线性回归算法

标签：loss gradient 回归 rate current 算法 points learning 线性

1.算法原理

y=w*x+b+ε

loss=Σ(w*xi+b-yi)²

w'=w-lr*(loss对w求偏导)           # 梯度下降算法

b'=b-lr*(loss对b求偏导)             # 梯度下降算法

 2.基于numpy实现

def compute_loss(b,w,points):
	loss = 0
	n = len(points)
	for i in range(n):
		x = points[i,0]
		y = points[i,1]
		loss += (y-(w*x+b))**2
	return loss/n

def step_gradient(current_b,current_w,points,learning_rate):
	b_gradient = 0
	w_gradient = 0
	n = len(points)
	for i in range(0,n):
		x = points[i,0]
		y = points[i,1]
		# grad_b = 2*(w*x+b-y)
		b_gradient += (2/n)*((current_w*x+current_b)-y)
		# grad_w = 2*(w*x+b-y)*x
		w_gradient += (2/n)*x*((current_w*x+current_b)-y)
	current_b = current_b - learning_rate * b_gradient
	current_w = current_w - learning_rate * w_gradient
	return current_b,current_w

def gradient_descent_runner(points,start_b,start_w,learning_rate,num):
	b = start_b
	w = start_w
	for _ in range(num):
		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
	b = 0
	w = 0
	num = 1000
	loss = compute_loss(b,w,points)
	print(w,b,loss)
	b,w = gradient_descent_runner(points,b,w,learning_rate,num)
	loss = compute_loss(b,w,points)
	print(w,b,loss)

　　

　　

标签：loss,gradient,回归,rate,current,算法,points,learning,线性
From： https://www.cnblogs.com/navysummer/p/17207142.html