wolffd@0: function inter = learn_struct_dbn_reveal(seqs, ns, max_fan_in, penalty)
wolffd@0: % LEARN_STRUCT_DBN_REVEAL Learn inter-slice adjacency matrix given fully observable discrete time series
wolffd@0: % inter = learn_struct_dbn_reveal(seqs, node_sizes, max_fan_in, penalty)
wolffd@0: % 
wolffd@0: % seqs{l}{i,t} = value of node i in slice t of time-series l.
wolffd@0: %   If you have a single time series in an N*T array D, use
wolffd@0: %      seqs = { num2cell(D) }.
wolffd@0: %   If you have L time series, each of length T, in an N*T*L array D, use
wolffd@0: %      seqs= cell(1,L); for l=1:L, seqs{l} = num2cell(D(:,:,l)); end
wolffd@0: %   or, in vectorized form,
wolffd@0: %      seqs = squeeze(num2cell(num2cell(D),[1 2]));
wolffd@0: % Currently the data is assumed to be discrete (1,2,...)
wolffd@0: %
wolffd@0: % node_sizes(i) is the number of possible values for node i
wolffd@0: % max_fan_in is the largest number of parents we allow per node (default: N)
wolffd@0: % penalty is weight given to the complexity penalty (default: 0.5)
wolffd@0: %  A penalty of 0.5 gives the BIC score.
wolffd@0: %  A penalty of 0 gives the ML score.
wolffd@0: %  Maximizing likelihood is equivalent to maximizing mutual information between parents and child.
wolffd@0: %
wolffd@0: % inter(i,j) = 1 iff node in slice t connects to node j in slice t+1
wolffd@0: %
wolffd@0: % The parent set for each node in slice 2 is computed by evaluating all subsets of nodes in slice 1,
wolffd@0: % and picking the largest scoring one. This takes O(n^k) time per node, where n is the num. nodes
wolffd@0: % per slice, and k <= n is the max fan in.
wolffd@0: % Since all the nodes are observed, we do not need to use an inference engine.
wolffd@0: % And since we are only learning the inter-slice matrix, we do not need to check for cycles.
wolffd@0: %
wolffd@0: % This algorithm is described in
wolffd@0: % - "REVEAL: A general reverse engineering algorithm for inference of genetic network
wolffd@0: %      architectures", Liang et al. PSB 1998
wolffd@0: % - "Extended dependency analysis of large systems",
wolffd@0: %       Roger Conant, Intl. J. General Systems, 1988, vol 14, pp 97-141
wolffd@0: % - "Learning the structure of DBNs", Friedman, Murphy and Russell, UAI 1998.
wolffd@0: 
wolffd@0: n = length(ns);
wolffd@0: 
wolffd@0: if nargin < 3, max_fan_in = n; end
wolffd@0: if nargin < 4, penalty = 0.5; end
wolffd@0: 
wolffd@0: inter = zeros(n,n);
wolffd@0: 
wolffd@0: if ~iscell(seqs)
wolffd@0:   data{1} = seqs;
wolffd@0: end
wolffd@0: 
wolffd@0: nseq = length(seqs);
wolffd@0: nslices = 0;
wolffd@0: data = cell(1, nseq);
wolffd@0: for l=1:nseq
wolffd@0:   nslices = nslices + size(seqs{l}, 2);
wolffd@0:   data{l} = cell2num(seqs{l})'; % each row is a case
wolffd@0: end
wolffd@0: ndata = nslices - nseq; % subtract off the initial slice of each sequence
wolffd@0: 
wolffd@0: % We concatenate the sequences as in the following example.
wolffd@0: % Let there be 2 sequences of lengths 4 and 5, with n nodes per slice,
wolffd@0: % and let i be the target node.
wolffd@0: % Then we construct following matrix D 
wolffd@0: %
wolffd@0: % s{1}{1,1} ... s{1}{1,3}     s{2}{1,1} ... s{2}{1,4}
wolffd@0: % ....
wolffd@0: % s{1}{n,1} ... s{1}{n,3}     s{2}{n,1} ... s{2}{n,4}
wolffd@0: % s{1}{i,2} ... s{1}{i,4}     s{2}{i,2} ... s{2}{i,5}
wolffd@0: %
wolffd@0: % D(1:n, i) is the i'th input and D(n+1, i) is the i'th output.
wolffd@0: % 
wolffd@0: % We concatenate each sequence separately to avoid treating the transition
wolffd@0: % from the end of one sequence to the beginning of another as a "normal" transition.
wolffd@0: 
wolffd@0: 
wolffd@0: for i=1:n
wolffd@0:   D = [];
wolffd@0:   for l=1:nseq
wolffd@0:     T = size(seqs{l}, 2);
wolffd@0:     A = cell2num(seqs{l}(:, 1:T-1));
wolffd@0:     B = cell2num(seqs{l}(i, 2:T));
wolffd@0:     C = [A;B];
wolffd@0:     D = [D C];
wolffd@0:   end
wolffd@0:   SS = subsets(1:n, max_fan_in, 1); % skip the empty set 
wolffd@0:   nSS = length(SS);
wolffd@0:   bic_score = zeros(1, nSS);
wolffd@0:   ll_score = zeros(1, nSS);
wolffd@0:   target = n+1;
wolffd@0:   ns2 = [ns ns(i)];
wolffd@0:   for h=1:nSS
wolffd@0:     ps = SS{h};
wolffd@0:     dom = [ps target];
wolffd@0:     counts = compute_counts(D(dom, :), ns2(dom));
wolffd@0:     CPT = mk_stochastic(counts);
wolffd@0:     [bic_score(h), ll_score(h)] = bic_score_family(counts, CPT, ndata);
wolffd@0:   end
wolffd@0:   if penalty == 0
wolffd@0:     h = argmax(ll_score);
wolffd@0:   else
wolffd@0:     h = argmax(bic_score);
wolffd@0:   end
wolffd@0:   ps = SS{h};
wolffd@0:   inter(ps, i) = 1;
wolffd@0: end