wolffd@0: % like mgram2, except we unroll the DBN so we can use smaller
wolffd@0: % state spaces for the early duration nodes:
wolffd@0: % the state spaces are D1 in {1}, D2 in {1,2}
wolffd@0: 
wolffd@0: past = 1;
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: 
wolffd@0: alphasize = 26*2;
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 O])=1;
wolffd@0: 
wolffd@0: T = 3;
wolffd@0: dag = unroll_dbn_topology(intra, inter, T);
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: ns = repmat(ns(:), [1 T]);
wolffd@0: for d=1:D
wolffd@0:   ns(d,L)=d; % max duration
wolffd@0: end
wolffd@0: ns = ns(:);
wolffd@0: 
wolffd@0: % Equiv class in brackets for D=3
wolffd@0: % The Lt's are not tied until t>=D, since they have different sizes.
wolffd@0: % W1 and W2 are not tied since they have different parent sets.
wolffd@0: 
wolffd@0: % W1 (1)  W2 (5) W3 (5) W4 (5)
wolffd@0: % L1 (2)  L2 (6) L3 (7) L4 (7)
wolffd@0: % F1 (3)  F2 (3) F3 (4) F3 (4)
wolffd@0: % O1 (4)  O2 (4) O2 (4) O4 (4)
wolffd@0: 
wolffd@0: % Since we are not learning, we can dispense with tying
wolffd@0: 
wolffd@0: % Make the bnet
wolffd@0: Wnodes = unroll_set(W, ss, T);
wolffd@0: Lnodes = unroll_set(L, ss, T);
wolffd@0: Fnodes = unroll_set(F, ss, T);
wolffd@0: Onodes = unroll_set(O, ss, T);
wolffd@0: 
wolffd@0: bnet = mk_bnet(dag, ns);
wolffd@0: eclass = bnet.equiv_class;
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: bnet.CPD{eclass(Wnodes(1))} = tabular_CPD(bnet, Wnodes(1), 'CPT', Wstart);
wolffd@0: for t=2:T
wolffd@0: bnet.CPD{eclass(Wnodes(t))} = hhmmQ_CPD(bnet, Wnodes(t), 'Fbelow', Fnodes(t-1), ...
wolffd@0: 					'startprob', Wstart,  'transprob', Wtrans);
wolffd@0: end
wolffd@0: 
wolffd@0: % always start in state d = length(word) for each bottom level HMM
wolffd@0: % and then count down
wolffd@0: % make downcounters
wolffd@0: RLtrans = mk_rightleft_transmat(D, 0); % 0 self loop prob
wolffd@0: Ltrans = repmat(RLtrans, [1 1 nwords]);
wolffd@0: 
wolffd@0: for t=1:T
wolffd@0:   Lstart = zeros(nwords, min(t,D));
wolffd@0:   for i=1:nwords
wolffd@0:     l = length(words{i});
wolffd@0:     Lstart(i,l)=1;
wolffd@0:     if d==1
wolffd@0:       bnet.CPD{eclass(Lnodes(1))} = tabular_CPD(bnet, Lnodes(1), 'CPT', Lstart);
wolffd@0:     else
wolffd@0:       bnet.CPD{eclass(Lnodes(t))} = hhmmQ_CPD(bnet, Lnodes(t), 'Fself', Fnodes(t-1), 'Qps', Wnodes(t), ...
wolffd@0: 					      'startprob', Lstart, 'transprob', Ltrans);
wolffd@0:     end
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: % Finish when downcoutner = 1
wolffd@0: Fprob = zeros(nwords, D, 2);
wolffd@0: Fprob(:,1,2)=1;
wolffd@0: Fprob(:,2:end,1)=1;
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: 
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: 
wolffd@0: if 0
wolffd@0: % To test it is generating correctly, we create an artificial
wolffd@0: % observation process that capitalizes at the start of a new segment
wolffd@0: % Oprob(Ft-1,Qt,Dt,Yt)
wolffd@0: Oprob = zeros(2,nwords,D,alphasize);
wolffd@0: Oprob(1,1,3,letter2num('t'),1)=1;
wolffd@0: Oprob(1,1,2,letter2num('h'),1)=1;
wolffd@0: Oprob(1,1,1,letter2num('e'),1)=1;
wolffd@0: Oprob(2,1,3,letter2num('T'),1)=1;
wolffd@0: Oprob(2,1,2,letter2num('H'),1)=1;
wolffd@0: Oprob(2,1,1,letter2num('E'),1)=1;
wolffd@0: Oprob(1,2,1,letter2num('a'),1)=1;
wolffd@0: Oprob(2,2,1,letter2num('A'),1)=1;
wolffd@0: Oprob(1,3,1,letter2num('b'),1)=1;
wolffd@0: Oprob(2,3,1,letter2num('B'),1)=1;
wolffd@0: Oprob(1,4,1,letter2num('c'),1)=1;
wolffd@0: Oprob(2,4,1,letter2num('C'),1)=1;
wolffd@0: 
wolffd@0: % Oprob1(Qt,Dt,Yt)
wolffd@0: Oprob1 = zeros(nwords,D,alphasize);
wolffd@0: Oprob1(1,3,letter2num('t'),1)=1;
wolffd@0: Oprob1(1,2,letter2num('h'),1)=1;
wolffd@0: Oprob1(1,1,letter2num('e'),1)=1;
wolffd@0: Oprob1(2,1,letter2num('a'),1)=1;
wolffd@0: Oprob1(3,1,letter2num('b'),1)=1;
wolffd@0: Oprob1(4,1,letter2num('c'),1)=1;
wolffd@0: 
wolffd@0: bnet.CPD{eclass(O,2)} = tabular_CPD(bnet, O+ss, 'CPT', Oprob);
wolffd@0: bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', Oprob1);
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 = num2letter(sample(4,:))
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: [log_obslik, obslik, match] = mk_mgram_obslik(lower(data), words, word_len, word_prob);
wolffd@0: % obslik(j,t,d)
wolffd@0: softCPDpot = cell(ss,T);
wolffd@0: ens = ns;
wolffd@0: ens(O)=1;
wolffd@0: ens2 = [ens ens];
wolffd@0: for t=2:T
wolffd@0:   dom = [F W+ss L+ss O+ss];
wolffd@0:   % tab(Ft-1, Q2, Dt)
wolffd@0:   tab = ones(2, nwords, D);
wolffd@0:   if past
wolffd@0:     tab(1,:,:)=1; % if haven't finished previous word, likelihood is 1
wolffd@0:     %tab(2,:,:) = squeeze(obslik(:,t,:)); % otherwise likelihood of this segment
wolffd@0:     for d=1:min(t,D)
wolffd@0:       tab(2,:,d) = squeeze(obslik(:,t,d));
wolffd@0:     end
wolffd@0:   else
wolffd@0:     for d=1:max(1,min(D,T+1-t))
wolffd@0:       tab(2,:,d) = squeeze(obslik(:,t+d-1,d));
wolffd@0:     end
wolffd@0:   end
wolffd@0:   softCPDpot{O,t} = dpot(dom, ens2(dom), tab);
wolffd@0: end
wolffd@0: t = 1;
wolffd@0: dom = [W L O];
wolffd@0: % tab(Q2, Dt)
wolffd@0: tab = ones(nwords, D);
wolffd@0: if past
wolffd@0:   %tab = squeeze(obslik(:,t,:));
wolffd@0:   tab(:,1) = squeeze(obslik(:,t,1));
wolffd@0: else
wolffd@0:   for d=1:min(D,T-t)
wolffd@0:     tab(:,d) = squeeze(obslik(:,t+d-1,d));
wolffd@0:   end
wolffd@0: end
wolffd@0: softCPDpot{O,t} = dpot(dom, ens(dom), tab);
wolffd@0: 
wolffd@0: 
wolffd@0: %bnet.observed = [];
wolffd@0: % uniformative observations
wolffd@0: %bnet.CPD{eclass(O,2)} = tabular_CPD(bnet, O+ss, 'CPT', mk_stochastic(ones(2,nwords,D,alphasize)));
wolffd@0: %bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', mk_stochastic(ones(nwords,D,alphasize)));
wolffd@0: 
wolffd@0: engine = jtree_dbn_inf_engine(bnet);
wolffd@0: evidence = cell(ss,T);
wolffd@0: % we add dummy data to O to force its effective size to be 1.
wolffd@0: % The actual values have already been incorporated into softCPDpot 
wolffd@0: evidence(O,:) = num2cell(ones(1,T));
wolffd@0: [engine, ll_dbn] = enter_evidence(engine, evidence, 'softCPDpot', softCPDpot);
wolffd@0: 
wolffd@0: 
wolffd@0: %evidence(F,:) = num2cell(2*ones(1,T));
wolffd@0: %[engine, ll_dbn] = enter_evidence(engine, evidence);
wolffd@0: 
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: 
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
wolffd@0: 
wolffd@0: