pytorch学习3 -- 自动求导系统autograd

对pytorch的自动求导系统中常用两个方法：torch.autograd.back和torch.autograd.grad进行介绍

torch.autograd.backward(tensors,grad_tensors=None,retain_graph=None,create_graph=False)

• tensors：用于求导的张量，如loss
• retain_graph：保存计算图
• create_graph：创建导数计算图，用于高阶求导
• grad_tensors：多梯度权重（多个loss的比例）

flag = True
#flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)a = torch.add(w, x)b = torch.add(w, 1)y = torch.mul(a, b)y.backward(retain_graph=True)#retain_graph=True保存计算图，从而可进行第二次计算print(w.grad)y.backward()

这里张量y.backward使用的就是torch里的backgrad.

flag = True
#flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)a = torch.add(w, x)     # retain_grad()b = torch.add(w, 1)y0 = torch.mul(a, b)    # y0 = (x+w) * (w+1)y1 = torch.add(a, b)    # y1 = (x+w) + (w+1)    dy1/dw = 2loss = torch.cat([y0, y1], dim=0)       # [y0, y1]grad_tensors = torch.tensor([1., 2.])#grad_tensor用于多个梯度之间权重的设置loss.backward(gradient=grad_tensors)    # gradient 传入 torch.autograd.backward()中的grad_tensorsprint(w.grad)

tensor([9.])

torch.autograd.grad(outputs,inputs,grad_outputs=None,retain_graph=None,create_graph=False)

• 功能：求取梯度
• outputs：用于求导的张量，如loss
• inputs：需要求梯度的张量
• create_graph：创建导数计算图，用于高阶求导
• retain_graph：保存计算图
• grad_outputs：多梯度权重

flag = True
#flag = False
if flag:x = torch.tensor([3.], requires_grad=True)y = torch.pow(x, 2)     # y = x**2grad_1 = torch.autograd.grad(y, x, create_graph=True)   # grad_1 = dy/dx = 2x = 2 * 3 = 6print(grad_1)grad_2 = torch.autograd.grad(grad_1[0], x)              # grad_2 = d(dy/dx)/dx = d(2x)/dx = 2print(grad_2)

(tensor([6.], grad_fn=),)
(tensor([2.]),)

autograd小贴士：

• 1.梯度不自动清零
• 2.依赖于叶子结点的结点，requires_grad默认为True
• 3.叶子结点不可执行in-place

flag = True
#flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)for i in range(4):a = torch.add(w, x)b = torch.add(w, 1)y = torch.mul(a, b)y.backward()print(w.grad)w.grad.zero_()#梯度清零，_下划线表示原位操作

tensor([5.])
tensor([5.])
tensor([5.])
tensor([5.])

flag = True
#flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)for i in range(4):a = torch.add(w, x)b = torch.add(w, 1)y = torch.mul(a, b)y.backward()print(w.grad)#w.grad.zero_()#梯度清零，_下划线表示原位操作

tensor([5.])
tensor([10.])
tensor([15.])
tensor([20.])

flag = True
#flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)a = torch.add(w, x)b = torch.add(w, 1)y = torch.mul(a, b)print(a.requires_grad, b.requires_grad, y.requires_grad)

True True True

flag = True
#flag = False
if flag:a = torch.ones((1, ))print(id(a), a)a = a + torch.ones((1, ))#会开辟一个新的内存地址，在新的地址中赋用aprint(id(a), a)a += torch.ones((1, ))#前后a的地址不变print(id(a), a)
flag = True
# flag = False
if flag:w = torch.tensor([1.], requires_grad=True)x = torch.tensor([2.], requires_grad=True)a = torch.add(w, x)b = torch.add(w, 1)y = torch.mul(a, b)w.add_(1)y.backward()2506753264160 tensor([1.])
2506753184248 tensor([2.])
2506753184248 tensor([3.])
Traceback (most recent call last):File "", line 23, in w.add_(1)RuntimeError: a leaf Variable that requires grad has been used in an in-place operation.

逻辑回归

逻辑回归模型是线性的二分类模型

模型表达式：

  f(x) 称为sigmoid函数，也称为logistic函数。

y< 0.5,  class 为0

线性回归是分析自变量x与因变量y（标量）之间关系的方法

对数几率回归

机器学习模型训练的五个步骤

获取数据、处理清洗数据

模型

损失函数模型选择

优化器

反复迭代训练

import torch
import torch.nn as nn
import matplotlib.pyplot as plt
import numpy as np
torch.manual_seed(10)#%%
# ============================ step 1/5 生成数据 ============================
sample_nums = 100
mean_value = 1.7
bias = 1
n_data = torch.ones(sample_nums, 2)
x0 = torch.normal(mean_value * n_data, 1) + bias      # 类别0 数据 shape=(100, 2)
y0 = torch.zeros(sample_nums)                         # 类别0 标签 shape=(100, 1)
x1 = torch.normal(-mean_value * n_data, 1) + bias     # 类别1 数据 shape=(100, 2)
y1 = torch.ones(sample_nums)                          # 类别1 标签 shape=(100, 1)
train_x = torch.cat((x0, x1), 0)
train_y = torch.cat((y0, y1), 0)# ============================ step 2/5 选择模型 ============================
class LR(nn.Module):def __init__(self):super(LR, self).__init__()self.features = nn.Linear(2, 1)self.sigmoid = nn.Sigmoid()def forward(self, x):x = self.features(x)x = self.sigmoid(x)return xlr_net = LR()   # 实例化逻辑回归模型# ============================ step 3/5 选择损失函数 ============================
loss_fn = nn.BCELoss()# ============================ step 4/5 选择优化器   ============================
lr = 0.01  # 学习率
optimizer = torch.optim.SGD(lr_net.parameters(), lr=lr, momentum=0.9)# ============================ step 5/5 模型训练 ============================
for iteration in range(1000):# 前向传播y_pred = lr_net(train_x)# 计算 lossloss = loss_fn(y_pred.squeeze(), train_y)# 反向传播loss.backward()# 更新参数optimizer.step()# 绘图if iteration % 20 == 0:mask = y_pred.ge(0.5).float().squeeze()  # 以0.5为阈值进行分类correct = (mask == train_y).sum()  # 计算正确预测的样本个数acc = correct.item() / train_y.size(0)  # 计算分类准确率plt.scatter(x0.data.numpy()[:, 0], x0.data.numpy()[:, 1], c='r', label='class 0')plt.scatter(x1.data.numpy()[:, 0], x1.data.numpy()[:, 1], c='b', label='class 1')w0, w1 = lr_net.features.weight[0]w0, w1 = float(w0.item()), float(w1.item())plot_b = float(lr_net.features.bias[0].item())plot_x = np.arange(-6, 6, 0.1)plot_y = (-w0 * plot_x - plot_b) / w1plt.xlim(-5, 7)plt.ylim(-7, 7)plt.plot(plot_x, plot_y)plt.text(-5, 5, 'Loss=%.4f' % loss.data.numpy(), fontdict={'size': 20, 'color': 'red'})plt.title("Iteration: {}\nw0:{:.2f} w1:{:.2f} b: {:.2f} accuracy:{:.2%}".format(iteration, w0, w1, plot_b, acc))plt.legend()plt.show()plt.pause(0.5)if acc > 0.99:break

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