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function bnet = mk_higher_order_dbn(intra, inter, node_sizes, varargin)
% MK_DBN Make a Dynamic Bayesian Network.
%
% BNET = MK_DBN(INTRA, INTER, NODE_SIZES, ...) makes a DBN with arcs
% from i in slice t to j in slice t iff intra(i,j) = 1, and
% from i in slice t to j in slice t+1 iff inter(i,j) = 1,
% for i,j in {1, 2, ..., n}, where n = num. nodes per slice, and t >= 1.
% node_sizes(i) is the number of values node i can take on.
% The nodes are assumed to be in topological order. Use TOPOLOGICAL_SORT if necessary.
% See also mk_bnet.
%
% Optional arguments [default in brackets]
% 'discrete' - list of discrete nodes [1:n]
% 'observed' - the list of nodes which will definitely be observed in every slice of every case [ [] ]
% 'eclass1' - equiv class for slice 1 [1:n]
% 'eclass2' - equiv class for slice 2 [tie nodes with equivalent parents to slice 1]
% equiv_class1(i) = j means node i in slice 1 gets its parameters from bnet.CPD{j},
% i.e., nodes i and j have tied parameters.
% 'intra1' - topology of first slice, if different from others
% 'names' - a cell array of strings to be associated with nodes 1:n [{}]
% This creates an associative array, so you write e.g.
% 'evidence(bnet.names{'bar'}) = 42' instead of 'evidence(2} = 42'
% assuming names = { 'foo', 'bar', ...}.
%
% For backwards compatibility with BNT2, arguments can also be specified as follows
% bnet = mk_dbn(intra, inter, node_sizes, dnodes, eclass1, eclass2, intra1)
%
% After calling this function, you must specify the parameters (conditional probability
% distributions) using bnet.CPD{i} = gaussian_CPD(...) or tabular_CPD(...) etc.
n = length(intra);
ss = n;
bnet.nnodes_per_slice = ss;
bnet.intra = intra;
bnet.inter = inter;
bnet.intra1 = intra;
% As this method is used to generate a higher order Markov Model
% also connect from time slice t - i -> t with i > 1 has to be
% taken into account.
%inter should be a three dimensional array where inter(:,:,i)
%describes the connections from time-slice t - i to t.
[rows,columns,order] = size(inter);
assert(rows == n);
assert(columns == n);
dag = zeros((order + 1)*n);
i = 0;
while i <= order
j = i;
while j <= order
if j == i
dag(1 + i*n:(i+1)*n,1+i*n:(i+1)*n) = intra;
else
dag(1+i*n:(i+1)*n,1+j*n:(j+1)*n) = inter(:,:,j - i);
end
j = j + 1;
end;
i = i + 1;
end;
bnet.dag = dag;
bnet.names = {};
directed = 1;
if ~acyclic(dag,directed)
error('graph must be acyclic')
end
% Calculation of the equivalence classes
bnet.eclass1 = 1:n;
bnet.eclass = zeros(order + 1,ss);
bnet.eclass(1,:) = 1:n;
for i = 1:order
bnet.eclass(i+1,:) = bnet.eclass(i,:);
for j = 1:ss
if(isequal(parents(dag,(i-1)*n+j)+ss,parents(dag,(i*n + j))))
%fprintf('%d has isomorphic parents, eclass %d \n',j,bnet.eclass(i,j))
else
bnet.eclass(i + 1,j) = max(bnet.eclass(i+1,:))+1;
%fprintf('%d has non isomorphic parents, eclass %d \n',j,bnet.eclass(i,j))
end;
end;
end;
bnet.eclass1 = 1:n;
% To be compatible with whe rest of the code
bnet.eclass2 = bnet.eclass(2,:);
dnodes = 1:n;
bnet.observed = [];
if nargin >= 4
args = varargin;
nargs = length(args);
if ~isstr(args{1})
if nargs >= 1 dnodes = args{1}; end
if nargs >= 2 bnet.eclass1 = args{2}; bnet.eclass(1,:) = args{2}; end
if nargs >= 3 bnet.eclass2 = args{3}; bnet.eclass(2,:) = args{2}; end
if nargs >= 4 bnet.intra1 = args{4}; end
else
for i=1:2:nargs
switch args{i},
case 'discrete', dnodes = args{i+1};
case 'observed', bnet.observed = args{i+1};
case 'eclass1', bnet.eclass1 = args{i+1}; bnet.eclass(1,:) = args{i+1};
case 'eclass2', bnet.eclass2 = args{i+1}; bnet.eclass(2,:) = args{i+1};
case 'eclass', bnet.eclass = args{i+1};
case 'intra1', bnet.intra1 = args{i+1};
%case 'ar_hmm', bnet.ar_hmm = args{i+1}; % should check topology
case 'names', bnet.names = assocarray(args{i+1}, num2cell(1:n));
otherwise,
error(['invalid argument name ' args{i}]);
end
end
end
end
bnet.observed = sort(bnet.observed); % for comparing sets
ns = node_sizes;
bnet.node_sizes_slice = ns(:)';
bnet.node_sizes = repmat(ns(:),1,order + 1);
cnodes = mysetdiff(1:n, dnodes);
bnet.dnodes_slice = dnodes;
bnet.cnodes_slice = cnodes;
bnet.dnodes = dnodes;
bnet.cnodes = cnodes;
% To adapt the function to higher order Markov models include dnodes for more
% time slices
for i = 1:order
bnet.dnodes = [bnet.dnodes dnodes+i*n];
bnet.cnodes = [bnet.cnodes cnodes+i*n];
end
% Generieren einer Matrix, deren i-te Spalte die Aequivalenzklassen
% der i-ten Zeitscheibe enthaelt.
bnet.equiv_class = [bnet.eclass(1,:)]';
for i = 2:(order + 1)
bnet.equiv_class = [bnet.equiv_class bnet.eclass(i,:)'];
end
bnet.CPD = cell(1,max(bnet.equiv_class(:)));
ss = n;
onodes = bnet.observed;
hnodes = mysetdiff(1:ss, onodes);
bnet.hidden_bitv = zeros(1,(order + 1)*ss);
for i = 0:order
bnet.hidden_bitv(hnodes +i*ss) = 1;
end;
bnet.parents = cell(1, (order + 1)*ss);
for i=1:(order + 1)*ss
bnet.parents{i} = parents(bnet.dag, i);
end
bnet.auto_regressive = zeros(1,ss);
% ar(i)=1 means (observed) node i depends on i in the previous slice
for o=bnet.observed(:)'
if any(bnet.parents{o+ss} <= ss)
bnet.auto_regressive(o) = 1;
end
end
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