基于Numpy+Python2.7的线性回归

最新推荐文章于 2024-09-01 10:56:34 发布

原创最新推荐文章于 2024-09-01 10:56:34 发布 · 1k 阅读

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本文通过Python实现了一种使用梯度下降法来优化线性回归模型参数的方法。该方法通过迭代调整斜率(m)和截距(b)，最小化预测误差的平方和。示例代码展示了如何从数据文件中读取数据并运行梯度下降算法。

 

 
#The optimal values of m and b can be actually calculated with way less effort than doing a linear regression. 
#this is just to demonstrate gradient descent

from numpy import *

# y = mx + b
# m is slope, b is y-intercept
def compute_error_for_line_given_points(b, m, points):
    totalError = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        totalError += (y - (m * x + b)) ** 2
    return totalError / float(len(points))

def step_gradient(b_current, m_current, points, learningRate):
    b_gradient = 0
    m_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
    new_b = b_current - (learningRate * b_gradient)
    new_m = m_current - (learningRate * m_gradient)
    return [new_b, new_m]

def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
    b = starting_b
    m = starting_m
    for i in range(num_iterations):
        b, m = step_gradient(b, m, array(points), learning_rate)
    return [b, m]

def run():
    points = genfromtxt("G:\\Workspaces\\py\\linear_regression_live-master\\data.csv", delimiter=",")
    learning_rate = 0.0001
    initial_b = 0 # initial y-intercept guess
    initial_m = 0 # initial slope guess
    num_iterations = 1000
    print "Starting gradient descent at b = {0}, m = {1}, error = {2}".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points))
    print "Running..."
    [b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
    print "After {0} iterations b = {1}, m = {2}, error = {3}".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points))

if __name__ == '__main__':
    run()
 

 

 

 

此代码来自Udacity Siraj的直播课程，代码与数据集下载地址：https://github.com/llSourcell/linear_regression_live

查看原文：http://data.1kapp.com/?p=331