【机器学习】线性回归·可运行源码

一，所要用到的函数

import numpy as np
from utils.features import prepare_for_training

class LinearRegression:

    def __init__(self, data, labels, polynomial_degree=0, sinusoid_degree=0, normalize_data=True):
        """
        1.对数据进行预处理操作
        2.先得到所有的特征个数
        3.初始化参数矩阵
        """
        (data_processed,
         features_mean, 
         features_deviation) = prepare_for_training(data, polynomial_degree, sinusoid_degree, normalize_data=True)
         
        self.data = data_processed
        self.labels = labels
        self.features_mean = features_mean
        self.features_deviation = features_deviation
        self.polynomial_degree = polynomial_degree
        self.sinusoid_degree = sinusoid_degree
        self.normalize_data = normalize_data
        
        num_features = self.data.shape[1]
        self.theta = np.zeros((num_features, 1))
        
    def train(self, alpha, num_iterations=500):
        """
                    训练模块，执行梯度下降
        """
        cost_history = self.gradient_descent(alpha, num_iterations)
        return self.theta, cost_history
        
    def gradient_descent(self, alpha, num_iterations):
        """
                    实际迭代模块，会迭代num_iterations次
        """
        cost_history = []
        for _ in range(num_iterations):
            self.gradient_step(alpha)
            cost_history.append(self.cost_function(self.data, self.labels))
        return cost_history
        
        
    def gradient_step(self,alpha):    
        """
                    梯度下降参数更新计算方法，注意是矩阵运算
        """
        num_examples = self.data.shape[0]
        prediction = LinearRegression.hypothesis(self.data, self.theta)
        delta = prediction - self.labels
        theta = self.theta
        theta = theta - alpha*(1/num_examples)*(np.dot(delta.T, self.data)).T
        self.theta = theta
        
        
    def cost_function(self, data, labels):
        """
                    损失计算方法
        """
        num_examples = data.shape[0]
        delta = LinearRegression.hypothesis(self.data, self.theta) - labels
        cost = (1/2)*np.dot(delta.T, delta)/num_examples
        return cost[0][0]
        
        
        
    @staticmethod
    def hypothesis(data, theta):
        predictions = np.dot(data, theta)
        return predictions
        
    def get_cost(self, data, labels):
        data_processed = prepare_for_training(data,
         self.polynomial_degree,
         self.sinusoid_degree,
         self.normalize_data
         )[0]
        
        return self.cost_function(data_processed, labels)
    def predict(self,data):
        """
                    用训练的参数模型，与预测得到回归值结果
        """
        data_processed = prepare_for_training(data,
         self.polynomial_degree,
         self.sinusoid_degree,
         self.normalize_data
         )[0]
         
        predictions = LinearRegression.hypothesis(data_processed, self.theta)
        
        return predictions
        
        
        
        

二、单个特征的线性回归

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from linear_regression import LinearRegression

data = pd.read_csv('../data/world-happiness-report-2017.csv')

# 得到训练和测试数据
train_data = data.sample(frac=0.8)
test_data = data.drop(train_data.index)

input_param_name = 'Economy..GDP.per.Capita.'
output_param_name = 'Happiness.Score'

x_train = train_data[[input_param_name]].values
y_train = train_data[[output_param_name]].values

x_test = test_data[[input_param_name]].values
y_test = test_data[[output_param_name]].values

plt.scatter(x_train, y_train, label='Train data')
plt.scatter(x_test, y_test, label='test data')
plt.xlabel(input_param_name)
plt.ylabel(output_param_name)
plt.title('Happy')
plt.legend()
plt.show()

num_iterations = 500
learning_rate = 0.01

linear_regression = LinearRegression(x_train, y_train)
(theta, cost_history) = linear_regression.train(learning_rate, num_iterations)

print('开始时的损失：', cost_history[0])
print('训练后的损失：', cost_history[-1])

plt.plot(range(num_iterations), cost_history)
plt.xlabel('Iter')
plt.ylabel('cost')
plt.title('GD')
plt.show()

predictions_num = 100
x_predictions = np.linspace(x_train.min(), x_train.max(), predictions_num).reshape(predictions_num, 1)
y_predictions = linear_regression.predict(x_predictions)

plt.scatter(x_train, y_train, label='Train data')
plt.scatter(x_test, y_test, label='test data')
plt.plot(x_predictions, y_predictions, 'r', label='Prediction')
plt.xlabel(input_param_name)
plt.ylabel(output_param_name)
plt.title('Happy')
plt.legend()
plt.show()

三、多特征的线性回归