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