BNW using Octave instead of Matlab.

This version of BNW should perform the same as the original version. The only difference is that it uses Octave instead of Matlab when running BayesNet Toolbox during parameter learning.

I am calling this BNW_1.02. It can be accessed at:
compbio.uthsc.edu/BNW_1.02

1 files changed, 197 insertions, 0 deletions

diff --git a/sourcecodes/bnt-master/HMM/fwdback.m b/sourcecodes/bnt-master/HMM/fwdback.m
new file mode 100644
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+++ b/sourcecodes/bnt-master/HMM/fwdback.m
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+function [alpha, beta, gamma, loglik, xi_summed, gamma2] = fwdback(init_state_distrib, ...
+   transmat, obslik, varargin)
+% FWDBACK Compute the posterior probs. in an HMM using the forwards backwards algo.
+%
+% [alpha, beta, gamma, loglik, xi, gamma2] = fwdback(init_state_distrib, transmat, obslik, ...)
+%
+% Notation:
+% Y(t) = observation, Q(t) = hidden state, M(t) = mixture variable (for MOG outputs)
+% A(t) = discrete input (action) (for POMDP models)
+%
+% INPUT:
+% init_state_distrib(i) = Pr(Q(1) = i)
+% transmat(i,j) = Pr(Q(t) = j | Q(t-1)=i)
+%  or transmat{a}(i,j) = Pr(Q(t) = j | Q(t-1)=i, A(t-1)=a) if there are discrete inputs
+% obslik(i,t) = Pr(Y(t)| Q(t)=i)
+%   (Compute obslik using eval_pdf_xxx on your data sequence first.)
+%
+% Optional parameters may be passed as 'param_name', param_value pairs.
+% Parameter names are shown below; default values in [] - if none, argument is mandatory.
+%
+% For HMMs with MOG outputs: if you want to compute gamma2, you must specify
+% 'obslik2' - obslik(i,j,t) = Pr(Y(t)| Q(t)=i,M(t)=j)  []
+% 'mixmat' - mixmat(i,j) = Pr(M(t) = j | Q(t)=i)  []
+%
+% For HMMs with discrete inputs:
+% 'act' - act(t) = action performed at step t
+%
+% Optional arguments:
+% 'fwd_only' - if 1, only do a forwards pass and set beta=[], gamma2=[]  [0]
+% 'scaled' - if 1,  normalize alphas and betas to prevent underflow [1]
+% 'maximize' - if 1, use max-product instead of sum-product [0]
+%
+% OUTPUTS:
+% alpha(i,t) = p(Q(t)=i | y(1:t)) (or p(Q(t)=i, y(1:t)) if scaled=0)
+% beta(i,t) = p(y(t+1:T) | Q(t)=i)*p(y(t+1:T)|y(1:t)) (or p(y(t+1:T) | Q(t)=i) if scaled=0)
+% gamma(i,t) = p(Q(t)=i | y(1:T))
+% loglik = log p(y(1:T))
+% xi(i,j,t-1)  = p(Q(t-1)=i, Q(t)=j | y(1:T))  - NO LONGER COMPUTED
+% xi_summed(i,j) = sum_{t=}^{T-1} xi(i,j,t)  - changed made by Herbert Jaeger
+% gamma2(j,k,t) = p(Q(t)=j, M(t)=k | y(1:T)) (only for MOG  outputs)
+%
+% If fwd_only = 1, these become
+% alpha(i,t) = p(Q(t)=i | y(1:t))
+% beta = []
+% gamma(i,t) = p(Q(t)=i | y(1:t))
+% xi(i,j,t-1)  = p(Q(t-1)=i, Q(t)=j | y(1:t))
+% gamma2 = []
+%
+% Note: we only compute xi if it is requested as a return argument, since it can be very large.
+% Similarly, we only compute gamma2 on request (and if using MOG outputs).
+%
+% Examples:
+%
+% [alpha, beta, gamma, loglik] = fwdback(pi, A, multinomial_prob(sequence, B));
+%
+% [B, B2] = mixgauss_prob(data, mu, Sigma, mixmat);
+% [alpha, beta, gamma, loglik, xi, gamma2] = fwdback(pi, A, B, 'obslik2', B2, 'mixmat', mixmat);
+
+if nargout >= 5, compute_xi = 1; else compute_xi = 0; end
+if nargout >= 6, compute_gamma2 = 1; else compute_gamma2 = 0; end
+
+[obslik2, mixmat, fwd_only, scaled, act, maximize, compute_xi, compute_gamma2] = ...
+   process_options(varargin, ...
+       'obslik2', [], 'mixmat', [], ...
+       'fwd_only', 0, 'scaled', 1, 'act', [], 'maximize', 0, ...
+                   'compute_xi', compute_xi, 'compute_gamma2', compute_gamma2);
+
+[Q T] = size(obslik);
+
+if isempty(obslik2)
+ compute_gamma2 = 0;
+end
+
+if isempty(act)
+ act = ones(1,T);
+ transmat = { transmat } ;
+end
+
+scale = ones(1,T);
+
+% scale(t) = Pr(O(t) | O(1:t-1)) = 1/c(t) as defined by Rabiner (1989).
+% Hence prod_t scale(t) = Pr(O(1)) Pr(O(2)|O(1)) Pr(O(3) | O(1:2)) ... = Pr(O(1), ... ,O(T))
+% or log P = sum_t log scale(t).
+% Rabiner suggests multiplying beta(t) by scale(t), but we can instead
+% normalise beta(t) - the constants will cancel when we compute gamma.
+
+loglik = 0;
+
+alpha = zeros(Q,T);
+gamma = zeros(Q,T);
+if compute_xi
+ xi_summed = zeros(Q,Q);
+else
+ xi_summed = [];
+end
+
+%%%%%%%%% Forwards %%%%%%%%%%
+
+t = 1;
+alpha(:,1) = init_state_distrib(:) .* obslik(:,t);
+if scaled
+ %[alpha(:,t), scale(t)] = normaliseC(alpha(:,t));
+ [alpha(:,t), scale(t)] = normalise(alpha(:,t));
+end
+assert(approxeq(sum(alpha(:,t)),1))
+for t=2:T
+ %trans = transmat(:,:,act(t-1))';
+ trans = transmat{act(t-1)};
+ if maximize
+   m = max_mult(trans', alpha(:,t-1));
+   %A = repmat(alpha(:,t-1), [1 Q]);
+   %m = max(trans .* A, [], 1);
+ else
+   m = trans' * alpha(:,t-1);
+ end
+ alpha(:,t) = m(:) .* obslik(:,t);
+ if scaled
+   %[alpha(:,t), scale(t)] = normaliseC(alpha(:,t));
+   [alpha(:,t), scale(t)] = normalise(alpha(:,t));
+ end
+ if compute_xi & fwd_only  % useful for online EM
+   %xi(:,:,t-1) = normaliseC((alpha(:,t-1) * obslik(:,t)') .* trans);
+   xi_summed = xi_summed + normalise((alpha(:,t-1) * obslik(:,t)') .* trans);
+ end
+ assert(approxeq(sum(alpha(:,t)),1))
+end
+if scaled
+ if any(scale==0)
+   loglik = -inf;
+ else
+   loglik = sum(log(scale));
+ end
+else
+ loglik = log(sum(alpha(:,T)));
+end
+
+if fwd_only
+ gamma = alpha;
+ beta = [];
+ gamma2 = [];
+ return;
+end
+
+%%%%%%%%% Backwards %%%%%%%%%%
+
+beta = zeros(Q,T);
+if compute_gamma2
+ M = size(mixmat, 2);
+ gamma2 = zeros(Q,M,T);
+else
+ gamma2 = [];
+end
+
+beta(:,T) = ones(Q,1);
+%gamma(:,T) = normaliseC(alpha(:,T) .* beta(:,T));
+gamma(:,T) = normalise(alpha(:,T) .* beta(:,T));
+t=T;
+if compute_gamma2
+ denom = obslik(:,t) + (obslik(:,t)==0); % replace 0s with 1s before dividing
+ gamma2(:,:,t) = obslik2(:,:,t) .* mixmat .* repmat(gamma(:,t), [1 M]) ./ repmat(denom, [1 M]);
+ %gamma2(:,:,t) = normaliseC(obslik2(:,:,t) .* mixmat .* repmat(gamma(:,t), [1 M])); % wrong!
+end
+for t=T-1:-1:1
+ b = beta(:,t+1) .* obslik(:,t+1);
+ %trans = transmat(:,:,act(t));
+ trans = transmat{act(t)};
+ if maximize
+   B = repmat(b(:)', Q, 1);
+   beta(:,t) = max(trans .* B, [], 2);
+ else
+   beta(:,t) = trans * b;
+ end
+ if scaled
+   %beta(:,t) = normaliseC(beta(:,t));
+   beta(:,t) = normalise(beta(:,t));
+ end
+ %gamma(:,t) = normaliseC(alpha(:,t) .* beta(:,t));
+ gamma(:,t) = normalise(alpha(:,t) .* beta(:,t));
+ if compute_xi
+   %xi(:,:,t) = normaliseC((trans .* (alpha(:,t) * b')));
+   xi_summed = xi_summed + normalise((trans .* (alpha(:,t) * b')));
+ end
+ if compute_gamma2
+   denom = obslik(:,t) + (obslik(:,t)==0); % replace 0s with 1s before dividing
+   gamma2(:,:,t) = obslik2(:,:,t) .* mixmat .* repmat(gamma(:,t), [1 M]) ./ repmat(denom, [1 M]);
+   %gamma2(:,:,t) = normaliseC(obslik2(:,:,t) .* mixmat .* repmat(gamma(:,t), [1 M]));
+ end
+end
+
+% We now explain the equation for gamma2
+% Let zt=y(1:t-1,t+1:T) be all observations except y(t)
+% gamma2(Q,M,t) = P(Qt,Mt|yt,zt) = P(yt|Qt,Mt,zt) P(Qt,Mt|zt) / P(yt|zt)
+%                = P(yt|Qt,Mt) P(Mt|Qt) P(Qt|zt) / P(yt|zt)
+% Now gamma(Q,t) = P(Qt|yt,zt) = P(yt|Qt) P(Qt|zt) / P(yt|zt)
+% hence
+% P(Qt,Mt|yt,zt) = P(yt|Qt,Mt) P(Mt|Qt) [P(Qt|yt,zt) P(yt|zt) / P(yt|Qt)] / P(yt|zt)
+%                = P(yt|Qt,Mt) P(Mt|Qt) P(Qt|yt,zt) / P(yt|Qt)