用pytorch实现一个简单的线性回归模型
我们使用pytorch实现一个简单的线性回归模型。(我是在jupyter notebook下做的，建议在这个环境下写代码)
首先我们先定义数据集：
#数据集中的样本值
x = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]
#数据集中的标签
y = [0.5, 14.0, 15.0, 28.0, 11.0, 8.0, 3.0, -4.0, 6.0, 13.0, 21.0]
x = torch.tensor(x)
y = torch.tensor(y)创建线性模型与损失函数，在这里我们的损失函数是平方均方误差函数：
def model(x, w, b):
return w * x + b
def loss_fn(y_pre, y):
squared_diffs = (y_pre - y) ** 2
return squared_diffs.mean()做分析(非必须)：
w = torch.ones(1)
b = torch.zeros(1)
y_pre = model(x, w, b)
y_pre
loss = loss_fn(y_pre, y)
loss之后我们要做梯度下降，做梯度下降，我就需要对w和b求偏导。
def loss_fn(y_pre, y):
squared_diffs = (y_pre - y) ** 2
return squared_diffs.mean()
def dloss_fn(y_pre, y):
dsq_diffs = 2 * (y_pre - y)
return dsq_diffs
def dmodel_dw(x, w, b):
return x
def dmodel_db(x, w, b):
return 1.0
def grad_fn(x, y, y_pre, w, b):
dloss_dw = dloss_fn(y_pre, y) * dmodel_dw(x, w, b)
dloss_db = dloss_fn(y_pre, y) * dmodel_db(x, w, b)
return torch.stack([dloss_dw.mean(), dloss_db.mean()])我们写最后训练函数：
def training_loop(n_epochs, learning_rate, params, x, y):
for epoch in range(1, n_epochs + 1):
w, b = params
y_pre = model(x, w, b)
loss = loss_fn(y_pre, y)
grad = grad_fn(x, y, y_pre, w, b)
params = params - learning_rate * grad
print('Epoch %d, Loss %f' % (epoch, float(loss)))
return params最后的训练效果：
全部代码示例：
import torch
#数据集中的样本值
x = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]
#数据集中的标签
y = [0.5, 14.0, 15.0, 28.0, 11.0, 8.0, 3.0, -4.0, 6.0, 13.0, 21.0]
x = torch.tensor(x)
y = torch.tensor(y)
def model(x, w, b):
return w * x + b
def loss_fn(y_pre, y):
squared_diffs = (y_pre - y) ** 2
return squared_diffs.mean()
w = torch.ones(1)
b = torch.zeros(1)
y_pre = model(x, w, b)
y_pre
loss = loss_fn(y_pre, y)
loss
def loss_fn(y_pre, y):
squared_diffs = (y_pre - y) ** 2
return squared_diffs.mean()
def dloss_fn(y_pre, y):
dsq_diffs = 2 * (y_pre - y)
return dsq_diffs
def dmodel_dw(x, w, b):
return x
def dmodel_db(x, w, b):
return 1.0
def grad_fn(x, y, y_pre, w, b):
dloss_dw = dloss_fn(y_pre, y) * dmodel_dw(x, w, b)
dloss_db = dloss_fn(y_pre, y) * dmodel_db(x, w, b)
return torch.stack([dloss_dw.mean(), dloss_db.mean()])
def training_loop(n_epochs, learning_rate, params, x, y):
for epoch in range(1, n_epochs + 1):
w, b = params
y_pre = model(x, w, b)
loss = loss_fn(y_pre, y)
grad = grad_fn(x, y, y_pre, w, b)
params = params - learning_rate * grad
print('Epoch %d, Loss %f' % (epoch, float(loss)))
return params
training_loop(
n_epoches = 20,
learning_rate = 1e-4,
params = torch.tensor([1.0, 0.0]),
x = x,
y = y
)
training_loop(
n_epoches = 20,
learning_rate = 1e-2,
params = torch.tensor([1.0, 0.0]),
x = x,
y = y
)
参考资料：
《Deep Learning with PyTorch》Essential Excepts. Eli Stevens, Luca Antiga.