后向算法给出了不同的答案

我试图解决结果似然问题在Matlab中实现前向和后向算法，但他们给出不同的答案。我不知道我在后向代码中做了什么错误（前向匹配的答案）。谁能帮我？后向算法给出了不同的答案

%Forward Algorithm for HMM Problem 
clc;clear; 

states=['A','B']; %The N "hidden" states 
N=length(states); 
emmision_letters=['x','y','z']; % the emission letters. 

%Initial Probabilities of states has equalized probablity. 
I_prob=repelem(1/N, N)'; 
% Transition probabilities of states 
T_prob=[0.303 0.697; 
     0.831 0.169 ]; 
% Emission prob(Prob of emission letters from given the state) 
E_prob=[0.533 0.065 0.402; 
     0.342 0.334 0.324]; 
input_em='xzyyzzyzyy'; % emission letters 
emlist=zeros(1,length(input_em)); %generate the list of the emission letters. 

for i =1:length(input_em) 
    if input_em(i)=='x' 
     emlist(i)=1; 
    elseif input_em(i)=='y' 
     emlist(i)=2; 
    elseif input_em(i)=='z' 
     emlist(i)=3; 
    end 
end 

lem=length(emlist); 

Fq=zeros(N,lem); 
Bq=zeros(N,lem);% the table hold the values 

%Forward 
for i=1:lem 
    if i==1 
     %for i=1, Fq(1)=a_qstart*eq(x1) 
     Fq(:,i)=I_prob.*E_prob(:,emlist(i)); 
    else 
     % for i=2...n, for each q in Q, Fq(i)=sum(Fq(i-1)*a_qq'*e_q(xi)) 
     for j=1:N 
      %Fq(i)=sum{fq(i-1)*Aqq'*Eq(xi)} 
      Fq(j,i)=sum(Fq(:,i-1).*T_prob(:,j)).*E_prob(j,emlist(i)); 
     end 
    end 
end 
sum(Fq(:,lem)) % the last one represent the whole sequence 


% Backward Algorithm for HMM Problem 
    for i=lem:-1:1 
     if i==lem 
      % for i =n, Bq(n)=1 
      Bq(:,i)=1; 
     else 
      % for i=n-1...1, for each q in Q 
      for j=1:N 
       % instead of calculate transition into A/B in i, 
       % calculate which jump out of A/B in step i+1 
       % Bq(i)=sum(Bq(i+1)*a_qq'*e_q(x_i+1)) 
       Bq(j,i)=sum(Bq(:,i+1).*T_prob(j,:)').* E_prob(j,emlist(i+1)); 
      end 
     end 
    end 

    sum(Bq(:,1))

我看不出有什么问题。谢谢大家的帮助！

来源

2017-02-22 Ellie

$$ B_q（i）= \ sum_ {q^\ prime \ in Q}（a_ {qq \ prime} e_ {q^\ prime x_ {i + 1}} B_ {q^{\ prime }}（我+ 1））$$

在您的for循环：

Bq(j,i)=sum(Bq(:,i+1).*T_prob(j,:)').* E_prob(:,emlist(i+1));

我认为这会工作。

来源

2017-02-22 22:37:15 DeltaMethod

非常感谢您的回答~~我刚才意识到后向算法中的发射概率是针对不同的状态的！ 'Bq（j，i）= sum（Bq（：，i + 1）。* T_prob（j，：）'。* E_prob（：，emlist（i + 1）））;'代码工作得很好。非常感谢。 – Ellie

后向算法给出了不同的答案

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