.. _sec_linear_scratch:
线性回归的从零开始实现
======================
在了解线性回归的关键思想之后，我们可以开始通过代码来动手实现线性回归了。
在这一节中，我们将从零开始实现整个方法，
包括数据流水线、模型、损失函数和小批量随机梯度下降优化器。
虽然现代的深度学习框架几乎可以自动化地进行所有这些工作，但从零开始实现可以确保我们真正知道自己在做什么。
同时，了解更细致的工作原理将方便我们自定义模型、自定义层或自定义损失函数。
在这一节中，我们将只使用张量和自动求导。
在之后的章节中，我们会充分利用深度学习框架的优势，介绍更简洁的实现方式。
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
%matplotlib inline
import random
import mindspore
from mindspore import grad, ops
from d2l import mindspore as d2l
mindspore.set_context(mode=mindspore.PYNATIVE_MODE)
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
%matplotlib inline
import random
import torch
from d2l import torch as d2l
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def synthetic_data(w, b, num_examples): #@save
"""生成y=Xw+b+噪声"""
X = ops.normal((num_examples, len(w)), 0, 1)
y = ops.matmul(X, w) + b
y += ops.normal(y.shape, 0, 0.01)
return X, y.reshape((-1, 1))
true_w = mindspore.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def synthetic_data(w, b, num_examples): #@save
"""生成y=Xw+b+噪声"""
X = torch.normal(0, 1, (num_examples, len(w)))
y = torch.matmul(X, w) + b
y += torch.normal(0, 0.01, y.shape)
return X, y.reshape((-1, 1))
true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
print('features:', features[0],'\nlabel:', labels[0])
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
features: [-0.20889263 -0.8909768 ]
label: [6.800602]
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
print('features:', features[0],'\nlabel:', labels[0])
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
features: tensor([ 0.9637, -0.5191])
label: tensor([7.9069])
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
d2l.set_figsize()
d2l.plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1);
.. figure:: output_linear-regression-scratch_58de05_30_0.png
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
d2l.set_figsize()
d2l.plt.scatter(features[:, 1].detach().numpy(), labels.detach().numpy(), 1);
.. figure:: output_linear-regression-scratch_58de05_33_0.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def data_iter(batch_size, features, labels):
num_examples = len(features)
indices = list(range(num_examples))
# 这些样本是随机读取的，没有特定的顺序
random.shuffle(indices)
for i in range(0, num_examples, batch_size):
batch_indices = mindspore.tensor(
indices[i: min(i + batch_size, num_examples)])
yield features[batch_indices], labels[batch_indices]
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def data_iter(batch_size, features, labels):
num_examples = len(features)
indices = list(range(num_examples))
# 这些样本是随机读取的，没有特定的顺序
random.shuffle(indices)
for i in range(0, num_examples, batch_size):
batch_indices = torch.tensor(
indices[i: min(i + batch_size, num_examples)])
yield features[batch_indices], labels[batch_indices]
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
batch_size = 10
for X, y in data_iter(batch_size, features, labels):
print(X, '\n', y)
break
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
[[-0.52196515 -1.2411339 ]
[ 0.426672 -0.9367338 ]
[ 0.18563181 -0.60898656]
[ 2.5301557 1.1043129 ]
[ 0.5228127 -0.40494388]
[-0.31774428 -0.493715 ]
[-1.3854753 0.6079953 ]
[ 1.8072062 -0.20559482]
[-0.3856648 0.2071189 ]
[ 0.61135113 2.1899505 ]]
[[ 7.3833084 ]
[ 8.237417 ]
[ 6.6334023 ]
[ 5.4871235 ]
[ 6.627047 ]
[ 5.2446094 ]
[-0.64384085]
[ 8.514305 ]
[ 2.7236497 ]
[-2.0350137 ]]
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
batch_size = 10
for X, y in data_iter(batch_size, features, labels):
print(X, '\n', y)
break
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
tensor([[-0.0284, 0.3367],
[ 0.1080, -0.7709],
[ 1.4706, -0.5471],
[-0.8948, -0.5443],
[-0.8450, -0.3996],
[-0.7061, -0.5463],
[-0.3852, -1.6035],
[-1.9838, 2.3938],
[-1.0044, -0.5224],
[ 0.3273, 2.4572]])
tensor([[ 3.0137],
[ 7.0441],
[ 9.0095],
[ 4.2585],
[ 3.8747],
[ 4.6504],
[ 8.8659],
[-7.9124],
[ 3.9680],
[-3.5111]])
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
w = ops.normal((2, 1), 0, 0.01)
b = ops.zeros(1)
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def linreg(X, w, b): #@save
"""线性回归模型"""
return d2l.matmul(X, w) + b
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def linreg(X, w, b): #@save
"""线性回归模型"""
return torch.matmul(X, w) + b
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def sgd(params, grads, lr, batch_size):
w, b = params
dw, db = grads
return w - lr * dw / batch_size, b - lr * db / batch_size
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
def sgd(params, lr, batch_size): #@save
"""小批量随机梯度下降"""
with torch.no_grad():
for param in params:
param -= lr * param.grad / batch_size
param.grad.zero_()
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss
def total_loss(w, b, X, y):
return loss(net(X, w, b), y).sum()
grad_fn = grad(total_loss, grad_position=(0, 1))
for epoch in range(num_epochs):
for X, y in data_iter(batch_size, features, labels):
grads = grad_fn(w, b, X, y) # 基于小批量数据，求解梯度；需要带入损失函数
w, b = sgd([w, b], grads, lr, batch_size) # 更新参数
train_l = loss(net(features, w, b), labels)
print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
epoch 1, loss 0.047889
epoch 2, loss 0.000213
epoch 3, loss 0.000051
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss
for epoch in range(num_epochs):
for X, y in data_iter(batch_size, features, labels):
l = loss(net(X, w, b), y) # X和y的小批量损失
# 因为l形状是(batch_size,1)，而不是一个标量。l中的所有元素被加到一起，
# 并以此计算关于[w,b]的梯度
l.sum().backward()
sgd([w, b], lr, batch_size) # 使用参数的梯度更新参数
with torch.no_grad():
train_l = loss(net(features, w, b), labels)
print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
epoch 1, loss 0.030402
epoch 2, loss 0.000102
epoch 3, loss 0.000048
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估计误差: {true_b - b}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
w的估计误差: [ 0.00070035 -0.0001452 ]
b的估计误差: [0.00030327]
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估计误差: {true_b - b}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
w的估计误差: tensor([ 0.0005, -0.0005], grad_fn=)
b的估计误差: tensor([0.0005], grad_fn=)
.. raw:: html
.. raw:: html
.. raw:: html
`讨论 `__
.. raw:: html
.. raw:: html
`讨论 `__
.. raw:: html
.. raw:: html