1. HMM
1.1 模型原理
HMM
中,有5个基本元素:{N,M,A,B,π},结合序列标志任务(NER)对其的概念定义为:
- N:状态的有限集合。在这里,是指每一个词语背后的标注。
- M:观察值的有限集合。在这里,是指每一个词语本身。
- A:状态转移概率矩阵。在这里,是指某一个标注转移到下一个标注的概率。
- B:观测概率矩阵,也就是发射概率矩阵。在这里,是指在某个标注下,生成某个词的概率。
- π:初始概率矩阵。在这里,是指每一个标注的初始化概率。
而以上的这些元素,都是可以从训练语料集中统计出来的。最后根据这些统计值,应用维特比(viterbi)
算法,算出词语序列背后的标注序列了,命名实体识别本质上就是序列标注,只需要定义好对应的标签以及模式串,就可以从标注序列中提取出实体
假设对于t时刻的一个词公式就可写作:
齐次马尔科夫性假设:隐藏的马尔科夫链在任意时刻t的状态只依赖于其前一时刻的状态,与其他时刻的状态及观测无关,也与时刻t无关
观测独立性假设:假设任意时刻的观测只依赖于该时刻的马尔科夫链的状态,与其他观测即状态无关.观测概率的公式可以表达如下:
将发射概率和转移概率相结合,得到整个句子最后的公式:
1.2 模型实现
class Model(object):
def __init__(self, hidden_status):
# param hidden_status: int, 隐状态数
self.hmm_N = hidden_status
# 状态转移概率矩阵 A[i][j]表示从i状态转移到j状态的概率
self.hmm_A = torch.zeros(self.hmm_N, self.hmm_N)
# 初始状态概率 Pi[i]表示初始时刻为状态i的概率
self.hmm_pi = torch.zeros(self.hmm_N)
def _build_corpus_map(self, sentences_list):
char2id = {}
for sentence in sentences_list:
for word in sentence:
if word not in char2id:
char2id[word] = len(char2id)
return char2id
def _init_emission(self):
self.hmm_M = len(self.word2id)
# 观测概率矩阵, B[i][j]表示i状态下生成j观测的概率
self.hmm_B = torch.zeros(self.hmm_N, self.hmm_M)
def train(self, sentences_list, tags_list):
"""
参数:
sentences_list: list,其中每个元素由字组成的列表,如 ['担','任','科','员']
tags_list: list,其中每个元素是由对应的标注组成的列表,如 ['O','O','B-TITLE', 'E-TITLE']
"""
start_time = time.time()
assert len(sentences_list) == len(tags_list), "the lens of tag_lists is not eq to word_lists"
logger.info('开始构建token字典...')
self.word2id = self._build_corpus_map(sentences_list)
self.tag2id = self._build_corpus_map(tags_list)
self.id2tag = dict((id_, tag) for tag, id_ in self.tag2id.items())
logger.info('训练语料总数:{}'.format(len(sentences_list)))
logger.info('词典总数:{}'.format(len(self.word2id)))
logger.info('标签总数:{}'.format(len(self.tag2id)))
assert self.hmm_N == len(self.tag2id), "hidden_status is {}, but total tag is {}".\
format(self.hmm_N, len(self.tag2id))
self._init_emission()
logger.info('构建词典完成{:>.4f}s'.format(time.time()-start_time))
logger.info('开始构建转移概率矩阵...')
# 估计转移概率矩阵
for tags in tqdm(tags_list):
seq_len = len(tags)
for i in range(seq_len - 1):
current_tagid = self.tag2id[tags[i]]
next_tagid = self.tag2id[tags[i+1]]
self.hmm_A[current_tagid][next_tagid] += 1.
# 问题:如果某元素没有出现过,该位置为0,这在后续的计算中是不允许的
# 解决方法:我们将等于0的概率加上很小的数
self.hmm_A[self.hmm_A == 0.] = 1e-10
self.hmm_A = self.hmm_A / self.hmm_A.sum(axis=1, keepdims=True)
logger.info('完成转移概率矩阵构建. {:>.4f}s'.format(time.time() - start_time))
logger.info('开始构建观测概率矩阵...')
# 估计观测概率矩阵
for tags, sentence in tqdm(zip(tags_list, sentences_list)):
assert len(tags) == len(sentence), \
"the lens of tag_list is not eq to word_list"
for tag, word in zip(tags, sentence):
tag_id = self.tag2id[tag]
word_id = self.word2id[word]
self.hmm_B[tag_id][word_id] += 1.
self.hmm_B[self.hmm_B == 0.] = 1e-10
self.hmm_B = self.hmm_B / self.hmm_B.sum(axis=1, keepdims=True)
logger.info('完成观测概率矩阵构建. {:>.4f}s'.format(time.time() - start_time))
logger.info('初始化初识状态概率...')
# 估计初始状态概率
for tags in tqdm(tags_list):
init_tagid = self.tag2id[tags[0]]
self.hmm_pi[init_tagid] += 1.
self.hmm_pi[self.hmm_pi == 0.] = 1e-10
self.hmm_pi = self.hmm_pi / self.hmm_pi.sum()
logger.info('完成初始状态概率构建. {:>.4f}s'.format(time.time() - start_time))
def predict(self, sentences_list):
pred_tag_lists = []
for sentence in tqdm(sentences_list):
pred_tag_list = self.decoding(sentence)
pred_tag_lists.append(pred_tag_list)
return pred_tag_lists
def decoding(self, word_list):
"""
使用维特比算法对给定观测序列求状态序列, 这里就是对字组成的序列,求其对应的标注。
维特比算法实际是用动态规划解隐马尔可夫模型预测问题,即用动态规划求概率最大路径(最优路径)
这时一条路径对应着一个状态序列
"""
A = torch.log(self.hmm_A)
B = torch.log(self.hmm_B)
Pi = torch.log(self.hmm_pi)
# 初始化 维比特矩阵viterbi 它的维度为[状态数, 序列长度]
seq_len = len(word_list)
viterbi = torch.zeros(self.hmm_N, seq_len)
# 等解码的时候,我们用backpointer进行回溯,以求出最优路径
backpointer = torch.zeros(self.hmm_N, seq_len).long()
start_wordid = self.word2id.get(word_list[0], None)
Bt = B.t()
if start_wordid is None:
# 如果字不再字典里,则假设状态的概率分布是均匀的
bt = torch.log(torch.ones(self.hmm_N) / self.hmm_N)
else:
bt = Bt[start_wordid]
viterbi[:, 0] = Pi + bt
backpointer[:, 0] = -1
for step in range(1, seq_len):
wordid = self.word2id.get(word_list[step], None)
# 处理字不在字典中的情况
# bt是在t时刻字为wordid时,状态的概率分布
if wordid is None:
# 如果字不再字典里,则假设状态的概率分布是均匀的
bt = torch.log(torch.ones(self.hmm_N) / self.hmm_N)
else:
bt = Bt[wordid] # 否则从观测概率矩阵中取bt
for tag_id in range(len(self.tag2id)):
max_prob, max_id = torch.max(
viterbi[:, step - 1] + A[:, tag_id],
dim=0
)
viterbi[tag_id, step] = max_prob + bt[tag_id]
backpointer[tag_id, step] = max_id
# 终止, t=seq_len 即 viterbi[:, seq_len]中的最大概率,就是最优路径的概率
best_path_prob, best_path_pointer = torch.max(
viterbi[:, seq_len - 1], dim=0
)
# 回溯,求最优路径
best_path_pointer = best_path_pointer.item()
best_path = [best_path_pointer]
for back_step in range(seq_len - 1, 0, -1):
best_path_pointer = backpointer[best_path_pointer, back_step]
best_path_pointer = best_path_pointer.item()
best_path.append(best_path_pointer)
# 将tag_id组成的序列转化为tag
assert len(best_path) == len(word_list)
tag_list = [self.id2tag[id_] for id_ in reversed(best_path)]
return tag_list
2. CRF
2.1 模型原理
相对于HMM,CRF有两个优势
- CRF不仅可以利用相邻词之间的关联,还可以设置更大的邻域
- CRF可以方便融合多特征
令是观测序列,是状态序列,是CRF
模型的参数,则的条件概率是:
其中是CRF
特征函数集,加上正则化项,在做对数变换就得到
CRF
训练的目的是求解令最大化的
2.2 模型实现(使用TorchCRF第三方库)
$ pip install TorchCRF
import torch
from TorchCRF import CRF
device = "cuda"
batch_size = 2
sequence_size = 3
num_labels = 5
mask = torch.ByteTensor([[1, 1, 1], [1, 1, 0]]).to(device) # (batch_size. sequence_size)
labels = torch.LongTensor([[0, 2, 3], [1, 4, 1]]).to(device) # (batch_size, sequence_size)
hidden = torch.randn((batch_size, sequence_size, num_labels), requires_grad=True).to(device)
crf = CRF(num_labels)
Computing log-likelihood (used where forward)
crf.forward(hidden, labels, mask)
>>> tensor([-7.6204, -3.6124], device='cuda:0', grad_fn=<ThSubBackward>)
crf.viterbi_decode(hidden, mask)
>>> [[0, 2, 2], [4, 0]]
3. BiLSTM+CRF
3.1 模型原理
应用于NER中的BiLSTM-CRF模型主要由Embedding层(主要有词向量,字向量以及一些额外特征),双向LSTM层,以及最后的CRF层构成。实验结果表明biLSTM-CRF已经达到或者超过了基于丰富特征的CRF模型,成为目前基于深度学习的NER方法中的最主流模型。在特征方面,该模型继承了深度学习方法的优势,无需特征工程,使用词向量以及字符向量就可以达到很好的效果,如果有高质量的词典特征,能够进一步获得提高
3.2 模型实现
class Model(nn.Module):
def __init__(self, config):
super(Model, self).__init__()
self.tagset_size = config.num_label + 2
self.hidden_dim = config.hidden_size
self.start_tag_id = config.num_label
self.end_tag_id = config.num_label + 1
self.device = config.device
self.embedding = nn.Embedding(config.vocab_size, config.emb_size, padding_idx=config.vocab_size - 1)
torch.nn.init.uniform_(self.embedding.weight, -0.10, 0.10)
self.encoder = nn.LSTM(config.emb_size, config.hidden_size, batch_first=True, bidirectional=True)
self.decoder = nn.LSTM(config.hidden_size * 2, config.hidden_size, batch_first=True, bidirectional=True)
self.linear = nn.Linear(2*config.hidden_size, self.tagset_size)
self.transitions = nn.Parameter(torch.randn(self.tagset_size, self.tagset_size))
self.transitions.data[self.start_tag_id, :] = -10000.
self.transitions.data[:, self.end_tag_id] = -10000.
self.hidden = self.init_hidden()
def init_hidden(self):
return (torch.randn(2, 1, self.hidden_dim).to(self.device),
torch.randn(2, 1, self.hidden_dim).to(self.device))
def _get_lstm_features(self, input_ids):
embeds = self.embedding(input_ids).view(1, input_ids.shape[1], -1)
self.encoder.flatten_parameters()
self.decoder.flatten_parameters()
encoder_out, _ = self.encoder(embeds, self.hidden)
decoder_out, _ = self.decoder(encoder_out, self.hidden)
decoder_out = decoder_out.view(input_ids.shape[1], -1)
lstm_logits = self.linear(decoder_out)
return lstm_logits
def log_sum_exp(self, smat):
# 每一列的最大数
vmax = smat.max(dim=0, keepdim=True).values
return torch.log(torch.sum(torch.exp(smat - vmax), axis=0, keepdim=True)) + vmax
def _forward_alg(self, feats):
alphas = torch.full((1, self.tagset_size), -10000.).to(self.device)
# 初始化分值分布. START_TAG是log(1)=0, 其他都是很小的值 "-10000"
alphas[0][self.start_tag_id] = 0.
# Iterate through the sentence
for feat in feats:
# log_sum_exp()内三者相加会广播: 当前各状态的分值分布(列向量) + 发射分值(行向量) + 转移矩阵(方形矩阵)
# 相加所得矩阵的物理意义见log_sum_exp()函数的注释; 然后按列求log_sum_exp得到行向量
alphas = self.log_sum_exp(alphas.T + self.transitions + feat.unsqueeze(0))
# 最后转到EOS,发射分值为0,转移分值为列向量 self.transitions[:, self.end_tag_id]
score = self.log_sum_exp(alphas.T + 0 + self.transitions[:, self.end_tag_id].view(-1, 1))
return score.flatten()
def _score_sentence(self, feats, tags):
# Gives the score of a provided tag sequence
score = torch.zeros(1).to(self.device)
tags = torch.cat([torch.tensor([self.start_tag_id], dtype=torch.long).to(self.device), tags])
for i, feat in enumerate(feats):
# emit = X0,start + x1,label + ... + xn-2,label + (xn-1, end[0])
# trans = 每一个状态的转移状态
score += self.transitions[tags[i], tags[i+1]] + feat[tags[i + 1]]
# 加上到END_TAG的转移
score += self.transitions[tags[-1], self.end_tag_id]
return score
def _viterbi_decode(self, feats):
backtrace = [] # 回溯路径; backtrace[i][j] := 第i帧到达j状态的所有路径中, 得分最高的那条在i-1帧是神马状态
alpha = torch.full((1, self.tagset_size), -10000.).to(self.device)
alpha[0][self.start_tag_id] = 0
for frame in feats:
smat = alpha.T + frame.unsqueeze(0) + self.transitions
backtrace.append(smat.argmax(0)) # 当前帧每个状态的最优"来源"
alpha = smat.max(dim=0, keepdim=True).values
# Transition to STOP_TAG
smat = alpha.T + 0 + self.transitions[:, self.end_tag_id].view(-1, 1)
best_tag_id = smat.flatten().argmax().item()
best_score = smat.max(dim=0, keepdim=True).values.item()
best_path = [best_tag_id]
for bptrs_t in reversed(backtrace[1:]): # 从[1:]开始,去掉开头的 START_TAG
best_tag_id = bptrs_t[best_tag_id].item()
best_path.append(best_tag_id)
best_path.reverse()
return best_score, best_path # 返回最优路径分值 和 最优路径
def forward(self, sentence_ids, tags_ids):
tags_ids = tags_ids.view(-1)
feats = self._get_lstm_features(sentence_ids)
forward_score = self._forward_alg(feats)
gold_score = self._score_sentence(feats, tags_ids)
outputs = (forward_score - gold_score, )
_, tag_seq = self._viterbi_decode(feats)
outputs = (tag_seq, ) + outputs
return outputs
def predict(self, sentence_ids):
lstm_feats = self._get_lstm_features(sentence_ids)
_, tag_seq = self._viterbi_decode(lstm_feats)
return tag_seq
4. IDCNN+CRF
4.1 模型原理
正常CNN
的filter,都是作用在输入矩阵一片连续的区域上,不断sliding做卷积。dilated CNN
为这个filter增加了一个dilation width
,作用在输入矩阵的时候,会skip所有dilation width
中间的输入数据;而filter本身的大小保持不变,这样filter获取到了更广阔的输入矩阵上的数据,看上去就像是膨胀了一般。具体使用时,dilated width
会随着层数的增加而指数增加。这样随着层数的增加,参数数量是线性增加的,而receptive field
却是指数增加的,可以很快覆盖到全部的输入数据。
图中可见感受域是以指数速率扩大的。原始感受域是位于中心点的1x1区域:
- 经由原始感受域按步长为1向外扩散,得到8个1x1的区域构成新的感受域,大小为3x3
- 经过步长为2的扩散,上一步3x3的感受域扩展为为7x7
- 经步长为4的扩散,原7x7的感受域扩大为15x15的感受域。每一层的参数数量是相互独立的。感受域呈指数扩大,但参数数量呈线性增加
对应在文本上,输入是一个一维的向量,每个元素是一个character embedding
:
IDCNN
对输入句子的每一个字生成一个logits
,这里就和BiLSTM
模型输出logits
完全一样,加入CRF
层,用Viterbi
算法解码出标注结果,在BiLSTM
或者IDCNN
这样的网络模型末端接上CRF
层是序列标注的一个很常见的方法。BiLSTM
或者IDCNN
计算出的是每个词的各标签概率,而CRF
层引入序列的转移概率,最终计算出loss反馈回网络
4.2 模型实现
class Model(nn.Module):
def __init__(self, config):
super(Model, self).__init__()
self.tagset_size = config.num_label + 2
self.hidden_dim = config.hidden_size
self.start_tag_id = config.num_label
self.end_tag_id = config.num_label + 1
self.device = config.device
self.embedding = nn.Embedding(config.vocab_size, config.emb_size, padding_idx=config.vocab_size - 1)
torch.nn.init.uniform_(self.embedding.weight, -0.10, 0.10)
self.encoder = nn.LSTM(config.emb_size, config.hidden_size, batch_first=True, bidirectional=True)
self.decoder = nn.LSTM(config.hidden_size * 2, config.hidden_size, batch_first=True, bidirectional=True)
self.linear = nn.Linear(2*config.hidden_size, self.tagset_size)
self.transitions = nn.Parameter(torch.randn(self.tagset_size, self.tagset_size))
self.transitions.data[self.start_tag_id, :] = -10000.
self.transitions.data[:, self.end_tag_id] = -10000.
self.hidden = self.init_hidden()
def init_hidden(self):
return (torch.randn(2, 1, self.hidden_dim).to(self.device),
torch.randn(2, 1, self.hidden_dim).to(self.device))
def _get_lstm_features(self, input_ids):
embeds = self.embedding(input_ids).view(1, input_ids.shape[1], -1)
self.encoder.flatten_parameters()
self.decoder.flatten_parameters()
encoder_out, _ = self.encoder(embeds, self.hidden)
decoder_out, _ = self.decoder(encoder_out, self.hidden)
decoder_out = decoder_out.view(input_ids.shape[1], -1)
lstm_logits = self.linear(decoder_out)
return lstm_logits
def log_sum_exp(self, smat):
# 每一列的最大数
vmax = smat.max(dim=0, keepdim=True).values
# return (smat - vmax).exp().sum(axis=0, keepdim=True).log() + vmax
return torch.log(torch.sum(torch.exp(smat - vmax), axis=0, keepdim=True)) + vmax
def _forward_alg(self, feats):
# Do the forward algorithm to compute the partition function
alphas = torch.full((1, self.tagset_size), -10000.).to(self.device)
# 初始化分值分布. START_TAG是log(1)=0, 其他都是很小的值 "-10000"
alphas[0][self.start_tag_id] = 0.
# Iterate through the sentence
for feat in feats:
# log_sum_exp()内三者相加会广播: 当前各状态的分值分布(列向量) + 发射分值(行向量) + 转移矩阵(方形矩阵)
# 相加所得矩阵的物理意义见log_sum_exp()函数的注释; 然后按列求log_sum_exp得到行向量
alphas = self.log_sum_exp(alphas.T + self.transitions + feat.unsqueeze(0))
# 最后转到EOS,发射分值为0,转移分值为列向量 self.transitions[:, self.end_tag_id]
score = self.log_sum_exp(alphas.T + 0 + self.transitions[:, self.end_tag_id].view(-1, 1))
return score.flatten()
def _score_sentence(self, feats, tags):
# Gives the score of a provided tag sequence
score = torch.zeros(1).to(self.device)
tags = torch.cat([torch.tensor([self.start_tag_id], dtype=torch.long).to(self.device), tags])
for i, feat in enumerate(feats):
# emit = X0,start + x1,label + ... + xn-2,label + (xn-1, end[0])
# trans = 每一个状态的转移状态
score += self.transitions[tags[i], tags[i+1]] + feat[tags[i + 1]]
# 加上到END_TAG的转移
score += self.transitions[tags[-1], self.end_tag_id]
return score
def _viterbi_decode(self, feats):
backtrace = [] # 回溯路径; backtrace[i][j] := 第i帧到达j状态的所有路径中, 得分最高的那条在i-1帧是神马状态
alpha = torch.full((1, self.tagset_size), -10000.).to(self.device)
alpha[0][self.start_tag_id] = 0
for frame in feats:
smat = alpha.T + frame.unsqueeze(0) + self.transitions
backtrace.append(smat.argmax(0)) # 当前帧每个状态的最优"来源"
alpha = smat.max(dim=0, keepdim=True).values
# Transition to STOP_TAG
smat = alpha.T + 0 + self.transitions[:, self.end_tag_id].view(-1, 1)
best_tag_id = smat.flatten().argmax().item()
best_score = smat.max(dim=0, keepdim=True).values.item()
best_path = [best_tag_id]
for bptrs_t in reversed(backtrace[1:]): # 从[1:]开始,去掉开头的 START_TAG
best_tag_id = bptrs_t[best_tag_id].item()
best_path.append(best_tag_id)
best_path.reverse()
return best_score, best_path # 返回最优路径分值 和 最优路径
def forward(self, sentence_ids, tags_ids):
tags_ids = tags_ids.view(-1)
feats = self._get_lstm_features(sentence_ids)
forward_score = self._forward_alg(feats)
gold_score = self._score_sentence(feats, tags_ids)
outputs = (forward_score - gold_score, )
_, tag_seq = self._viterbi_decode(feats)
outputs = (tag_seq, ) + outputs
return outputs
def predict(self, sentence_ids):
lstm_feats = self._get_lstm_features(sentence_ids)
_, tag_seq = self._viterbi_decode(lstm_feats)
return tag_seq
5. BERT+CRF
5.1 模型原理
BERT模型+全连接层
:BERT的encoding vector通过FC layer
映射到标签集合后,单个token的output vector经过Softmax处理,每一维度的数值就表示该token的词性为某一词性的概率。基于此数据便可计算loss并训练模型。但根据BiLSTM+CRF
模型的启发,在BERT+FC layer
的基础上增加CRF layer
加入一些约束来保证最终的预测结果是有效的。这些约束可以在训练数据时被CRF层自动学习得到,从而减少预测错误的概率
5.2 模型实现
class BertCrfForNer(BertPreTrainedModel):
def __init__(self, config):
super(BertCrfForNer, self).__init__(config)
self.bert = BertModel(config)
self.dropout = nn.Dropout(config.hidden_dropout_prob)
self.classifier = nn.Linear(config.hidden_size, config.num_labels)
self.crf = CRF(num_tags=config.num_labels, batch_first=True)
self.init_weights()
def forward(self, input_ids, token_type_ids=None, attention_mask=None,labels=None):
outputs =self.bert(input_ids = input_ids,attention_mask=attention_mask,token_type_ids=token_type_ids)
sequence_output = outputs[0]
sequence_output = self.dropout(sequence_output)
logits = self.classifier(sequence_output)
outputs = (logits,)
if labels is not None:
loss = self.crf(emissions = logits, tags=labels, mask=attention_mask)
outputs =(-1*loss,)+outputs
return outputs # (loss), scores
6. BERT+BiLSTM+CRF
6.1 模型原理
BiLSTM+CRF优点是泛化能力强;缺点是需要大量的标注样本。在样本很少的情况下,效果会很不理想。为了更快速地实现一个实体提取器,提高系统易用性,可以采用迁移学习的思想,在先验知识的基础上进行模型训练,从而使用BERT+BiLSTM+CRF
同样的,输入是wordPiece tokenizer得到的tokenid
,进入Bert预训练模型抽取丰富的文本特征得到的输出向量,输出向量过BiLSTM
从中提取实体识别所需的特征,得到的向量,最终进入CRF
层进行解码,计算最优的标注序列
6.2 模型实现
class BertBiLstmCrf(nn.Module):
def __init__(self, vocab_size, emb_size, hidden_size, out_size, drop_out=0.1, use_pretrained_w2v=False):
super(BertBiLstmCrf, self).__init__()
self.bert_path = get_chinese_wwm_ext_pytorch_path()
self.bert_config = BeitConfig.from_pretrained(self.bert_path)
self.bert = BertModel.from_pretrained(self.bert_path)
emb_size = 768
for param in self.bert.parameters():
param.requires_grad = True
self.bilstm = nn.LSTM(emb_size, hidden_size, batch_first=True, bidirectional=True)
self.fc = nn.Linear(hidden_size*2, out_size)
self.dropout = nn.Dropout(drop_out)
self.transition = nn.Parameter(torch.ones(out_size, out_size) * 1 / out_size)
self.device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
def forward(self, x, lengths):
emb = self.bert(x)[0]
emb = nn.utils.rnn.pack_padded_sequence(emb, lengths, batch_first=True)
emb, _ = self.bilstm(emb)
output, _ = nn.utils.rnn.pad_packed_sequence(emb, batch_first=True, padding_value=0., total_length=x.shape[1])
output = self.dropout(output)
emission = self.fc(output)
batch_size, max_len, out_size = emission.size()
crf_scores = emission.unsqueeze(2).expand(-1, -1, out_size, -1) + self.transition.unsqueeze(0)
return crf_scores
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