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前言

梯度下降算法学习。

一、数据集介绍

波士顿房价数据集：波士顿房价数据集，用于线性回归预测

二、预测房价代码

1.引入库

from sklearn.linear_model import LinearRegression as LR
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_boston as boston 
import matplotlib.pyplot as plt
from sklearn.utils import shuffle
import numpy as np
from sklearn.metrics import mean_squared_error

2.数据

def preprocess():
    # get the dataset of boston
    X = boston().data
    y = boston().target
    name_data = boston().feature_names
 
    # draw the figure of relationship between feature and price
    plt.figure(figsize=(20,20))
    for i in range(len(X[0])):
        
        plt.subplot(5, 3, i + 1)
        plt.scatter(X[:, i], y, s=20)
        plt.title(name_data[i])
    plt.show()
    # 删除相关性较低的特征
    # X = np.delete(X, [0, 1, 3, 4, 6, 7, 8, 9, 11], axis=1)
 
    # normalization
    for i in range(len(X[0])):
        X[:, i] = (X[:, i] - X[:, i].min()) / (X[:, i].max() - X[:, i].min())
 
    # split into test and train
    Xtrain, Xtest, Ytrain, Ytest = train_test_split(X, y, test_size=0.3, random_state=10)
    
    return Xtrain, Xtest, Ytrain, Ytest, X

def lr(Xtrain, Xtest, Ytrain, Ytest, if_figure):
    # use LinearRegression
    reg = LR().fit(Xtrain, Ytrain)
    y_pred = reg.predict(Xtest)
    loss = mean_squared_error(Ytest, y_pred)
 
    print("*************LR*****************")
    print("w\t= {}".format(reg.coef_))
    print("b\t= {:.4f}".format(reg.intercept_))
 
    # draw the figure of predict results
    if if_figure:
        plt.figure(figsize = (14,6),dpi = 80)
        plt.plot(range(len(Ytest)), Ytest, c="blue", label="real")
        plt.plot(range(len(y_pred)), y_pred, c="red", linestyle=':', label="predict")
        plt.title("predict results from row LR")
        plt.legend()
        plt.show()
 
    return loss

3.梯度下降

def gradDescnet(Xtrain, Xtest, Ytrain, Ytest, X, if_figure, rate):
    # 梯度下降
    def grad(y, yp, X):
        grad_w = (y - yp) * (-X)
        grad_b = (y - yp) * (-1)
        return [grad_w, grad_b]
 
    # 设置训练参数
    epoch_train = 100
    learning_rate = rate
    w = np.random.normal(0.0, 1.0, (1, len(X[0])))
    b = 0.0   
    loss_train = []
    loss_test = []
    for epoch in range(epoch_train + 1):
        loss1 = 0
        for i in range(len(Xtrain)):
            yp = w.dot(Xtrain[i]) + b
            # 计算损失
            err = Ytrain[i] - yp
            loss1 += err ** 2
            # 迭代更新 w 和 b
            gw = grad(Ytrain[i], yp, Xtrain[i])[0]
            gb = grad(Ytrain[i], yp, Xtrain[i])[1]
            w = w - learning_rate * gw
            b = b - learning_rate * gb
        # 记录损失
        loss_train.append(loss1 / len(Xtrain))
 
        loss11 = 0
        for i in range(len(Xtest)):
            yp2 = w.dot(Xtest[i]) + b
            err2 = Ytest[i] - yp2
            loss11 += err2 ** 2
        # 记录损失
        loss_test.append(loss11 / len(Xtest))
 
        # shuffle the data
        Xtrain, Ytrain = shuffle(Xtrain, Ytrain)
 
    # draw the figure of loss
    if if_figure:
        plt.figure()
        plt.title("figure of loss")
        plt.plot(range(len(loss_train)), loss_train, c="blue", linestyle=":", label="train")
        plt.plot(range(len(loss_test)), loss_test, c="red", label="test")
        plt.legend()
        plt.show()
    # draw figure of predict results
    if if_figure:
        Predict_value = []
        for i in range(len(Xtest)):
            Predict_value.append(w.dot(Xtest[i]) + b)
        plt.figure()
        plt.title("predict results from gradScent")
        plt.plot(range(len(Xtest)), Ytest, c="blue", label="real")
        plt.plot(range(len(Xtest)), Predict_value, c="red", linestyle=':', label="predict")
        plt.legend()
        plt.show()
 
    return loss_test[-1], w, b

def test():
    if_figure = True
    Xtrain, Xtest, Ytrain, Ytest, X = preprocess()
    loss_lr = lr(Xtrain, Xtest, Ytrain, Ytest, if_figure)
    loss_gd, w, b = gradDescnet(Xtrain, Xtest, Ytrain, Ytest, X, if_figure, 0.01)
    print("*************GD*****************")      
    print("w\t: {}".format(w))
    print("b\t: {}".format(b))
    print("************loss****************")
    print("lr\t: %.4f" % loss_lr)
    print("gd\t: %.4f" % loss_gd)

def searchRate():
    if_figure = False
    Xtrain, Xtest, Ytrain, Ytest, X = preprocess()
 
    loss_grad = []
    w_grad = []
    b_grad = []
    rates = list(np.arange(0.001, 0.05, 0.001))
    epoch = 1
    for rate in rates:
        loss, w, b = gradDescnet(Xtrain, Xtest, Ytrain, Ytest, X, if_figure, rate)
        loss_grad.append(loss[0])
        w_grad.append(w)
        b_grad.append(b)
        print("epoch %d: %.4f" % (epoch, loss_grad[-1]))
        epoch += 1
 
    plt.figure()
    plt.plot(rates, loss_grad)
    plt.title("loss under different rate")
    plt.show()
    loss_grad_min = min(loss_grad)
    position = loss_grad.index(loss_grad_min)
    w = w_grad[position]
    b = b_grad[position]
    rate = rates[position]
    loss_lr = lr(Xtrain, Xtest, Ytrain, Ytest, if_figure)
    print("*************GD*****************")
    print("w\t: {}".format(w))
    print("b\t: {}".format(b))
    print("rate: %.3f" % rate)
    print("************loss****************")
    print("lr\t: %.4f" % loss_lr)
    print("gd\t: %.4f" % loss_grad_min)

data = boston
Xtrain, Xtest, Ytrain, Ytest, X = preprocess()

lr(Xtrain, Xtest, Ytrain, Ytest,True)

test()

searchRate()

总结

通过此次学习，对梯度下降算法有了更深的认识。