Python求解回归问题

灰太狼 2022-09-08 00:10 164阅读 0赞

--------------------

title: Python求解回归问题  
cover: https://gitee.com/Asimok/picgo/raw/master/img/MacBookPro/20210801104603.png  
categories: 机器学习  
tags:

*  Python
 *  机器学习  
    keywords: ‘机器学习,Python’  
    date: 2021-8-1

--------------------

# Python求解回归问题 #

y=wx+b

import numpy as np
    import matplotlib.pyplot as plt

# 计算给定(w,b)的平均误差
    def compute_error_for_line_given_points(b, w, points):
        totalError = 0
        for i in range(0, len(points)):
            x = points[i, 0]
            y = points[i, 1]
            # computer mean-squared-error
            totalError += (y - (w * x + b)) ** 2
        # average loss for each point
        return totalError / float(len(points))

def step_gradient(b_current, w_current, points, learningRate):
        b_gradient = 0
        w_gradient = 0
        N = float(len(points))
        for i in range(0, len(points)):
            x = points[i, 0]
            y = points[i, 1]
            # 求导数 除N取平均值
            # grad_b = 2(wx+b-y)
            b_gradient += (2/N) * ((w_current * x + b_current) - y)
            # grad_w = 2(wx+b-y)*x
            w_gradient += (2/N) * x * ((w_current * x + b_current) - y)
        # update b' w' 
        # 梯度指向极大值方向 因此反方向更新梯度
        new_b = b_current - (learningRate * b_gradient)
        new_w = w_current - (learningRate * w_gradient)
        temploss = compute_error_for_line_given_points(new_b, new_w, points)
        loss.append(temploss)
        return [new_b, new_w]

def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
        b = starting_b
        w = starting_w
        # update for several times
        for i in range(num_iterations):
            b, w = step_gradient(b, w, np.array(points), learning_rate)
        return [b, w]

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

loss = []
    run()

Starting gradient descent at b = 0, w = 0, error = 5565.107834483211
    Running...
    After 1000 iterations b = 0.08893651993741346, w = 1.4777440851894448, error = 112.61481011613473

x = [i for i in range(0, len(loss))]
    plt.plot(x,loss)

[<matplotlib.lines.Line2D at 0x7f82b2c8bd90>]

![png][]

[png]: /images/20220829/9cf38c96acea44fb85793f9cb20e37d8.png