条件随机场的代码理解（pytorch）
CRF
本文用来记录学习过程，自己也是一个初学者，如果有什么问题还请指出.
概率图模型
概率图模型可以分为有向图和无向图，其中无向图是联合概率的生成图模型，常见的比如马尔科夫网络。其中给定一组输入随机变量X的条件下，假设输出随机变量Y是马尔科夫随机场，这就是条件随机场（CRF）。这里所说的是线性条件随机场用于序列标注问题，给定输入序列预测输出序列的判别式模型。马尔科夫网络可以被分为若干个最大团的乘积。 P ( Y ) = 1 Z ( x ) ∏ c = 1 n ψ c ( c ) P(Y)=\frac{1}{Z(x)}\prod_{c=1}^n\psi_c(c) P(Y)=Z(x)1∏c=1nψc(c)
CRF公式可以表示为： P ( y ∣ x ) = 1 z ( x ) e x p ( ∑ i ∑ k λ k t k ( y i − 1 , y i , x , i ) + ∑ i ∑ l μ l s l ( y i , x , i ) ) P(y|x)=\frac{1}{z(x)}exp(\sum_{i}\sum_k\lambda_kt_k(y_{i-1},y_i,x,i)+\sum_{i}\sum_l\mu_ls_l(y_i,x,i)) P(y∣x)=z(x)1exp(i∑k∑λktk(yi−1,yi,x,i)+i∑l∑μlsl(yi,x,i))
最大化P(Y)得到所需结果
根据所学最大化似然估计可以求出参数，即所求目标转变为最小化 l o g Z ( x ) − ∑ i , k λ k t k ( y i − 1 , y i , x , i ) + ∑ i , l μ l s l ( y i , x , i ) ) logZ(x)-\sum_{i,k}\lambda_kt_k(y_{i-1},y_i,x,i)+\sum_{i,l}\mu_ls_l(y_i,x,i)) logZ(x)−i,k∑λktk(yi−1,yi,x,i)+i,l∑μlsl(yi,x,i))
代码推理
所用的代码来自官方pytorch源码，自己做一些梳理和解释。
- 训练数据集合为，句子和对应的词性标签
training_data = [(
"the wall street journal reported today that apple corporation made money".split(),
"B I I I O O O B I O O".split()
), (
"georgia tech is a university in georgia".split(),
"B I O O O O B".split()
)]
- 标记句子中的每一个单词，同时也将标签编号
word_to_ix = {}
for sentence, tags in training_data:
for word in sentence:
if word not in word_to_ix:
word_to_ix[word] = len(word_to_ix)#为每一个单词进行编码
tag_to_ix = {"B": 0, "I": 1, "O": 2, START_TAG: 3, STOP_TAG: 4}
- 将句子中的单词按照上面的字典转化为序列
def prepare_sequence(seq, to_ix):
idxs = [to_ix[w] for w in seq]#将句子转化为序列号
return torch.tensor(idxs, dtype=torch.long)
- 将标签也转化为序列
targets = torch.tensor([tag_to_ix[t] for t in tags], dtype=torch.long)
- 按照上述公式计算最大似然估计，这里的forward_score gold_score分别对应上述公式的俩个部分
loss = model.neg_log_likelihood(sentence_in, targets)
def neg_log_likelihood(self, sentence, tags):
feats = self._get_lstm_features(sentence)
forward_score = self._forward_alg(feats)
gold_score = self._score_sentence(feats, tags)
return forward_score - gold_score
通过lstm获取句子的特征feats，这里使用的是单层双向LSTM模型提取句子的特征，同时要将其转化为标签的维度，通过一个线性层实现
self.lstm = nn.LSTM(embedding_dim, hidden_dim // 2,
num_layers=1, bidirectional=True)
self.hidden2tag = nn.Linear(hidden_dim, self.tagset_size)
先说分子部分也就是后面一部分_score_sentence函数，首先将标签转化为序列，同时将开头标签加入其中，然后根据给定的公式分别求和状态值和转移值，最后将转移到结尾的值加上，注意start和end没有状态值
def _score_sentence(self, feats, tags):
# Gives the score of a provided tag sequence
score = torch.zeros(1)
tags = torch.cat([torch.tensor([self.tag_to_ix[START_TAG]], dtype=torch.long), tags])
for i, feat in enumerate(feats):
score = score + \
self.transitions[tags[i + 1], tags[i]] + feat[tags[i + 1]]
score = score + self.transitions[self.tag_to_ix[STOP_TAG], tags[-1]]
return score
第二部分： Z ( x ) = ∑ s l o g ( e x p ( ∑ i λ k t k ( y i − 1 , y i , x , i ) + ∑ i μ l s l ( y i , x , i ) ) ) Z(x)=\sum_slog(exp(\sum_{i}\lambda_kt_k(y_{i-1},y_i,x,i)+\sum_{i}\mu_ls_l(y_i,x,i))) Z(x)=∑slog(exp(∑iλktk(yi−1,yi,x,i)+∑iμlsl(yi,x,i)))
将所有的序列求和，然后求log_sum_exp,因为要避免上溢出，所以等价于求
def log_sum_exp(vec):
max_score = vec[0, argmax(vec)]
max_score_broadcast = max_score.view(1, -1).expand(1, vec.size()[1])
return max_score + \
torch.log(torch.sum(torch.exp(vec - max_score_broadcast)))
遍历所有的序列，遍历每一个标签，然后累加转移状态，特征状态，进行logsumexp求和。初始化将start标签特征矩阵置为0其余为-10000
def _forward_alg(self, feats):
# Do the forward algorithm to compute the partition function
init_alphas = torch.full((1, self.tagset_size), -10000.)
# 第一个标签必然是start标签，得分必然是1
init_alphas[0][self.tag_to_ix[START_TAG]] = 0.
# Wrap in a variable so that we will get automatic backprop
forward_var = init_alphas
# Iterate through the sentence
for feat in feats:
alphas_t = [] # The forward tensors at this timestep
for next_tag in range(self.tagset_size):
# broadcast the emission score: it is the same regardless of
# the previous tag
emit_score = feat[next_tag].view(
1, -1).expand(1, self.tagset_size)
# the ith entry of trans_score is the score of transitioning to
# next_tag from i
trans_score = self.transitions[next_tag].view(1, -1)
# The ith entry of next_tag_var is the value for the
# edge (i -> next_tag) before we do log-sum-exp
next_tag_var = forward_var + trans_score + emit_score
# The forward variable for this tag is log-sum-exp of all the
# scores.
alphas_t.append(log_sum_exp(next_tag_var).view(1))
forward_var = torch.cat(alphas_t).view(1, -1)
terminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]
alpha = log_sum_exp(terminal_var)
return alpha
- 接下来对其进行迭代，计算损失，得到最佳参数
for epoch in range(
300): # again, normally you would NOT do 300 epochs, it is toy data
for sentence, tags in training_data:
# Step 1. Remember that Pytorch accumulates gradients.
# We need to clear them out before each instance
model.zero_grad()
# Step 2. Get our inputs ready for the network, that is,
# turn them into Tensors of word indices.
sentence_in = prepare_sequence(sentence, word_to_ix)
targets = torch.tensor([tag_to_ix[t] for t in tags], dtype=torch.long)
# Step 3. Run our forward pass.
loss = model.neg_log_likelihood(sentence_in, targets)
# Step 4. Compute the loss, gradients, and update the parameters by
# calling optimizer.step()
loss.backward()
optimizer.step()
- 计算viterbi解码
遍历每一个序列
遍历每一个标签
计算累加和（这里不包括特征状态值），选择最大得分对应的序号（标签中的序号）保存在bptrs_t,同时将得分保存在viterbivars_t中。
将得分都加上特征得分，保存在forward_var中
将bptrs_t列表添加到backpointers用来回溯
添加stop标签转移值，计算出最终得分的最大一个序号，然后根据保存的path_score计算出序号，输出序号
- 所有的代码
# Author: Robert Guthrie
import torch
import torch.autograd as autograd
import torch.nn as nn
import torch.optim as optim
torch.manual_seed(1)
def argmax(vec):
# return the argmax as a python int
_, idx = torch.max(vec, 1)
return idx.item()
def prepare_sequence(seq, to_ix):
idxs = [to_ix[w] for w in seq]#将句子转化为序列号
return torch.tensor(idxs, dtype=torch.long)
# Compute log sum exp in a numerically stable way for the forward algorithm
def log_sum_exp(vec):
max_score = vec[0, argmax(vec)]
max_score_broadcast = max_score.view(1, -1).expand(1, vec.size()[1])
return max_score + \
torch.log(torch.sum(torch.exp(vec - max_score_broadcast)))
class BiLSTM_CRF(nn.Module):
def __init__(self, vocab_size, tag_to_ix, embedding_dim, hidden_dim):#单词数量 标签字典
super(BiLSTM_CRF, self).__init__()
self.embedding_dim = embedding_dim
self.hidden_dim = hidden_dim
self.vocab_size = vocab_size
self.tag_to_ix = tag_to_ix
self.tagset_size = len(tag_to_ix)#标签数量
self.word_embeds = nn.Embedding(vocab_size, embedding_dim)
self.lstm = nn.LSTM(embedding_dim, hidden_dim // 2,
num_layers=1, bidirectional=True)
# Maps the output of the LSTM into tag space.
self.hidden2tag = nn.Linear(hidden_dim, self.tagset_size)
# Matrix of transition parameters. Entry i,j is the score of
# transitioning *to* i *from* j.
self.transitions = nn.Parameter(
torch.randn(self.tagset_size, self.tagset_size))#转移矩阵
# These two statements enforce the constraint that we never transfer
# to the start tag and we never transfer from the stop tag
self.transitions.data[tag_to_ix[START_TAG], :] = -10000
self.transitions.data[:, tag_to_ix[STOP_TAG]] = -10000
self.hidden = self.init_hidden()
def init_hidden(self):
return (torch.randn(2, 1, self.hidden_dim // 2),
torch.randn(2, 1, self.hidden_dim // 2))
def _forward_alg(self, feats):
# Do the forward algorithm to compute the partition function
init_alphas = torch.full((1, self.tagset_size), -10000.)
# 第一个标签必然是start标签，得分必然是1
init_alphas[0][self.tag_to_ix[START_TAG]] = 0.
# Wrap in a variable so that we will get automatic backprop
forward_var = init_alphas
# Iterate through the sentence
for feat in feats:
alphas_t = [] # The forward tensors at this timestep
for next_tag in range(self.tagset_size):
# broadcast the emission score: it is the same regardless of
# the previous tag
emit_score = feat[next_tag].view(
1, -1).expand(1, self.tagset_size)
# the ith entry of trans_score is the score of transitioning to
# next_tag from i
trans_score = self.transitions[next_tag].view(1, -1)
# The ith entry of next_tag_var is the value for the
# edge (i -> next_tag) before we do log-sum-exp
next_tag_var = forward_var + trans_score + emit_score
# The forward variable for this tag is log-sum-exp of all the
# scores.
alphas_t.append(log_sum_exp(next_tag_var).view(1))
forward_var = torch.cat(alphas_t).view(1, -1)
terminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]
alpha = log_sum_exp(terminal_var)
return alpha
def _get_lstm_features(self, sentence):
self.hidden = self.init_hidden()
embeds = self.word_embeds(sentence).view(len(sentence), 1, -1)
lstm_out, self.hidden = self.lstm(embeds, self.hidden)
lstm_out = lstm_out.view(len(sentence), self.hidden_dim)
lstm_feats = self.hidden2tag(lstm_out)
return lstm_feats
def _score_sentence(self, feats, tags):
# Gives the score of a provided tag sequence
score = torch.zeros(1)
tags = torch.cat([torch.tensor([self.tag_to_ix[START_TAG]], dtype=torch.long), tags])
for i, feat in enumerate(feats):
score = score + \
self.transitions[tags[i + 1], tags[i]] + feat[tags[i + 1]]
score = score + self.transitions[self.tag_to_ix[STOP_TAG], tags[-1]]
return score
def _viterbi_decode(self, feats):
backpointers = []
# Initialize the viterbi variables in log space
init_vvars = torch.full((1, self.tagset_size), -10000.)
init_vvars[0][self.tag_to_ix[START_TAG]] = 0
# forward_var at step i holds the viterbi variables for step i-1
forward_var = init_vvars
for feat in feats:#遍历一个句子中的单词数量
bptrs_t = [] # holds the backpointers for this step
viterbivars_t = [] # holds the viterbi variables for this step
for next_tag in range(self.tagset_size):
next_tag_var = forward_var + self.transitions[next_tag]
best_tag_id = argmax(next_tag_var)#转移到该标签下的最大值
bptrs_t.append(best_tag_id)
viterbivars_t.append(next_tag_var[0][best_tag_id].view(1))
# Now add in the emission scores, and assign forward_var to the set
# of viterbi variables we just computed
forward_var = (torch.cat(viterbivars_t) + feat).view(1, -1)
backpointers.append(bptrs_t)
# Transition to STOP_TAG
terminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]
best_tag_id = argmax(terminal_var)#取最大的一个值，是第几个位置，确定了它是哪一个标签
path_score = terminal_var[0][best_tag_id]#最大的值
# Follow the back pointers to decode the best path.
best_path = [best_tag_id]
for bptrs_t in reversed(backpointers):
best_tag_id = bptrs_t[best_tag_id]
best_path.append(best_tag_id)
# Pop off the start tag (we dont want to return that to the caller)
start = best_path.pop()
assert start == self.tag_to_ix[START_TAG] # Sanity check
best_path.reverse()
return path_score, best_path
def neg_log_likelihood(self, sentence, tags):
feats = self._get_lstm_features(sentence)
forward_score = self._forward_alg(feats)
gold_score = self._score_sentence(feats, tags)
return forward_score - gold_score
def forward(self, sentence): # dont confuse this with _forward_alg above.
# Get the emission scores from the BiLSTM
lstm_feats = self._get_lstm_features(sentence)#将文字进行lstm编码然后转化成tag_size输出
# Find the best path, given the features.
score, tag_seq = self._viterbi_decode(lstm_feats)
return score, tag_seq
START_TAG = ""
STOP_TAG = ""
EMBEDDING_DIM = 5
HIDDEN_DIM = 4
# Make up some training data
training_data = [(
"the wall street journal reported today that apple corporation made money".split(),
"B I I I O O O B I O O".split()
), (
"georgia tech is a university in georgia".split(),
"B I O O O O B".split()
)]
word_to_ix = {}
for sentence, tags in training_data:
for word in sentence:
if word not in word_to_ix:
word_to_ix[word] = len(word_to_ix)#为每一个单词进行编码
tag_to_ix = {"B": 0, "I": 1, "O": 2, START_TAG: 3, STOP_TAG: 4}
model = BiLSTM_CRF(len(word_to_ix), tag_to_ix, EMBEDDING_DIM, HIDDEN_DIM)
optimizer = optim.SGD(model.parameters(), lr=0.01, weight_decay=1e-4)
# Check predictions before training
with torch.no_grad():
precheck_sent = prepare_sequence(training_data[0][0], word_to_ix)
precheck_tags = torch.tensor([tag_to_ix[t] for t in training_data[0][1]], dtype=torch.long)
print(model(precheck_sent))
# Make sure prepare_sequence from earlier in the LSTM section is loaded
for epoch in range(
300): # again, normally you would NOT do 300 epochs, it is toy data
for sentence, tags in training_data:
# Step 1. Remember that Pytorch accumulates gradients.
# We need to clear them out before each instance
model.zero_grad()
# Step 2. Get our inputs ready for the network, that is,
# turn them into Tensors of word indices.
sentence_in = prepare_sequence(sentence, word_to_ix)
targets = torch.tensor([tag_to_ix[t] for t in tags], dtype=torch.long)
# Step 3. Run our forward pass.
loss = model.neg_log_likelihood(sentence_in, targets)
# Step 4. Compute the loss, gradients, and update the parameters by
# calling optimizer.step()
loss.backward()
optimizer.step()
# Check predictions after training
with torch.no_grad():
precheck_sent = prepare_sequence(training_data[0][0], word_to_ix)
print(model(precheck_sent))
# We got it!