pytorch学习笔记3--回归问题

最新推荐文章于 2023-12-25 21:50:19 发布

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本文深入探讨了线性回归的基本原理，包括损失函数的定义及其最小化过程。通过梯度下降算法优化参数，实现了从理论到实践的转换。同时，文章提供了详细的代码示例，帮助读者理解如何计算误差并迭代更新权重。

                    
                        
                    
                    回归问题
linear regression
y∈[−∞,+∞]y \in [-\infty, +\infty]y∈[−∞,+∞]

logistics regression
把y值压缩到[0,1]，变为概率问题

代码：
loss=(WX+b−y)2loss = (WX+b-y)^2loss=(WX+b−y)2

代码实现如下：  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]
  		totalError += (y-(w*x+b)) ** 2
  	return totalError / float(len(points))
  ```

w′=w−lr∗∂loss∂ww&#x27; = w -lr * \frac{\partial loss}{\partial w}w′=w−lr∗∂w∂loss​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 = point[i,0]
		y = point[i,1]
		b_gradient += -(2/N) * (y-(w_current * x) + b_current)
		w_gradient += -(2/N) * x * (y - ((w_current * x) + b_current))
	new_b = b_current - (learningRate * b_gradient)
	new_m = w_current - (learningRate * w_gradient)

Iterate to optimize	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,np.array(points),learning_rate)
		return [b,m]





                