comparison toolboxes/FullBNT-1.0.7/bnt/general/determine_elim_constraints.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function partial_order = determine_elim_constraints(bnet, onodes)
+% DETERMINE_ELIM_CONSTRAINTS Determine what the constraints are (if any) on the elimination ordering.
+% partial_order = determine_elim_constraints(bnet, onodes)
+%
+% A graph with different kinds of nodes (e.g., discrete and cts, or decision and rnd) is called marked. 
+% A strong root is guaranteed to exist if the marked graph is triangulated and does not have any paths of
+% the form discrete -> cts -> discrete. In general we need to add extra edges to
+% the moral graph to ensure this (see example in Lauritzen (1992) fig 3b).
+% However, a simpler sufficient condition is to eliminate all the cts nodes before the discrete ones,
+% because then, as we move from the leaves to the root, the cts nodes get marginalized away
+% and we are left with purely discrete cliques.
+%
+% partial_order(i,j)=1 if we must marginalize j *before* i
+% (so i will be nearer the strong root).
+% If the hidden nodes are either all discrete or all cts, we set partial_order = [].
+%
+% For details, see
+% - Jensen, Jensen and Dittmer, "From influence diagrams to junction trees", UAI 94.
+% - Lauritzen, "Propgation of probabilities, means, and variances in mixed graphical
+%   association models", JASA 87(420):1098--1108, 1992.
+% - K. Olesen, "Causal probabilistic networks with both discrete and continuous variables",
+%      IEEE Pami 15(3), 1993
+
+
+n = length(bnet.dag);
+pot_type = determine_pot_type(bnet, onodes);
+if (pot_type == 'd') | (pot_type == 'g')
+  partial_order = [];
+  return;
+end
+
+
+partial_order = sparse(n,n);
+partial_order(bnet.dnodes, bnet.cnodes) = 1;
+
+% Integrate out cts nodes before their discrete parents - see Olesen (1993) p9
+% This method gives the wrong results on cg1.m!
+if 0
+for i=bnet.cnodes(:)'
+  dps = myintersect(parents(bnet.dag, i), bnet.dnodes);
+  partial_order(dps, i)=1;
+end
+end