命名实体识别（NER）：LSTM + CRF

 

LSTM+CRF：框架

 

 

 

对观测序列X，状态序列y，其误差函数

 

利用Softmax函数，我们为每一个正确的tag序列定义一个概率值（Y_x代表所有的tag序列，包括不可能出现的）

 

 

因而在训练中，我们只需要最大化似然概率即可，这里我们利用对数似然

 

 

最难理解的就是上面公式的log部分的计算，这里用一种简便的方法，对于到词w_(i+1)的路径，可以先把到词 w_i 的log-sum-exp计算出来，有点类似递推的意思。

 

此外，算法里面涉及一个采用维特比解码解码过程，这是一个DP算法。

 

 

code:

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]
    return torch.tensor(idxs, dtype=torch.long)

#TODO 以一种数值稳定性算法求log_sum_exp: 先标准化，取出行中最大值进行broadcast，让每个元素减去最大值后求exp然后再求和
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):
        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) # tag_size : 3 + 2
        self.word_embeds = nn.Embedding(vocab_size, embedding_dim)
        self.lstm = nn.LSTM(embedding_dim, hidden_dim // 2,
                            num_layers=1, bidirectional=True)

        #TODO 把LSTM 输出映射到状态空间（tag space）
        self.hidden2tag = nn.Linear(hidden_dim, self.tagset_size)

        #TODO 状态转移矩阵参数:T(i,j)表示从状态 j 转移到状态 i 的概率，这样第i行就是所有状态转移到状态i的概率
        self.transitions = nn.Parameter(torch.randn(self.tagset_size,self.tagset_size))

        #TODO 根据上面矩阵元素定义：限制不能从其他状态转移到起始状态，不能从结束状态转移到其他任何状态
        self.transitions.data[tag_to_ix[START_TAG], :] = -10000
        self.transitions.data[:, tag_to_ix[STOP_TAG]] = -10000
        self.hidden = self.init_hidden()

    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)

        # Find the best path, given the features.
        score, tag_seq = self._viterbi_decode(lstm_feats)
        return score, tag_seq

    def init_hidden(self):
        return (torch.randn(2, 1, self.hidden_dim // 2),
                torch.randn(2, 1, self.hidden_dim // 2))
    '''
        _forward_alg求出的是损失函数的log-sum-exp这一项，另一项比较简单
        因为计算误差score需要计算每一条可能路径的分数。这里用一种简便的方法，对于到词w_(i+1)的路径，
        可以先把到词w_i的log-sum-exp计算出来，然后累加，类似递推的思想
    '''

    def _forward_alg(self, feats):
        init_alphas = torch.full((1, self.tagset_size), -10000.)
        #TODO 起始状态score定义为0
        init_alphas[0][self.tag_to_ix[START_TAG]] = 0.
        forward_var = init_alphas

        #TODO 依次遍历句子中的所有词
        # feats : (seq_len,tag_size) LSTM映射到tag space的结果
        for feat in feats:
            alphas_t = []  # 当前时间步的forward tensor
            for next_tag in range(self.tagset_size): # TODO 遍历当前时间步(word)的所有可能状态
                #TODO 广播当前状态值为tag_size大小，用于和转移到当前时间步的那些状态操作，即 transiton[next_tag]
                emit_score = feat[next_tag].view(1, -1).expand(1, self.tagset_size)

                #TODO 其他状态转移到next_tag（当前状态）的概率
                trans_score = self.transitions[next_tag].view(1, -1)

                # TODO next_tag_var[i] 是 计算log-sum-exp 之前 状态 i -> 到状态 next_tag 值
                next_tag_var = forward_var + trans_score + emit_score

                alphas_t.append(log_sum_exp(next_tag_var).view(1)) # view(1) 把scalar变为[scalar]
            #TODO 此时 forward_var:size (1，tag_size) 作为下一个词word_(i+1)的初始值
            forward_var = torch.cat(alphas_t).view(1, -1)
        # TODO 最优加上所有状态转移到结束状态的值
        terminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]
        # TODO 求出最终log-sum-exp值
        alpha = log_sum_exp(terminal_var)
        return alpha

    def _get_lstm_features(self, sentence):
        self.hidden = self.init_hidden()
        # self.word_embeds(sentence).shape : (seq_len,voca_size)
        embeds = self.word_embeds(sentence).view(len(sentence), 1, -1)# seq_len x batch_size x voca_size
        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
    '''
        这里求出损失函数另一项
    '''
    def _score_sentence(self, feats, tags):
        # Gives the score of a provided tag sequence
        score = torch.zeros(1)
        #TODO 加上起始状态
        tags = torch.cat([torch.tensor([self.tag_to_ix[START_TAG]], dtype=torch.long), tags])
        # TODO 根据损失函数定义 transitions[tags[i + 1], tags[i]] 表示从 状态i到状态(i+1)的概率
        # TODO feat[tag[i]] 表示 word[i] 到 tag[i] 的发射概率，这里用 tag[i+1] 因为前面填充了起始状态，
        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 = []

        # Initialieze the viterbi variables in log spac
        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:
            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[i] holds the viterbi variable for tag i at the
                # previous step, plus the score of transitioning
                # from tag i to next_tag.
                # We don't include the emission scores here because the max
                # does not depend on them (we add them in below)
                next_tag_var = forward_var + self.transitions[next_tag]
                best_tag_id = argmax(next_tag_var)
                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)
        # TODO 到达STOP_TAG最大的分数
        path_score = terminal_var[0][best_tag_id]

        # 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) # size : (seq_len,tag_size)
        forward_score = self._forward_alg(feats)
        gold_score = self._score_sentence(feats, tags)
        return forward_score - gold_score


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)

tag_to_ix = {"B": 0, "I": 1, "O": 2, START_TAG: 3, STOP_TAG: 4}
ix_to_tag = {}
for k,v in tag_to_ix.items():
    ix_to_tag[v] = k
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.
        # TODO 这里区别于一般的训练模型，一般模型是从forward的输出用于计算误差
        # TODO 而这里因为加上了CRF模型，在neg_log_likelihood定义了CRF误差用于梯度更新
        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()



def get_entity(char_seq,tag_seq):
    length = len(char_seq)
    entity = []
    for i,(char,tag) in enumerate(zip(char_seq,tag_seq)):
        if tag == 'B':
            if 'ent' in locals().keys():
                entity.append(ent)
                del ent
            ent = char
            if i+1 == length:
                entity.append(ent)
        if tag =='I':
            ent = ent + " " + char
            if i+1 == length:
                entity.append(ent)
        if tag not in ['B','I']:
            if 'ent' in locals().keys():
                entity.append(ent)
                del ent
            continue
    return entity

# Check predictions after training
with torch.no_grad():
    precheck_sent = prepare_sequence(training_data[0][0], word_to_ix)
    # print(model(precheck_sent)) # 返回路径最大分数和维特比算法得出的路线
    path_score,state_path = model(precheck_sent)
    y_pred = [ix_to_tag[x] for x in state_path]
    entity_list = get_entity(training_data[0][0],y_pred)
    for x in entity_list:
        print(x)
# We got it!

相关链接：

LSTM+CRF论文：https://arxiv.org/abs/1603.01360

HMM、CRF、BiLSTM、BiLSTM + CRF:https://zhuanlan.zhihu.com/p/61227299

LSTM+CRF误差计算方法：https://createmomo.github.io/2017/11/11/CRF-Layer-on-the-Top-of-BiLSTM-5/

一个博主关于误差计算方法的理解：https://blog.csdn.net/cuihuijun1hao/article/details/79405740

对于LSTM层的作用解释以及对CRF的通俗理解：https://blog.csdn.net/Tianweidadada/article/details/102677383