Python求解回归问题

y=wx+b

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import numpy as np
import matplotlib.pyplot as plt
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# 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))
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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]
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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]

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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))
          )
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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

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x = [i for i in range(0, len(loss))]
plt.plot(x,loss)
[<matplotlib.lines.Line2D at 0x7f82b2c8bd90>]

png