Daniel@0: function bnet = mk_map_hhmm(varargin)
Daniel@0: 
Daniel@0: % p is the prob of a successful move (defines the reliability of motors)
Daniel@0: p = 1;
Daniel@0: obs_model = 'unique';
Daniel@0: 
Daniel@0: for i=1:2:length(varargin)
Daniel@0:   switch varargin{i},
Daniel@0:    case 'p', p = varargin{i+1};
Daniel@0:    case 'obs_model', obs_model = varargin{i+1};
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: q = 1-p;
Daniel@0: unique_obs = strcmp(obs_model, 'unique');
Daniel@0: 
Daniel@0: % assign numbers to the nodes in topological order
Daniel@0: U = 1; A = 2; C = 3; F = 4;
Daniel@0: if unique_obs
Daniel@0:   onodes = 5;
Daniel@0: else
Daniel@0:   N = 5; E = 6; S = 7; W = 8; % north, east, south, west
Daniel@0:   onodes = [N E S W];
Daniel@0: end
Daniel@0: 
Daniel@0: % create graph structure
Daniel@0: 
Daniel@0: ss = 4 + length(onodes); % slice size
Daniel@0: intra = zeros(ss,ss);
Daniel@0: intra(U,F)=1;
Daniel@0: intra(A,[C F onodes])=1;
Daniel@0: intra(C,[F onodes])=1;
Daniel@0: 
Daniel@0: inter = zeros(ss,ss);
Daniel@0: inter(U,[A C])=1;
Daniel@0: inter(A,[A C])=1;
Daniel@0: inter(F,[A C])=1;
Daniel@0: inter(C,C)=1;
Daniel@0: 
Daniel@0: % node sizes
Daniel@0: ns = zeros(1,ss);
Daniel@0: ns(U) = 2; % left/right
Daniel@0: ns(A) = 2;
Daniel@0: ns(C) = 3;
Daniel@0: ns(F) = 2;
Daniel@0: if unique_obs
Daniel@0:   ns(onodes) = 5; % we will assign each state a unique symbol
Daniel@0: else
Daniel@0:   ns(onodes) = 2;
Daniel@0: end
Daniel@0: l = 1; r = 2; % left/right
Daniel@0: L = 1; R = 2;
Daniel@0: 
Daniel@0: % Make the DBN
Daniel@0: bnet = mk_dbn(intra, inter, ns, 'observed', onodes);
Daniel@0: eclass = bnet.equiv_class;
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: % Define CPDs for slice 1
Daniel@0: % We clamp all the CPDs that are not tied,
Daniel@0: % since we cannot learn them from a single sequence.
Daniel@0: 
Daniel@0: % uniform probs over actions (the input could be chosen from a policy)
Daniel@0: bnet.CPD{eclass(U,1)} = tabular_CPD(bnet, U, 'CPT', mk_stochastic(ones(ns(U),1)), ...
Daniel@0: 				    'adjustable', 0);
Daniel@0: 
Daniel@0: % uniform probs over starting abstract state
Daniel@0: bnet.CPD{eclass(A,1)} = tabular_CPD(bnet, A, 'CPT', mk_stochastic(ones(ns(A),1)), ...
Daniel@0: 				    'adjustable', 0);
Daniel@0: 
Daniel@0: % Uniform probs over starting concrete state, modulo the fact
Daniel@0: % that corridor 2 is only of length 2.
Daniel@0: CPT = zeros(ns(A), ns(C)); % CPT(i,j) = P(C starts in j | A=i)
Daniel@0: CPT(1, :) = [1/3 1/3 1/3];
Daniel@0: CPT(2, :) = [1/2 1/2 0];
Daniel@0: bnet.CPD{eclass(C,1)} = tabular_CPD(bnet, C, 'CPT', CPT, 'adjustable', 0);
Daniel@0: 
Daniel@0: % Termination probs
Daniel@0: CPT = zeros(ns(U), ns(A), ns(C), ns(F));
Daniel@0: CPT(r,1,1,:) = [1 0];
Daniel@0: CPT(r,1,2,:) = [1 0];
Daniel@0: CPT(r,1,3,:) = [q p];
Daniel@0: CPT(r,2,1,:) = [1 0];
Daniel@0: CPT(r,2,2,:) = [q p];
Daniel@0: CPT(l,1,1,:) = [q p];
Daniel@0: CPT(l,1,2,:) = [1 0];
Daniel@0: CPT(l,1,3,:) = [1 0];
Daniel@0: CPT(l,2,1,:) = [q p];
Daniel@0: CPT(l,2,2,:) = [1 0];
Daniel@0: 
Daniel@0: bnet.CPD{eclass(F,1)} = tabular_CPD(bnet, F, 'CPT', CPT);
Daniel@0: 
Daniel@0: 
Daniel@0: % Observation model
Daniel@0: if unique_obs
Daniel@0:   CPT = zeros(ns(A), ns(C), 5);
Daniel@0:   CPT(1,1,1)=1;  % Theo state 4
Daniel@0:   CPT(1,2,2)=1;  % Theo state 5
Daniel@0:   CPT(1,3,3)=1; % Theo state 6
Daniel@0:   CPT(2,1,4)=1; % Theo state 9
Daniel@0:   CPT(2,2,5)=1; % Theo state 10
Daniel@0:   %CPT(2,3,:) undefined
Daniel@0:   O = onodes(1);
Daniel@0:   bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', CPT);
Daniel@0: else
Daniel@0:   % north/east/south/west can see wall (1) or opening (2)
Daniel@0:   CPT = zeros(ns(A), ns(C), 2);
Daniel@0:   CPT(:,:,1) = q;
Daniel@0:   CPT(:,:,2) = p;
Daniel@0:   bnet.CPD{eclass(W,1)} = tabular_CPD(bnet, W, 'CPT', CPT);
Daniel@0:   bnet.CPD{eclass(E,1)} = tabular_CPD(bnet, E, 'CPT', CPT);
Daniel@0:   CPT = zeros(ns(A), ns(C), 2);
Daniel@0:   CPT(:,:,1) = p;
Daniel@0:   CPT(:,:,2) = q;
Daniel@0:   bnet.CPD{eclass(S,1)} = tabular_CPD(bnet, S, 'CPT', CPT);
Daniel@0:   bnet.CPD{eclass(N,1)} = tabular_CPD(bnet, N, 'CPT', CPT);
Daniel@0: end
Daniel@0: 
Daniel@0: % Define the CPDs for slice 2
Daniel@0: 
Daniel@0: % Abstract
Daniel@0: 
Daniel@0: % Since the top level never resets, the starting distribution is irrelevant:
Daniel@0: % A2 will be determined by sampling from transmat(A1,:).
Daniel@0: % But the code requires we specify it anyway; we make it all 0s, a dummy value.
Daniel@0: startprob = zeros(ns(U), ns(A));
Daniel@0: 
Daniel@0: transmat = zeros(ns(U), ns(A), ns(A));
Daniel@0: transmat(R,1,:) = [q p];
Daniel@0: transmat(R,2,:) = [0 1];
Daniel@0: transmat(L,1,:) = [1 0];
Daniel@0: transmat(L,2,:) = [p q];
Daniel@0: 
Daniel@0: % Qps are the parents we condition the parameters on, in this case just
Daniel@0: % the past action.
Daniel@0: bnet.CPD{eclass(A,2)} = hhmm2Q_CPD(bnet, A+ss, 'Fbelow', F, ...
Daniel@0: 				  'startprob', startprob, 'transprob', transmat);
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: % Concrete
Daniel@0: 
Daniel@0: transmat = zeros(ns(C), ns(U), ns(A), ns(C));
Daniel@0: transmat(1,r,1,:) = [q p 0.0];
Daniel@0: transmat(2,r,1,:) = [0.0 q p];
Daniel@0: transmat(3,r,1,:) = [0.0 0.0 1.0];
Daniel@0: transmat(1,r,2,:) = [q p 0.0];
Daniel@0: transmat(2,r,2,:) = [0.0 1.0 0.0];
Daniel@0: %
Daniel@0: transmat(1,l,1,:) = [1.0 0.0 0.0];
Daniel@0: transmat(2,l,1,:) = [p q 0.0];
Daniel@0: transmat(3,l,1,:) = [0.0 p q];
Daniel@0: transmat(1,l,2,:) = [1.0 0.0 0.0];
Daniel@0: transmat(2,l,2,:) = [p q 0.0];
Daniel@0: 
Daniel@0: % Add a new dimension for A(t-1), by copying old vals,
Daniel@0: % so the matrix is the same size as startprob
Daniel@0: 
Daniel@0: 
Daniel@0: transmat = reshape(transmat, [ns(C) ns(U) ns(A) 1 ns(C)]);
Daniel@0: transmat = repmat(transmat, [1 1 1 ns(A) 1]);
Daniel@0: 
Daniel@0: % startprob(C(t-1), U(t-1), A(t-1), A(t), C(t))
Daniel@0: startprob = zeros(ns(C), ns(U), ns(A), ns(A), ns(C));
Daniel@0: startprob(1,L,1,1,:) = [1.0 0.0 0.0];
Daniel@0: startprob(3,R,1,2,:) = [1.0 0.0 0.0];
Daniel@0: startprob(3,R,1,1,:) = [0.0 0.0 1.0];
Daniel@0: % 
Daniel@0: startprob(1,L,2,1,:) = [0.0 0.0 010];
Daniel@0: startprob(2,L,2,1,:) = [1.0 0.0 0.0];
Daniel@0: startprob(2,R,2,2,:) = [0.0 1.0 0.0];
Daniel@0: 
Daniel@0: % want transmat(U,A,C,At,Ct), ie. in topo order
Daniel@0: transmat = permute(transmat, [2 3 1 4 5]);
Daniel@0: startprob  = permute(startprob, [2 3 1 4 5]);
Daniel@0: bnet.CPD{eclass(C,2)} = hhmm2Q_CPD(bnet, C+ss, 'Fself', F, ...
Daniel@0: 				  'startprob', startprob, 'transprob', transmat);
Daniel@0: 
Daniel@0: