一，基础函数库
import numpy as np
from utils.features import prepare_for_trainingclass 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_processedself.labels = labelsself.features_mean = features_meanself.features_deviation = features_deviationself.polynomial_degree = polynomial_degreeself.sinusoid_degree = sinusoid_degreeself.normalize_data = normalize_datanum_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_historydef 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_historydef 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.labelstheta = self.thetatheta = theta - alpha*(1/num_examples)*(np.dot(delta.T, self.data)).Tself.theta = thetadef cost_function(self, data, labels):"""损失计算方法"""num_examples = data.shape[0]delta = LinearRegression.hypothesis(self.data, self.theta) - labelscost = (1/2)*np.dot(delta.T, delta)/num_examplesreturn cost[0][0]@staticmethoddef hypothesis(data, theta):predictions = np.dot(data, theta)return predictionsdef 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 pltfrom linear_regression import LinearRegressiondata = 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]].valuesx_test = test_data[[input_param_name]].values
y_test = test_data[[output_param_name]].valuesplt.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 = 0.01linear_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
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import plotly
import plotly.graph_objs as goplotly.offline.init_notebook_mode()
from linear_regression import LinearRegressiondata = pd.read_csv('../data/world-happiness-report-2017.csv')train_data = data.sample(frac=0.8)
test_data = data.drop(train_data.index)input_param_name_1 = 'Economy..GDP.per.Capita.'
input_param_name_2 = 'Freedom'
output_param_name = 'Happiness.Score'x_train = train_data[[input_param_name_1, input_param_name_2]].values
y_train = train_data[[output_param_name]].valuesx_test = test_data[[input_param_name_1, input_param_name_2]].values
y_test = test_data[[output_param_name]].values# Configure the plot with training dataset.
plot_training_trace = go.Scatter3d(x=x_train[:, 0].flatten(),y=x_train[:, 1].flatten(),z=y_train.flatten(),name='Training Set',mode='markers',marker={'size': 10,'opacity': 1,'line': {'color': 'rgb(255, 255, 255)','width': 1},}
)plot_test_trace = go.Scatter3d(x=x_test[:, 0].flatten(),y=x_test[:, 1].flatten(),z=y_test.flatten(),name='Test Set',mode='markers',marker={'size': 10,'opacity': 1,'line': {'color': 'rgb(255, 255, 255)','width': 1},}
)plot_layout = go.Layout(title='Date Sets',scene={'xaxis': {'title': input_param_name_1},'yaxis': {'title': input_param_name_2},'zaxis': {'title': output_param_name} },margin={'l': 0, 'r': 0, 'b': 0, 't': 0}
)plot_data = [plot_training_trace, plot_test_trace]plot_figure = go.Figure(data=plot_data, layout=plot_layout)plotly.offline.plot(plot_figure)num_iterations = 500
learning_rate = 0.01
polynomial_degree = 0
sinusoid_degree = 0 linear_regression = LinearRegression(x_train, y_train, polynomial_degree, sinusoid_degree)(theta, cost_history) = linear_regression.train(learning_rate,num_iterations
)print('开始损失', cost_history[0])
print('结束损失', cost_history[-1])plt.plot(range(num_iterations), cost_history)
plt.xlabel('Iterations')
plt.ylabel('Cost')
plt.title('Gradient Descent Progress')
plt.show()predictions_num = 10x_min = x_train[:, 0].min()
x_max = x_train[:, 0].max()y_min = x_train[:, 1].min()
y_max = x_train[:, 1].max()x_axis = np.linspace(x_min, x_max, predictions_num)
y_axis = np.linspace(y_min, y_max, predictions_num)x_predictions = np.zeros((predictions_num * predictions_num, 1))
y_predictions = np.zeros((predictions_num * predictions_num, 1))x_y_index = 0
for x_index, x_value in enumerate(x_axis):for y_index, y_value in enumerate(y_axis):x_predictions[x_y_index] = x_valuey_predictions[x_y_index] = y_valuex_y_index += 1z_predictions = linear_regression.predict(np.hstack((x_predictions, y_predictions)))plot_predictions_trace = go.Scatter3d(x=x_predictions.flatten(),y=y_predictions.flatten(),z=z_predictions.flatten(),name='Prediction Plane',mode='markers',marker={'size': 1,},opacity=0.8,surfaceaxis=2,
)plot_data = [plot_training_trace, plot_test_trace, plot_predictions_trace]
plot_figure = go.Figure(data=plot_data, layout=plot_layout)
plotly.offline.plot(plot_figure)
四，非线性回归
import numpy as np
import pandas as pd
import matplotlib.pyplot as pltfrom linear_regression import LinearRegressiondata = pd.read_csv('../data/non-linear-regression-x-y.csv')x = data['x'].values.reshape((data.shape[0], 1))
y = data['y'].values.reshape((data.shape[0], 1))#data.head(10)plt.plot(x, y)
plt.show()num_iterations = 50000
learning_rate = 0.02
polynomial_degree = 15
sinusoid_degree = 15
normalize_data = True linear_regression = LinearRegression(x, y, polynomial_degree, sinusoid_degree, normalize_data)(theta, cost_history) = linear_regression.train(learning_rate,num_iterations
)print('开始损失: {:.2f}'.format(cost_history[0]))
print('结束损失: {:.2f}'.format(cost_history[-1]))theta_table = pd.DataFrame({'Model Parameters': theta.flatten()})plt.plot(range(num_iterations), cost_history)
plt.xlabel('Iterations')
plt.ylabel('Cost')
plt.title('Gradient Descent Progress')
plt.show()predictions_num = 1000
x_predictions = np.linspace(x.min(), x.max(), predictions_num).reshape(predictions_num, 1);
y_predictions = linear_regression.predict(x_predictions)plt.scatter(x, y, label='Training Dataset')
plt.plot(x_predictions, y_predictions, 'r', label='Prediction')
plt.show()
