附件为HMM隐马尔科夫模型——学习问题

function [a, b] = HMM_Forward_Backward(a, b, V) % Find the probability transition matrices a,b from sample data using the forward-backward algorithm % % Inputs: % a - Initial estimate of the transition probability matrix % b - Initial estimate of the output generator matrix % V - Observed output sequence % % Output: % a - Estimated transition probability matrix % b - Estimated output generator matrix old_a = randn(size(a)); old_b = randn(size(b)); initial_alpha = (ones(1,size(a,1))/size(a,1)); theta = 1e-6; while (max(sum(sum(abs(a-old_a))),sum(sum(abs(b-old_b)))) > theta), %Normalize a and b (for numeric reasons) a = a ./ (sum(a')' * ones(1,size(a,2))); b = b ./ (sum(b')' * ones(1,size(b,2))); %Compute alpha and beta [m, alpha] = HMM_Forward (a,b,initial_alpha.*b(:,V(1))',V); [m, beta] = HMM_Backward(a,b,(ones(1,size(a,1))/size(a,1)).*b(:,V(end))',V); %Compute Gamma (via Zeta) for t = 1:length(V)-1, mul = alpha(:,t) * (beta(:,t+1).*b(:,V(t+1)))' .* a; if (sum(mul(:)) > 0), Zeta(:,:,t) = mul./sum(mul(:)); end Gamma(:,t) = sum(Zeta(:,:,t),2); end Gamma(:,length(V)) = zeros(size(a,1),1); initial_alpha = Gamma(:,1)'; %Compute a_hat from a and b by Eq. 140 (DHS Chapter 3) a_hat = sum(Zeta,3)./(sum(Gamma,2)*ones(1,size(a,2))); %Compute b_hat from a and b by Eq. 141 (DHS Chapter 3) b_hat = zeros(size(b)); for j = 1:size(b,1), for k = 1:size(b,2), b_hat(j,k)=sum(Gamma(j,:).*(V==k))/sum(Gamma(j,:)); end end %Save old a and b old_a = a; old_b = b; %a_ij <- a_hat_ij, b_jk <- b_hat_jk a = a_hat; b = b_hat; end