comparison toolboxes/FullBNT-1.0.7/bnt/learning/learn_struct_dbn_reveal.m @ 0:e9a9cd732c1e tip

first hg version after svn

+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