,X,y)            sum_error += np.abs(grad3[j]-(cost1-cost2)/float(2*epsilon))            def train(self,X,y):        m, n = X.shape  # 400,15           theta = np.random.random((n, 1))  #[15,1]        #our intial prediction        prev_cost = None        loop_num = 0        while(True):                                  #intial cost            cost,grad = self.get_cost_grad(theta,X,y)                        theta = theta- self.alpha * grad                        loop_num+=1            if loop_num%100==0:                print (cost,loop_num)            if prev_cost:                if prev_cost - cost <= self.threhold:                    break            if loop_num>1000:                break            prev_cost = cost                                           self.theta = theta        print (theta,loop_num)            def predict(self,X):        return self.sigmoid(X.dot(self.theta))