wolffd@0: % a multigram is a degenerate 2HHMM where the bottom level HMMs emit deterministic strings
wolffd@0: % and the the top level abstract states are independent of each other
wolffd@0: % cf. HSMM/test_mgram2 
wolffd@0: 
wolffd@0: words = {'the', 't', 'h', 'e'};
wolffd@0: data = 'the';
wolffd@0: nwords = length(words);
wolffd@0: word_len = zeros(1, nwords);
wolffd@0: word_prob = normalise(ones(1,nwords));
wolffd@0: word_logprob = log(word_prob);
wolffd@0: for wi=1:nwords
wolffd@0:   word_len(wi)=length(words{wi});
wolffd@0: end
wolffd@0: D = max(word_len);
wolffd@0: 
wolffd@0: alphasize = 26;
wolffd@0: data = letter2num(data);
wolffd@0: T = length(data);
wolffd@0: 
wolffd@0: % node numbers
wolffd@0: W = 1; % top level state = word id
wolffd@0: L = 2; % bottom level state = letter position within word
wolffd@0: F = 3;
wolffd@0: O = 4;
wolffd@0: 
wolffd@0: ss = 4;
wolffd@0: intra = zeros(ss,ss);
wolffd@0: intra(W,[F L O])=1;
wolffd@0: intra(L,[O F])=1;
wolffd@0: 
wolffd@0: inter = zeros(ss,ss);
wolffd@0: inter(W,W)=1;
wolffd@0: inter(L,L)=1;
wolffd@0: inter(F,[W L])=1;
wolffd@0: 
wolffd@0: % node sizes
wolffd@0: ns = zeros(1,ss);
wolffd@0: ns(W) = nwords;
wolffd@0: ns(L) = D;
wolffd@0: ns(F) = 2;
wolffd@0: ns(O) = alphasize;
wolffd@0: 
wolffd@0: 
wolffd@0: % Make the DBN
wolffd@0: bnet = mk_dbn(intra, inter, ns, 'observed', O);
wolffd@0: eclass = bnet.equiv_class;
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: % uniform start distrib over words, uniform trans mat
wolffd@0: Wstart = normalise(ones(1,nwords));
wolffd@0: Wtrans = mk_stochastic(ones(nwords,nwords));
wolffd@0: 
wolffd@0: % always start in state 1 for each bottom level HMM
wolffd@0: delta1_start = zeros(1, D);
wolffd@0: delta1_start(1) = 1;
wolffd@0: Lstart = repmat(delta1_start, nwords, 1);
wolffd@0: LRtrans = mk_leftright_transmat(D, 0); % 0 self loop prob
wolffd@0: Ltrans = repmat(LRtrans, [1 1 nwords]);
wolffd@0: 
wolffd@0: % Finish in the last letter of each word
wolffd@0: Fprob = zeros(nwords, D, 2);
wolffd@0: Fprob(:,:,1)=1;
wolffd@0: for i=1:nwords
wolffd@0:   Fprob(i,length(words{i}),2)=1;
wolffd@0:   Fprob(i,length(words{i}),1)=0;
wolffd@0: end
wolffd@0: 
wolffd@0: % Each state uniquely emits a letter
wolffd@0: Oprob = zeros(nwords, D, alphasize);
wolffd@0: for i=1:nwords
wolffd@0:   for l=1:length(words{i})
wolffd@0:     a = double(words{i}(l))-96;
wolffd@0:     Oprob(i,l,a)=1;
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: % Define CPDs for slice 
wolffd@0: bnet.CPD{eclass(W,1)} = tabular_CPD(bnet, W, 'CPT', Wstart);
wolffd@0: bnet.CPD{eclass(L,1)} = tabular_CPD(bnet, L, 'CPT', Lstart);
wolffd@0: bnet.CPD{eclass(F,1)} = tabular_CPD(bnet, F, 'CPT', Fprob);
wolffd@0: bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', Oprob);
wolffd@0: 
wolffd@0: % Define CPDs for slice 2
wolffd@0: bnet.CPD{eclass(W,2)} = hhmmQ_CPD(bnet, W+ss, 'Fbelow', F, 'startprob', Wstart,  'transprob', Wtrans);
wolffd@0: bnet.CPD{eclass(L,2)} = hhmmQ_CPD(bnet, L+ss, 'Fself', F, 'Qps', W+ss, 'startprob', Lstart, 'transprob', Ltrans);
wolffd@0: 
wolffd@0: evidence = cell(ss,T);
wolffd@0: evidence{W,1}=1;
wolffd@0: sample = cell2num(sample_dbn(bnet, 'length', T, 'evidence', evidence));
wolffd@0: str = lower(sample(4,:))
wolffd@0: 
wolffd@0: engine = jtree_dbn_inf_engine(bnet);
wolffd@0: evidence = cell(ss,T);
wolffd@0: evidence(O,:) = num2cell(data);
wolffd@0: [engine, ll_dbn] = enter_evidence(engine, evidence);
wolffd@0: 
wolffd@0: gamma = zeros(nwords, T);
wolffd@0: for t=1:T
wolffd@0:   m = marginal_nodes(engine, [W F], t);
wolffd@0:   gamma(:,t) = m.T(:,2);
wolffd@0: end
wolffd@0: gamma
wolffd@0: 
wolffd@0: xidbn = zeros(nwords, nwords);
wolffd@0: for t=1:T-1
wolffd@0:   m = marginal_nodes(engine, [W F W+ss], t);
wolffd@0:   xidbn = xidbn + squeeze(m.T(:,2,:));
wolffd@0: end
wolffd@0: 
wolffd@0: % thee
wolffd@0: % xidbn(1,4)  = 0.9412  the->e
wolffd@0: % (2,3)=0.0588 t->h
wolffd@0: % (3,4)=0.0588 h-e
wolffd@0: % (4,4)=0.0588 e-e