1. 技术文章
  2. CRF总结

CRF总结

由 雨燕双飞 提交于 2020-02-02 05:15:45

文章目录

  • CRF 是无向图模型code
    • 它是一个判别式模型
    • 建模了每个状态和整个观测序列的依赖

https://www.unclewang.info/learn/machine-learning/756/
https://blog.csdn.net/u012421852/article/details/80287567

计算下Z（矩阵）

import numpy as np

y0=1#start
y4=1#stop

从start到stop的所有路径的规范化因子Z，其实就是上面所有路径的非规范化概率之和

class CCRF(object):
    """
    条件随机场的矩阵表示实现
    """
    def __init__(self,M):
        self.M=M#条件随机场的矩阵形式的存储体
        self.Z=None#规范化因子
        self.MP=[]#矩阵乘积
        
        self.work()
        return
        
    def work(self):
        print('work......')
        self.MP=np.full(shape=(np.shape(self.M[0])),fill_value=1.0)
#         print(self.MP)
        for i in range(np.shape(self.M)[0]):#四个矩阵就循环四次
            print('\nML=\n',self.MP)
            print('M%d=\n'%i,self.M[i])
            self.MP=np.dot(self.MP,self.M[i])#矩阵乘法
            print('dot=\n',self.MP)
        
    def ZValue(self):
        return self.MP[0,0]

def CCRF_manual():
    M1 = np.array([[0.5, 0.5],[0,   0]])#a01 a02-A
    M2 = np.array([[0.3, 0.7],[0.7, 0.3]])#b11,b12,b21,b22-B
    M3 = np.array([[0.5, 0.5],[0.6, 0.4]])
    M4 = np.array([[1, 0],[1, 0]])
        
    M=[]
    M.append(M1)
    M.append(M2)
    M.append(M3)
    M.append(M4)
    M=np.array(M)
    print('CRF 矩阵：\n',M)
    crf=CCRF(M)
    ret=crf.ZValue()
    print('从start到stop的规范因子Z:',ret)
    
if __name__=='__main__':
    CCRF_manual()


CRF 矩阵：
 [[[0.5 0.5]
  [0.  0. ]]

 [[0.3 0.7]
  [0.7 0.3]]

 [[0.5 0.5]
  [0.6 0.4]]

 [[1.  0. ]
  [1.  0. ]]]
work......

ML=
 [[1. 1.]
 [1. 1.]]
M0=
 [[0.5 0.5]
 [0.  0. ]]
dot=
 [[0.5 0.5]
 [0.5 0.5]]

ML=
 [[0.5 0.5]
 [0.5 0.5]]
M1=
 [[0.3 0.7]
 [0.7 0.3]]
dot=
 [[0.5 0.5]
 [0.5 0.5]]

ML=
 [[0.5 0.5]
 [0.5 0.5]]
M2=
 [[0.5 0.5]
 [0.6 0.4]]
dot=
 [[0.55 0.45]
 [0.55 0.45]]

ML=
 [[0.55 0.45]
 [0.55 0.45]]
M3=
 [[1. 0.]
 [1. 0.]]
dot=
 [[1. 0.]
 [1. 0.]]
从start到stop的规范因子Z: 1.0

1.1 一般参数形式

在这里插入图片描述
在这里插入图片描述

	import torch
	import torch.nn as nn


	sequence_len = 3;
	y_size = 2;
	k=5
	l=4
	#转移
	#每个t有k组，每个y有2种状态，y1->y2,y2->y3,序列长3（k,i=1,2,y_i->y_i+1)
	t=torch.tensor( [[[[0,1],[0,0]],[[0,1],[0,0]]],
	                 [[[1,0],[0,0]],[[0,0],[0,0]]],
	                 [[[0,0],[0,0]],[[0,0],[1,0]]],
	                 [[[0,0],[1,0]],[[0,0],[0,0]]],
	                 [[[0,0],[0,0]],[[0,0],[0,1]]]],dtype=float);
	lamb=torch.tensor([1,0.5,1,1,0.2])
	# 发射
	# 序列长3，每个y和x出现的情况(l,t(y),状态）
	s=torch.tensor( [[[1,0],[0,0],[0,0]],
	                 [[0,1],[0,1],[0,0]],
	                 [[0,0],[1,0],[1,0]],
	                 [[0,0],[0,0],[0,1]]],dtype=float)
	mu = torch.tensor([1, 0.5, 0.8, 0.5])
	#比上面多了个开始y0和结束y4
	def P_y_x_condition(y):# 参数形式
	        sumt=0
	        sums=0
	        for i in range(k):
	            for j in range(len(y)-1):
	                sumt+=lamb[i]*t[i,j,y[j],y[j+1]]
	                # print(i,j,lamb[i]*t[i,j,y[j],y[j+1]])
	        for i in range(l):
	            for j in range(len(y)):
	                sums+=mu[i]*s[i,j,y[j]]
	        print(sums+sumt)
	        return torch.exp(sums+sumt)
	    
	y=[0,1,1]
	print("p(y|x)=p(y1=1,y2=2,y3=3|x)=",P_y_x_condition(y))

tensor(3.2000, dtype=torch.float64)
p(y|x)=p(y1=1,y2=2,y3=3|x)= tensor(24.5325, dtype=torch.float64)

1.2 简化形式

在这里插入图片描述

  • 这里也引入了起点，下面代码中引入了起点和终点（只要起点就行）
f=torch.tensor([ [[[0,0],[0,0]],[[0,1],[0,0]],[[0,1],[0,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[1,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[0,0],[0,0]],[[0,0],[1,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[0,0],[1,0]],[[0,0],[0,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,1]],[[0,0],[0,0]]],
                 [[[1,0],[1,0]],[[0,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,0]]],
                 [[[0,1],[0,1]],[[0,1],[0,1]],[[0,0],[0,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[1,0],[1,0]],[[1,0],[1,0]],[[0,0],[0,0]]],
                 [[[0,0],[0,0]],[[0,0],[0,0]],[[0,1],[0,1]],[[0,0],[0,0]]]],dtype=float);
w=torch.tensor([1,0.5,1,1,0.2,1, 0.5, 0.8, 0.5])
def P_y_x_condition_with_f( y):
        sum=0
        for i in range(k+l):
            for j in range(len(y)-1):
                sum+=w[i]*f[i,j,y[j],y[j+1]]
        print(sum)
        return torch.exp(sum)
p_y_x_con=P_y_x_condition_with_f([0,0,1,1,0])
print("p(y|x)=p(y1=1,y2=2,y3=3|x)=",p_y_x_con)

tensor(3.2000, dtype=torch.float64)
p(y|x)=p(y1=1,y2=2,y3=3|x)= tensor(24.5325, dtype=torch.float64)

Z

在这里插入图片描述

1.3 矩阵形式

在这里插入图片描述
a01表示从start=y0=1到y1=1的概率，
b21表示从y1=2到y2=1的概率
在这里插入图片描述

w=torch.tensor([1,0.5,1,1,0.2,1, 0.5, 0.8, 0.5])
M=f;
# print(M[0])
for i in range(k+l):
    M[i]=w[i]*f[i]
print(torch.sum(M,axis=0))
M=torch.exp(torch.sum(M,axis=0))
print("M(i,y_i-1,y_i):\n",M)
# 因为y0=0,yn+1=0
# 所以可以令M[0,1,0],M[0,1,1],M[3,0,1],M[3,1,1]=0
# M[0,1,0]=M[0,1,1]=M[3,0,1]=M[3,1,1]=0
# print("M(i,y_i-1,y_i):\n",M)#与上图对应上了


tensor([[[1.0000, 0.5000],
         [1.0000, 0.5000]],

        [[1.3000, 1.5000],
         [1.8000, 0.5000]],

        [[0.8000, 1.5000],
         [1.8000, 0.7000]],

        [[0.0000, 0.0000],
         [0.0000, 0.0000]]], dtype=torch.float64)
M(i,y_i-1,y_i):
 tensor([[[2.7183, 1.6487],
         [2.7183, 1.6487]],

        [[3.6693, 4.4817],
         [6.0496, 1.6487]],

        [[2.2255, 4.4817],
         [6.0496, 2.0138]],

        [[1.0000, 1.0000],
         [1.0000, 1.0000]]], dtype=torch.float64)

1.3.2 Z

Z=(M1(x)M2(x)...Mn+1(x))start,stopZ=(M_1(x)M_2(x)...M_{n+1}(x))_{start,stop}
从start到stop对应于y=(1,1,1),y=(1,1,2), …, y=(2,2,2)个路径的非规范化概率分别是：

  • a01b11c11，a01b11c12，a01b12c21，a01b12c22

      a02b21c11，a01b21c12，a02b22c21，a02b22c22

然后按式11.12求规范化因子，通过计算矩阵乘积M1(x) M2(x) M3(x) M4(x)可知，其第一行第一列的元素为

  • a01b11c11+ a01b11c12 + a01b12c21+ a01b12c22 +a02b21c11 + a01b21c12+ a02b22c21 + a02b22c22

恰好等于从start到stop的所有路径的非规范化概率之和，即规范化因子Z(x)。

def Z_M(M):
    z=M[0]
    for i in range(1,sequence_len+1):
        z=torch.matmul(z,M[i])
    return z[0,0]
print(Z_M(M))


tensor(253.9492, dtype=torch.float64)

def P_y_x_condition_with_M(y):
    p=1;
    for i in range(len(y)-1):
        p*=M[i,y[i],y[i+1]]
    print(p)
    return p/Z_M(M)
p_y_x_con=P_y_x_condition_with_M([0,0,1,1,0])
print("p(y|x)=p(y1=1,y2=2,y3=3|x)=",p_y_x_con)

tensor(24.5325, dtype=torch.float64)
p(y|x)=p(y1=1,y2=2,y3=3|x)= tensor(0.0966, dtype=torch.float64)

2.维特比算法

在这里插入图片描述

print(torch.log(M))

tensor([[[1.0000, 0.5000],
         [1.0000, 0.5000]],

        [[1.3000, 1.5000],
         [1.8000, 0.5000]],

        [[0.8000, 1.5000],
         [1.8000, 0.7000]],

        [[0.0000, 0.0000],
         [0.0000, 0.0000]]], dtype=torch.float64)

def Viterbi_M():
    delta=torch.zeros(3,2)
    logM=torch.log(M)
    delta[0]=logM[0,0]
    torch.max(delta[0].reshape(y_size,1)+logM[1],axis=0)
    indices=[]
    for i in range(1,sequence_len):
        print(delta[i-1].reshape(y_size,1)+logM[i])
        delta[i],indice=torch.max(delta[i-1].reshape(y_size,1)+logM[i],axis=0)
        indices.append(indice)        
    print(delta)
#     print(indices)
    path=torch.zeros(sequence_len,dtype=torch.int)
#     print(path)
    path[sequence_len-1]=torch.argmax(delta[sequence_len-1])
#     print(path)
    for i in range(sequence_len-2,-1,-1):
        
        path[i]=indices[i][path[i+1]]
#     print(path)
    return path
    
Viterbi_M()

tensor([[2.3000, 2.5000],
        [2.3000, 1.0000]], dtype=torch.float64)
tensor([[3.1000, 3.8000],
        [4.3000, 3.2000]], dtype=torch.float64)
tensor([[1.0000, 0.5000],
        [2.3000, 2.5000],
        [4.3000, 3.8000]])





tensor([0, 1, 0], dtype=torch.int32)

3.前向算法

在这里插入图片描述在这里插入图片描述在这里插入图片描述在这里插入图片描述

  • 一般

α0(y0∣x)={1y0=start=10y0!=start这个是一个值：αi+1(yi+1∣x)=αi(yi∣x)Mi+1(yi+1,yi∣x)\alpha_0(y_0|x)=\begin{cases}1&y_0=start=1\\0&y_0!=start\end{cases}\\ 这个是一个值：\alpha_{i+1}(y_{i+1}|x)=\alpha_i(y_i|x)M_{i+1}(y_{i+1},y_i|x)

  • 矩阵形式

这是一个向量：αi(x)=(αi(yi=1∣x)αi(yi=2∣x)...αi(yi=m−1∣x)αi(yi=m∣x))Tαi+1T(x)=αiT(x)Mi+1(x)M1=M[0],M2=M[1],M3=M[2],M4=M[3]这是一个向量：\alpha_i(x)=(\alpha_i(y_i=1|x)\alpha_i(y_i=2|x)...\alpha_i(y_i=m-1|x)\alpha_i(y_i=m|x))^T\\ \alpha_{i+1}^T(x)=\alpha_i^T(x)M_{i+1}(x)\\ M_1=M[0],M_2=M[1],M_3=M[2],M_4=M[3]

M[0,1,0]=M[0,1,1]=M[3,0,1]=M[3,1,1]=0
def alpha():
    alpha=torch.zeros(sequence_len+2,y_size,dtype=float)
    alpha[0,0]=1
    for i in range(sequence_len+1):
        alpha[i+1]=torch.matmul(alpha[i].reshape(1,y_size),M[i])
    print(alpha)
    return alpha
alpha=alpha()

tensor([[  1.0000,   0.0000],
        [  2.7183,   1.6487],
        [ 19.9484,  14.9008],
        [134.5403, 119.4088],
        [253.9492,   0.0000]], dtype=torch.float64)

4.后向算法

βi(yi∣x)=Mi+1(yi,yi+1∣x)βi+1(yi+1∣x)β0(y0∣x)={1yn+1=stop=10yn+1!=stop向量形式：βi(x)=Mi+1(x)βi+1(x)Z(x)=αnT(x)⋅1=1T⋅β1(x)\beta_i(y_i|x)=M_{i+1}(y_i,y_{i+1}|x)\beta_{i+1}(y_{i+1}|x)\\ \beta_0(y_0|x)=\begin{cases}1&y_{n+1}=stop=1\\0&y_{n+1}!=stop\end{cases}\\ 向量形式：\\ \beta_i(x)=M_{i+1}(x)\beta_{i+1}(x)\\ Z(x)=\alpha_n^T(x)·1=1^T·\beta_1(x)

def beta():
    beta=torch.zeros(sequence_len+2,y_size,dtype=float)
    beta[sequence_len+1,0]=1
    for i in range(sequence_len,-1,-1):
#         print(M[i],beta[i+1].reshape(y_size,1))
        beta[i]=torch.matmul(M[i],beta[i+1].reshape(y_size,1)).reshape(y_size)
    print(beta)
    return beta
beta=beta()

tensor([[253.9492,   0.0000],
        [ 60.7485,  53.8707],
        [  6.7072,   8.0634],
        [  1.0000,   1.0000],
        [  1.0000,   0.0000]], dtype=torch.float64)

def Z_alpha(alpha):
    return torch.sum(alpha[sequence_len+1])
print(Z_alpha(alpha))

tensor(253.9492, dtype=torch.float64)

def Z_beta(beta):
#     print(beta)
    return torch.sum(beta[0])

print(Z_beta(betta))

tensor(253.9492, dtype=torch.float64)

5.使用前向后向的概率计算

这是一个值p(yi∣x)=αiT(yi∣x)βi(yi∣x)Z(x)p(yi−1,yi∣x)=αi−1T(yi∣x)Mi(yi−1,yi∣x)βi(yi∣x)Z(x)这是一个值p(y_i|x)=\frac{\alpha_i^T(y_i|x)\beta_i(y_i|x)}{Z(x)}\\ p(y_{i-1},y_i|x)=\frac{\alpha_{i-1}^T(y_i|x)M_i(y_{i-1},y_i|x)\beta_i(y_i|x)}{Z(x)}

推导：
p(yt=i∣x)=Σy1,y2,...,yt−1,yt,...,yTp(y∣x)=Σy1,y2,...,yt−1Σyt,...,yTp(y∣x)=Σy1,y2,...,yt−1Σyt,...,yT1ZΠt′=1TΦt′(yt′−1,yt′,x)=1ZΣy1,y2,...,yt−1Πt′=1tΦt′(yt′−1,yt′,x)Σyt,...,yTΠt′=t+1TΦt′(yt′−1,yt′,x)=1ZΔleftΔrightαt(i)=Δleft=Σy1,y2,...,yt−1Πt′=1tΦt′(yt′−1,yt′,x)=Σy1,y2,...,yt−1Φ1(y0,y1,x)Φ2(y1,y2,x)...Φt−1(yt−2,yt−1,x)Φt(yt−1,yt=i,x)=Σyt−1Φ(yt−1,yt,x)Σyt−2Φ(yt−2,yt−1,x)...Σy1Φ(y1,y2,x)Σy0Φ1(y0,y1,x)βt(i)=Δright=Σyt,...,yTΠt′=t+1TΦt′(yt′−1,yt′,x)p(y_t=i|x)=\Sigma_{y_1,y_2,...,y_{t-1},y_t,...,y_T}p(y|x)\\ =\Sigma_{y_1,y_2,...,y_{t-1}}\Sigma_{y_t,...,y_T}p(y|x)\\ =\Sigma_{y_1,y_2,...,y_{t-1}}\Sigma_{y_t,...,y_T}\frac{1}{Z}\Pi_{t'=1}^T\Phi_{t'}(y_{t'-1},y_{t'},x)\\ =\frac{1}{Z}\Sigma_{y_1,y_2,...,y_{t-1}}\Pi_{t'=1}^{t}\Phi_{t'}(y_{t'-1},y_{t'},x)\Sigma_{y_t,...,y_T}\Pi_{t'=t+1}^T\Phi_{t'}(y_{t'-1},y_{t'},x)\\ =\frac{1}{Z}\Delta_{left}\Delta_{right}\\ \alpha_t(i)=\Delta_{left}=\Sigma_{y_1,y_2,...,y_{t-1}}\Pi_{t'=1}^{t}\Phi_{t'}(y_{t'-1},y_{t'},x)\\ =\Sigma_{y_1,y_2,...,y_{t-1}}\Phi_1(y_0,y_1,x)\Phi_2(y_1,y_2,x)...\Phi_{t-1}(y_{t-2},y_{t-1},x)\Phi_t(y_{t-1},y_t=i,x)\\ =\Sigma_{y_{t-1}}\Phi(y_{t-1},y_{t},x)\Sigma_{y_{t-2}}\Phi(y_{t-2},y_{t-1},x)...\Sigma_{y_1}\Phi(y_1,y_2,x)\Sigma_{y_0}\Phi_1(y_0,y_1,x)\\ \beta_t(i)=\Delta_{right}=\Sigma_{y_t,...,y_T}\Pi_{t'=t+1}^T\Phi_{t'}(y_{t'-1},y_{t'},x)

def p_y_x_condition_alpha_beta(alpha,beta):
    #p(y_i|x)
    p_y_x=alpha*beta/Z_alpha(alpha)
    
#     print(alpha[2].reshape(1,y_size)*beta[2].reshape(y_size,1))
    return p_y_x
        
        
    
y=[0,1,1]
p_y_x_condition_alpha_beta(alpha,beta)

tensor([[1.0000, 0.0000],
        [0.6503, 0.3497],
        [0.5269, 0.4731],
        [0.5298, 0.4702],
        [1.0000, 0.0000]], dtype=torch.float64)

def p_y12_x_condition_alpha_beta(alpha,beta):
    p=M.clone().detach()
    for i in range(sequence_len+1):
        p[i]=alpha[i].reshape(y_size,1)*p[i]*beta[i+1]
    return p/Z_alpha(alpha);
        
p_y12_x_condition_alpha_beta(alpha,beta)

tensor([[[0.6503, 0.3497],
         [0.0000, 0.0000]],

        [[0.2634, 0.3868],
         [0.2634, 0.0863]],

        [[0.1748, 0.3520],
         [0.3550, 0.1182]],

        [[0.5298, 0.0000],
         [0.4702, 0.0000]]], dtype=torch.float64)

6.期望计算

在这里插入图片描述

def E_fk_py_x(k,alpha,beta):#E_{p(y|x)}(f_k)
    return torch.sum(f[k]*p_y12_x_condition_alpha_beta(alpha,beta))
E_fk_py_x(1,alpha,beta)

tensor(0.1317, dtype=torch.float64)

7.参数估计（学习）

θ^=argmaxΠi=1Np(y(i)∣x(i))λ^,η^=argmaxλ,ηΠi=1Np(y(i)∣x(i))Σi=1Nlogp(y(i)∣x(i))=Σi=1N(−log(Z)+Σt=1T(λTf(yt−1,yt,x)+ηTg(yt,x)))=L∂L∂λ=Σi=1Nlogp(y(i)∣x(i))=Σi=1N(−∂∂λlog(Z)+Σt=1Tf(yt−1,yt,x))log−partitionfunction:∂∂λlog(Z)=(积分就是期望）E(Σt=1Tf(yt−1,yt,x(i)))=ΣyP(y∣x(i))Σt=1Tf(yt−1,yt,x(i))=Σt=1TΣyP(y∣x(i))f(yt−1,yt,x(i))=Σt=1TΣy1,y2,...,yt−2Σyt−1ΣytΣyt+1,yt+2,...,yTP(y∣x(i))f(yt−1,yt,x(i))=Σt=1TΣyt−1Σyt(Σy1,y2,...,yt−2Σyt+1,yt+2,...,yTP(y∣x(i))f(yt−1,yt,x(i)))=Σt=1TΣyt−1ΣytP(yt−1,yt∣x(i))f(yt−1,yt,x(i))\hat{\theta}=argmax\Pi_{i=1}^N p(y^{(i)}|x^{(i)})\\ \hat{\lambda},\hat{\eta}=argmax_{\lambda,\eta}\Pi_{i=1}^N p(y^{(i)}|x^{(i)})\\ \Sigma_{i=1}^Nlog p(y^{(i)}|x^{(i)})=\Sigma_{i=1}^N(-log(Z)+\Sigma_{t=1}^T(\lambda^Tf(y_{t-1},y_t,x)+\eta^Tg(y_t,x)))\\ =L\\ \frac{\partial L}{\partial \lambda}=\Sigma_{i=1}^Nlog p(y^{(i)}|x^{(i)})=\Sigma_{i=1}^N(-\frac{\partial }{\partial \lambda} log(Z)+\Sigma_{t=1}^Tf(y_{t-1},y_t,x))\\ log-partition function:\\ \frac{\partial }{\partial \lambda} log(Z)\\ =(积分就是期望）E(\Sigma_{t=1}^Tf(y_{t-1},y_t,x^{(i)}))\\ =\Sigma_y P(y|x^{(i)})\Sigma_{t=1}^T f(y_{t-1},y_t,x^{(i)})\\ =\Sigma_{t=1}^T\Sigma_y P(y|x^{(i)}) f(y_{t-1},y_t,x^{(i)})\\ =\Sigma_{t=1}^T\Sigma_{y_1,y_2,...,y_{t-2}}\Sigma_{y_{t-1}}\Sigma_{y_t}\Sigma_{y_{t+1},y_{t+2},...,y_T} P(y|x^{(i)}) f(y_{t-1},y_t,x^{(i)})\\ =\Sigma_{t=1}^T\Sigma_{y_{t-1}}\Sigma_{y_t} (\Sigma_{y_1,y_2,...,y_{t-2}}\Sigma_{y_{t+1},y_{t+2},...,y_T}P(y|x^{(i)}) f(y_{t-1},y_t,x^{(i)}))\\ =\Sigma_{t=1}^T\Sigma_{y_{t-1}}\Sigma_{y_t}P(y_{t-1},y_t|x^{(i)}) f(y_{t-1},y_t,x^{(i)})
p(yi−1,yi∣x)=αi−1T(yi∣x)Mi(yi−1,yi∣x)βi(yi∣x)Z(x)p(y_{i-1},y_i|x)=\frac{\alpha_{i-1}^T(y_i|x)M_i(y_{i-1},y_i|x)\beta_i(y_i|x)}{Z(x)}

7.1 梯度上升

λt+1=λt+step∗∂L∂ληt+1=ηt+step∗∂L∂η\lambda^{t+1}=\lambda^t+step*\frac{\partial L}{\partial \lambda}\\ \eta^{t+1}=\eta^t+step*\frac{\partial L}{\partial \eta}

def delta_log_L(self,alpha,beta,y):
    # print(self.f[:,3,[0,0,1,1],[0,1,1,0]])
    #y=[0,1,1]
    delta=torch.sum(self.f[:,len(y),[0]+y,y+[9]],axis=(1))-torch.sum(self.f* self.p_y12_x_condition_alpha_beta(alpha, beta),axis=(1,2,3))
    return delta

def predict(self,x):
    self.sequence_len = len(x)
    self.get_ts(x)
    self.M = self.f2M()
    return self.Viterbi_M()


def train(self,traindata):
    delta=0
    batch_size=100
    num_batch=int(len(traindata[0])/batch_size)
    for e in range(num_batch):
        delta=0
        for i in range(batch_size):

            x = traindata[0][e*batch_size+i]
            y = traindata[1][e*batch_size+i]
            self.sequence_len =len(x)
            # print(x)
            self.get_ts(x)
            self.M=self.f2M()
            alpha = self.alpha()
            beta = self.beta()
                delta += self.delta_log_L(alpha, beta, y)
                print(delta)
                print(self.Viterbi_M())
                print(y)
            self.w = self.w + 0.0001 * delta

  • ◼实际上, 梯度上升收敛非常慢

  • ⚫ 替代选择:

    • ◆ 共轭梯度方法
    • ◆ 内存受限拟牛顿法

  • 目前的实现速度贼慢……以后再改

参考文献

  1. 国科大prml课程
  2. 国科大nlp课程
  3. 条件随机场CRF(一)从随机场到线性链条件随机场
  4. 统计学习方法（李航）
  5. 白板推导CRF
  6. 一个crf实现（用了他的特征函数）
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