算法:贪心算法,穷举法,分治法,动态规划
visdom可视化工具
np.meshgrid()用于三维图
训练失败可能是学习率太大
线性模型
import numpy as np
import matplotlib.pyplot as plt
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
def forward(x):
return x * w
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) * (y_pred - y)
w_list = []
mse_list = []
for w in np.arange(0.0, 4.1, 0.1):
print('w=', w)
l_sum = 0
for x_val, y_val in zip(x_data, y_data):
y_pred_val = forward(x_val)
loss_val = loss(x_val, y_val)
l_sum += loss_val
print('\t', x_val, y_val, y_pred_val, loss_val)
print('MSE=', l_sum / 3)
w_list.append(w)
mse_list.append(l_sum / 3)
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()
梯度下降
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = 1.0
def forward(x):
return x * w
def cost(xs, ys):
cost = 0
for x, y in zip(xs, ys):
y_pred = forward(x)
cost += (y_pred - y) ** 2
return cost / len(xs)
def gradient(xs, ys):
grad = 0
for x, y in zip(xs, ys):
grad += 2 * x * (x * w - y) # 求导的导数公式
return grad / len(xs)
print('predict (before training)', 4, forward(4))
for epoch in range(100):
cost_val = cost(x_data, y_data)
grad_val = gradient(x_data, y_data)
w -= 0.01 * grad_val
print('epoch:', epoch, 'w=', w, 'loss=', cost_val)
print('predict (after training)', 4, forward(4))
随机梯度下降:取一个损失更新(以前是平均全部损失)(一加入了噪声,二大样本计算量大)
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = 1.0
def forward(x):
return x * w
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) ** 2
def gradient(x, y):
return 2 * x * (x * w - y)
print('predict (before training)', 4, forward(4))
for epoch in range(100):
for x, y in zip(x_data, y_data):
grad = gradient(x, y)
w -= 0.01 * grad # 及时更新,没办法并行运算,,batch
print('\tgrad:', x, y, grad)
l = loss(x, y)
print("progress:", epoch, "w=", w, "loss", l)
print('predict (after training)', 4, forward(4))
反向传播
import torch
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = torch.Tensor([1.0])
w.requires_grad = True # 需要计算梯度
def forward(x):
return x * w # tensor
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) ** 2
print('predict (before training)', 4, forward(4).item())
for epoch in range(100):
for x, y in zip(x_data, y_data):
l = loss(x, y) # 前向,计算loss
l.backward() # 做完后计算图会释放
print('\tgrad:', x, y, w.grad.item()) # item取值,要是张量计算图一直累积
w.data -= 0.01 * w.grad.data # 不取data会是TENSOR有计算图
w.grad.data.zero_() # 计算出来的梯度不清零会累加
print("progress:", epoch, l.item())
print('predict (after training)', 4, forward(4).item())
pytorch 实现线性回归
import torch
x_data = torch.Tensor([[1.0], [2.0], [3.0]])
y_data = torch.Tensor([[2.0], [4.0], [6.0]]) # 这是几位的?3x1还是1x3
class LinearModel(torch.nn.Module): # 可记住这个模板
def __init__(self): # 构造函数
super(LinearModel, self).__init__()
self.linear = torch.nn.Linear(1, 1) # 构造对象,权重和偏执,,1是特征,输入输出维度
def forward(self, x): # model类自动反向传播
y_pred = self.linear(x)
return y_pred
model = LinearModel() # 实例化,可调用
criterion = torch.nn.MSELoss(size_average=False)
optimizer = torch.optim.SGD(model.parameters(), lr=0.01) # 优化器不会构建计算图,能找到参数
# Adagrad,Adam,Adamax,ASGD,LBFGS,RMSprop,Rprop
for epoch in range(100):
y_pred = model(x_data)
loss = criterion(y_pred, y_data)
print(epoch, loss) # 自动调用__str__,loss不会产生计算图
optimizer.zero_grad() # 清零
loss.backward() # 反向传播
optimizer.step() # 权重更新
print('w=', model.linear.weight.item())
print('b=', model.linear.bias.item())
x_test = torch.Tensor([[4.0]])
y_test = model(x_test)
print('y_pred=', y_test.data)
Logistic回归σ输出0-1
import torch
import torch.nn.functional as F
# import torchvision
# train_set = torchvision.datasets.MNIST(root='../dataset/mnist', train=True, download=True)
# test_set = torchvision.datasets.MNIST(root='../dataset/mnist', train=False, download=True)
x_data = torch.Tensor([[1.0], [2.0], [3.0]])
y_data = torch.Tensor([[0], [0], [1]]) # 变化
class LogisticRegressionModel(torch.nn.Module):
def __init__(self):
super(LogisticRegressionModel, self).__init__()
self.linear = torch.nn.Linear(1, 1)
def forward(self, x):
y_pred = F.sigmoid(self.linear(x)) # 变化
return y_pred
model = LogisticRegressionModel()
criterion = torch.nn.BCELoss(size_average=False) # 变化
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)
for epoch in range(100):
y_pred = model(x_data)
loss = criterion(y_pred, y_data)
print(epoch, loss)
optimizer.zero_grad()
loss.backward()
optimizer.step()
多特征输入
xy = np.loadtxt('diabetes.csv.gz', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1]) # 所有行,不要最后一列
y_data = torch.from_numpy(xy[:, [-1]]) # 所有行,只要最后一列,且为矩阵
# x_data = torch.Tensor([[1.0], [2.0], [3.0]])
# y_data = torch.Tensor([[0], [0], [1]])
class Model(torch.nn.Module):
def __init__(self):
super(Model, self).__init__()
self.linear1 = torch.nn.Linear(8, 6)
self.linear2 = torch.nn.Linear(6, 4)
self.linear3 = torch.nn.Linear(4, 1)
self.activate = torch.nn.Sigmoid() # 与上一个不同,这个是nn下的,一个模块,没有参数只需要一个
# self.activate = torch.nn.ReLU() # 用这个激活时,forward最后一个最好用sigmoid平滑一下
def forward(self, x):
x = self.activate(self.linear1(x))
x = self.activate(self.linear2(x))
x = self.activate(self.linear3(x))
return x
加载数据集
import torch
import numpy as np
from torch.utils.data import Dataset, DataLoader
class DiabeteDataset(Dataset):
def __init__(self, filepath):
xy = np.loadtxt(filepath, delimiter=',', dtype=np.float32)
self.len = xy.shape[0] # xy是n行9列,shape得到n
self.x_data = torch.from_numpy(xy[:, :-1])
self.y_data = torch.from_numpy(xy[:, [-1]])
def __getitem__(self, index): # 方便获得索引
return self.x_data[index], self.y_data[index]
def __len__(self):
return self.len # 方便返回长度?
dataset = DiabeteDataset('diabates.CGV.gz')
train_loader = DataLoader(dataset=dataset,
batch_size=32,
shuffle=True,
num_workers=2)
class Model(torch.nn.Module):
def __init__(self):
super(Model, self).__init__()
self.linear1 = torch.nn.Linear(8, 6)
self.linear2 = torch.nn.Linear(6, 4)
self.linear3 = torch.nn.Linear(4, 1)
self.sigmoid = torch.nn.Sigmoid() # 与上一个不同,这个是nn下的,一个模块,没有参数只需要一个
# self.activate = torch.nn.ReLU()
def forward(self, x):
x = self.sigmoid(self.linear1(x))
x = self.sigmoid(self.linear2(x))
x = self.sigmoid(self.linear3(x))
return x
model = Model()
criterion = torch.nn.BCELoss(size_average=False)
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)
if __name__=='__main__': # 封装
for epoch in range(100):
for i, data in enumerate(train_loader, 0): # 获得第几次迭代,0是从0开始枚举,数据自动转为tensor
inputs, labels = data
# for i, (inputs, labels) in enumerate()
y_pred = model(inputs)
loss = criterion(y_pred, labels)
print(epoch, loss.item())
optimizer.zero_grad()
loss.backward()
optimizer.step()
多分类问题
torch.nn.CrossEntropyLoss=LogSoftmax+NLLLoss
交叉熵损失:最后一层的非线性变换不做,包含在交叉熵计算中,与标签做的ONE-HOT,得loss,标签的是长整型LongTensor
y = np.array([1, 0, 0])
z = np.array([0.2, 0.1, -0.1])
y_pred = np.exp(z) / np.exp(z).sum()
loss = (- y * np.log(y_pred)).sum()
print(loss)
import torch
from torchvision import transforms, datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim
batch_size = 64
transforms = transforms.Compose([
transforms.ToTensor(), # 单通道变多通道,前面加一维1,convert the PIL Image to Tensor
transforms.Normalize((0.1307, ), (0.3081, )) # 归一化,均值,标准差,,因为01发布数据效果更好
])
train_dataset = datasets.MNIST(root='../dataset/mnist/',
train=True,
download=True,
transform=transforms)
train_loader = DataLoader(train_dataset,
shuffle=True,
batch_size=batch_size)
test_dataset = datasets.MNIST(root='../dataset/mnist/',
train=True,
download=True,
transform=transforms)
test_loader = DataLoader(test_dataset,
shuffle=False,
batch_size=batch_size)
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.l1 = torch.nn.Linear(784, 512)
self.l2 = torch.nn.Linear(512, 256)
self.l3 = torch.nn.Linear(256, 128)
self.l4 = torch.nn.Linear(128, 64)
self.l5 = torch.nn.Linear(64, 10)
def forward(self, x):
x = x.view(-1, 784) # 这个图片数变成一行
x = F.relu(self.l1(x))
x = F.relu(self.l2(x))
x = F.relu(self.l3(x))
x = F.relu(self.l4(x))
return self.l5(x)
model = Net()
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
def train(epoch):
running_loss = 0.0
for batch_idx, (inputs, target) in enumerate(train_loader, 0):
optimizer.zero_grad()
outputs = model(inputs)
loss = criterion(outputs, target)
loss.backward()
optimizer.step()
running_loss += loss.item()
if batch_idx % 300 == 299:
print('[%d, %5d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
def test():
correct = 0
total = 0
with torch.no_grad(): # test中不需要计算梯度
for data in test_loader:
images, labels = data
outputs = model(images)
_, predicted = torch.max(outputs.data, dim=1) # 沿着行的维度,返回最大值和最大值下标
total += labels.size(0)
correct += (predicted == labels).sum().item()
print('Accuracy on test set: %d %%' % (100 * correct / total))
if __name__=='__main__':
for epoch in range(10):
train(epoch)
test()
卷积神经网络
import torch
in_channels, out_channels = 5, 10
width, height = 100, 100
kernel_size = 3
batch_size = 1
in_put = torch.randn(batch_size,
in_channels,
width,
height)
# input = [3, 4, 5, 6, 7,
# 2, 4, 6, 8, 2,
# 3, 5, 6, 6, 2,
# 3, 5, 6, 6, 4,
# 4, 8, 6, 4, 1]
# input = torch.Tensor(input).view(1, 1, 5, 5) # B C W H
conv_layer = torch.nn.Conv2d(in_channels,
out_channels,
kernel_size=kernel_size) # padding=1, bias=False
# maxpooling_layer = torch.nn.MaxPool2d(kernel_size=2) # 默认卷积核为2x2取最大
# kernel = torch.Tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]).view(1, 1, 3, 3) # 卷积核,改变形状(输出o输入I W H)
# conv_layer.weight.data = kernel.data
output = conv_layer(in_put)
print(in_put.shape)
print(output.shape)
print(conv_layer.weight.shape)
gpu:先模型
device = torch.device(“cuda:0” if torch.cuda.is_available() else “cpu”)
model.to(device)
训练时的输入输出
inputs, target = inputs.to(device), target.to(device)
测试时
inputs, target = inputs.to(device), target.to(device)
高级卷积神经网络
gugolenet(多种形式的卷积核)
1x1的卷积核 改变通道数,实际运算量会变小。
每一层训练好后加锁才训练下一层,解决梯度消失(难)。跳连接(倒数+1来防止梯度消失
class InceptionA(nn.Module):
def __init__(self, in_channels):
super(InceptionA, self).__init__()
self.branch1x1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch5x5_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch5x5_2 = nn.Conv2d(16, 24, kernel_size=5, padding=2)
self.branch3x3_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch3x3_2 = nn.Conv2d(16, 24, kernel_size=3, padding=1)
self.branch3x3_3 = nn.Conv2d(24, 24, kernel_size=3, padding=1)
self.branch_pool = nn.Conv2d(in_channels, 24, kernel_size=1)
def forward(self, x):
branch1x1 = self.branch1x1(x)
branch5x5 = self.branch5x5_1(x)
branch5x5 = self.branch5x5_2(branch5x5)
branch3x3 = self.branch3x3_1(x)
branch3x3 = self.branch3x3_2(branch3x3)
branch3x3 = self.branch3x3_3(branch3x3)
branch_pool = F.avg_pool2d(x, kernel_size=3, stride=1, padding=1)
branch_pool = self.branch_pool(branch_pool)
outputs = [branch1x1, branch5x5, branch3x3, branch_pool]
return torch.cat(outputs, dim=1)
identity mappings in deep residual networks论文有很多块设计
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = nn.Conv2d(88, 20, kernel_size=5)
self.incep1 = InceptionA(in_channels=10)
self.incep2 = InceptionaA(in_channels=20)
self.mp = nn.MaxPool2d(2)
self.fc = nn.Linear(1408, 10)
def forwatd(self, x):
in_size = x.size(0)
x = F.relu(self.mp(self.conv1(x)))
x = self.incep1(x)
x = F.relu(self.mp(self.conv2(x)))
x = self.incep2(x)
x = x.view(in_size, -1)
x = self.fc(x)
return x
1.深度学习》理论
2. 阅读pytorch文档,至少通读一遍
3. 复现经典工作,《读代码,自己尝试写》,能跑通只是环境配好了。
4. 扩充视野。
循环神经网络
(dense, deep)全连接
import torch
batch_size = 1
seq_len = 3
input_size = 4
hidden_size = 2
num_layers = 1
cell = torch.nn.RNN(input_size=input_size, hidden_size=hidden_size,
num_layers=num_layers)
inputs = torch.randn(seq_len, batch_size, input_size)
hidden = torch.zeros(num_layers, batch_size, hidden_size)
for idx, input in enumerate(inputs):
print('=' * 20, idx, '=' * 20)
print('Input size', input.shape)
out, hidden = cell(inputs, hidden)
print('outputs size', hidden.shape)
print(hidden)
batch_first方便再接线性层
idx2char = ['e', 'h', 'l', 'o']
x_data = [1, 0, 2, 2, 3]
y_data = [3, 1, 2, 3, 2]
one_hot_lookup = [[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]
x_one_hot = [one_hot_lookup[x] for x in x_data]
inputs = torch.Tensor(x_one_hot).view(-1, batch_size, input_size)
labels = torch.LongTensor(y_data).view(-1, 1)
class Model(torch.nn.Module):
def __init__(self, input_size, hidden_size, batch_size):
super(Model, self).__init__()
self.batch_size = batch_size
self.input_size = input_size
self.hidden_size = hidden_size
self.rnncell = torch.nn.RNNCell(input_size=self.input_size,
hidden_size=self.hidden_size)
def forward(self, input, hidden):
hidden = self.rnncell(input, hidden)
return hidden
def init_hidden(self):
return torch.zeros(self.batch_size, self.hidden_size)
net = Model(input_size, hidden_size, batch_size)
criterion = torch.nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(net.parameters(), lr=0.05)
for epoch in range(15):
loss = 0
optimizer.zero_grad()
hidden = net.init_hidden()
print('predicted string:', end='')
for input, label in zip(inputs, labels):
hidden = net(input, hidden)
loss += criterion(hidden, label)
_, idx = hidden.max(dim=1) # 找到最大下标
print(idx2char[idx.item()], end='')
loss.backward()
optimizer.step()
print(', epoch [%d/5] loss=%.4f' % (epoch+1, loss.item()))
class NameDataset(Dataset):
def __init__(self, is_train_set=True):
filename = 'data/names_train.csv.gz' if is_train_set else 'data/names_test.csv.gz'
with gzip.open(filename, 'rt') as f: # 相应的包读取相应的数据
reader = csv.reader(f)
rows = list(reader)
self.names = [row[0] for row in rows] # 每一行的第0个元素
self.len = len(self.names)
self.countries = [row[1] for row in rows]
self.country_list = list(sorted(set(self.countries))) #set把列表变成集合,去除重复元素,SORTED排序,再变列表
self.country_dict = self.getCountryDict() # 列表转词典
self.country_num = len(self.country_list)
def __getitem__(self, index):
return self.names[index], self.country_dict[self.countries[index]]
def __len__(self):
return len
def getCountryDict(self):
country_dict = dict()
for idx, country_name in enumerate(self.country_list, 0):
country_dict[country_name] = idx
return country_dict
def idx2country(self, index): # return country name giving index
return self.country_list[index]
def getCountriesNum(self): # return the number of countries
return self.country_num
trainset = NameDataset(is_train_set=True)
trainloader = DataLoader(trainset, batch_size=BATCH_SIZE, shuffle=True)
testset = NameDataset(is_train_set=False)
testloader = DataLoader(testset, batch_size=BATCH_SIZE, shuffle=False)
N_COUNTRY = trainset.getCountryNum()
HIDDEN_SIZE = 100
BATCH_SIZE = 256
N_LAYER = 2
N_EPOCHS = 100
N_CHARS = 128
USE_GPU = False
class RNNClassifier(torch.nn.Module):
def __init__(self, input_size, hidden_size, output_size, n_layers=1, bidirectional=True):
super(RNNClassifier, self).__init__()
self.hidden_size = hidden_size
self.n_layers = n_layers
self.n_directions = 2 if bidirectional else 1
self.embedding = torch.nn.Embedding(input_size, hidden_size)
self.gru = torch.nn.GRU(hidden_size, hidden_size, n_layers, bidirectional=bidirectional)
self.fc = torch.nn.Linear(hidden_size * self.n_directions, output_size)
def __init_hidden(self, batch_size):
hidden = torch.zeros(self.n_layers * self.n_directions,
batch_size, self.hidden_size)
return create_tensor(hidden)
def forward(self, input, seq_lengths):
input = input.t()
batch_size = input.size(1)
hidden = self.__init_hidden(batch_size)
embedding = self.embedding(input)
gru_input = pack_padded_sequence(embedding, seq_lengths)
output, hidden = self.gru(gru_input, hidden)
if self.n_directions == 2:
hidden_cat = torch.cat([hidden[-1], hidden[-2]], dim=1)
else:
hidden_cat = hidden[-1]
fc_output = self.fc(hidden_cat)
return fc_output
def make_tensors(names, countries):
sequences_and_lengths = [name2list(name) for name in names] # 把每一个名字变成一个列表,name2list返回元组(列表本身,列表长度)
name_sequences = [s1[0] for s1 in sequences_and_lengths]
seq_lengths = torch.LongTensor([s1[1] for s1 in sequences_and_lengths])
countries = countries.long()
seq_tensor = torch.zeros(len(name_sequences), seq_lengths.max()).long()
for idx, (seq, seq_len) in enumerate(zip(name_sequences, seq_lengths), 0):
seq_tensor[idx, :seq_len] = torch.nn.LongTensor(seq) # 建立一个全0,将数据贴上去覆盖0
seq_lengths, perm_idx = seq_lengths.sort(dim=0, descending=True) # 按序列长度排序
seq_tensor = seq_tensor[perm_idx]
countries = countries[perm_idx]
return create_temsor(seq_tensor),\
create_tensor(seq_lengths),\
creare_tensor(countries)
def trainModel():
total_loss = 0
for i, (names, countries) in enumerate(trainloader, 1):
inputs, seq_lengths, target = make_tensors(names, countries)
output = classifier(inputs, seq_lengths)
loss = criterion(output, target)
optimizer.zero_grad()
loss.backward()
optimizer.step()
total_loss += loss.item()
if i % 10 == 0:
print(f'[{time_since(start)}] epoch {epoch}', end='')
print(f'[{i * len(inputs)}/{len(trainset)}]', end='')
print(f'loss={total_loss / (i * len(inputs))}')
return total_loss
def testModel():
correct = 0
total = len(testset)
print("evaluating trained model ...")
with torch.no_grad():
for i, (names, countries) in enumerate(testloader, 1):
inputs, seq_lengths, target = make_tensors(names, countries)
output = classifier(inputs, seq_lengths)
pred = output.max(dim=1, keepdim=True)[1]
correct += pred.eq(target.view_as(pred)).sum().item()
precent = '%.2f' % (100 * correct / total)
print(f'test set: accuracy {correct} / {total} {precent}%')
return correct / total