---

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 bostonX = boston().datay = boston().targetname_data = boston().feature_names# draw the figure of relationship between feature and priceplt.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)# normalizationfor i in range(len(X[0])):X[:, i] = (X[:, i] - X[:, i].min()) / (X[:, i].max() - X[:, i].min())# split into test and trainXtrain, 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 LinearRegressionreg = 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 resultsif 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 = 100learning_rate = ratew = 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 = 0for i in range(len(Xtrain)):yp = w.dot(Xtrain[i]) + b# 计算损失err = Ytrain[i] - yploss1 += err ** 2# 迭代更新 w 和 bgw = grad(Ytrain[i], yp, Xtrain[i])[0]gb = grad(Ytrain[i], yp, Xtrain[i])[1]w = w - learning_rate * gwb = b - learning_rate * gb# 记录损失loss_train.append(loss1 / len(Xtrain))loss11 = 0for i in range(len(Xtest)):yp2 = w.dot(Xtest[i]) + berr2 = Ytest[i] - yp2loss11 += err2 ** 2# 记录损失loss_test.append(loss11 / len(Xtest))# shuffle the dataXtrain, Ytrain = shuffle(Xtrain, Ytrain)# draw the figure of lossif 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 resultsif 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 = TrueXtrain, 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 = FalseXtrain, Xtest, Ytrain, Ytest, X = preprocess()loss_grad = []w_grad = []b_grad = []rates = list(np.arange(0.001, 0.05, 0.001))epoch = 1for 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 += 1plt.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。