如何使用Pytorch用感知机模型拟合小数据集

Question

我试图用3层感知器模型拟合一个小数据集(只有7x1大小)，但损失无法收敛。我是机器学习领域的新手，有人能给我点提示来调整我的代码吗?

import torch
import torch.nn as nn
import torch.nn.functional as F
vec_shape = [7, 1]
x_0 = [500, 1000, 2000, 4000, 5000, 8000, 10000]
y_0 = [1.171467, 1.486507, 11.7738, 34.448421, 75.402871, 225.319848, 492.262426]
# x = torch.tensor(x_0).reshape(vec_shape).float()
x = torch.log(torch.tensor(x_0).reshape(vec_shape).float())
y = torch.tensor(y_0).reshape(vec_shape).float()
class Net(nn.Module):
def __init__(self,n_input,n_hidden,n_output):
super(Net,self).__init__()
self.hidden1 = nn.Linear(n_input,n_hidden)
self.hidden2 = nn.Linear(n_hidden,n_hidden)
self.predict = nn.Linear(n_hidden,n_output)
def forward(self,input):
out = self.hidden1(input)
out = F.relu(out)
out = self.hidden2(out)
out = torch.sigmoid(out)
out =self.predict(out)
return out
def weight_init(self):
for op in self.modules():
if isinstance(op, nn.Linear):
nn.init.normal_(op.weight.data)
nn.init.normal_(op.bias.data)
net = Net(1,10,1)
net.weight_init()
# print(net)
optimizer = torch.optim.SGD(net.parameters(),lr = 0.1)
loss_func = torch.nn.MSELoss()
for t in range(500):
prediction = net(x)
loss = loss_func(prediction, y)
optimizer.zero_grad()
loss.backward()
optimizer.step()
if(t%50 == 0):
print('Loss = %.4f' % loss.data)

我试着扩展或缩小模型，但这两种变化都不起作用。

Answer 1

重新缩放和归一化是机器学习的关键，你的设置很好，你应用了一些缩放，但还不够。在有限的数据点数量下，范围太大了。就像处理x_0一样，将torch.log应用于y_0。你可以在训练后缩减预测。下面你可以找到修改后的代码，我修改了两处:

• torch.logony_0
• 对0.01的学习率
• 到50000的迭代次数
• 增加了一个打印语句来显示预测的缩放

import torch
import torch.nn as nn
import torch.nn.functional as F
vec_shape = [7, 1]
x_0 = [500, 1000, 2000, 4000, 5000, 8000, 10000]
y_0 = [1.171467, 1.486507, 11.7738, 34.448421, 75.402871, 225.319848, 492.262426]
# x = torch.tensor(x_0).reshape(vec_shape).float()
x = torch.log(torch.tensor(x_0).reshape(vec_shape).float())
y = torch.log(torch.tensor(y_0).reshape(vec_shape).float()) # modified
class Net(nn.Module):
def __init__(self,n_input,n_hidden,n_output):
super(Net,self).__init__()
self.hidden1 = nn.Linear(n_input,n_hidden)
self.hidden2 = nn.Linear(n_hidden,n_hidden)
self.predict = nn.Linear(n_hidden,n_output)
def forward(self,input):
out = self.hidden1(input)
out = F.relu(out)
out = self.hidden2(out)
out = torch.sigmoid(out)
out =self.predict(out)
return out
def weight_init(self):
for op in self.modules():
if isinstance(op, nn.Linear):
nn.init.normal_(op.weight.data)
nn.init.normal_(op.bias.data)
net = Net(1,10,1)
net.weight_init()
# print(net)
optimizer = torch.optim.SGD(net.parameters(),lr = 0.01) # modified
loss_func = torch.nn.MSELoss()
for t in range(50000): # modified
prediction = net(x)
loss = loss_func(prediction, y)
optimizer.zero_grad()
loss.backward()
optimizer.step()
if(t%50 == 0):
print('Loss = %.4f' % loss.data)
print(torch.exp(net(x))) # added

我还建议在对数重新缩放后对数据集进行规范化，例如除以标准差并减去平均值。