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1 function partial_order = determine_elim_constraints(bnet, onodes)
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2 % DETERMINE_ELIM_CONSTRAINTS Determine what the constraints are (if any) on the elimination ordering.
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3 % partial_order = determine_elim_constraints(bnet, onodes)
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4 %
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5 % A graph with different kinds of nodes (e.g., discrete and cts, or decision and rnd) is called marked.
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6 % A strong root is guaranteed to exist if the marked graph is triangulated and does not have any paths of
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7 % the form discrete -> cts -> discrete. In general we need to add extra edges to
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8 % the moral graph to ensure this (see example in Lauritzen (1992) fig 3b).
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9 % However, a simpler sufficient condition is to eliminate all the cts nodes before the discrete ones,
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10 % because then, as we move from the leaves to the root, the cts nodes get marginalized away
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11 % and we are left with purely discrete cliques.
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12 %
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13 % partial_order(i,j)=1 if we must marginalize j *before* i
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14 % (so i will be nearer the strong root).
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15 % If the hidden nodes are either all discrete or all cts, we set partial_order = [].
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16 %
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17 % For details, see
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18 % - Jensen, Jensen and Dittmer, "From influence diagrams to junction trees", UAI 94.
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19 % - Lauritzen, "Propgation of probabilities, means, and variances in mixed graphical
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20 % association models", JASA 87(420):1098--1108, 1992.
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21 % - K. Olesen, "Causal probabilistic networks with both discrete and continuous variables",
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22 % IEEE Pami 15(3), 1993
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23
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24
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25 n = length(bnet.dag);
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26 pot_type = determine_pot_type(bnet, onodes);
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27 if (pot_type == 'd') | (pot_type == 'g')
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28 partial_order = [];
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29 return;
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30 end
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31
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32
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33 partial_order = sparse(n,n);
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34 partial_order(bnet.dnodes, bnet.cnodes) = 1;
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35
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36 % Integrate out cts nodes before their discrete parents - see Olesen (1993) p9
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37 % This method gives the wrong results on cg1.m!
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38 if 0
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39 for i=bnet.cnodes(:)'
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40 dps = myintersect(parents(bnet.dag, i), bnet.dnodes);
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41 partial_order(dps, i)=1;
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42 end
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43 end
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