Mauch MIREX 2010

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