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1 function marginal = marginal_family(engine, i, t)
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2 % MARGINAL_FAMILY Compute the marginal on the specified family (ff)
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3 % marginal = marginal_family(engine, i, t)
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4
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5 if nargin < 3, t = 1; end
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6
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7 % The method is similar to the following HMM equation:
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8 % xi(i,j,t) = normalise( alpha(i,t) * transmat(i,j) * obsmat(j,t+1) * beta(j,t+1) )
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9 % where xi(i,j,t) = Pr(Q(t)=i, Q(t+1)=j | y(1:T))
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10
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11 bnet = bnet_from_engine(engine);
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12
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13 if myismember(i, engine.onodes)
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14 ps = parents(bnet.dag, i);
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15 p = ps(1);
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16 marginal = pot_to_marginal(engine.marginals{p,t});
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17 marginal.domain = [p i];
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18 return;
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19 end
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20
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21 if t==1
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22 marginal = pot_to_marginal(engine.marginals{i,t});
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23 return;
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24 end
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25
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26 bnet = bnet_from_engine(engine);
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27 ss = length(bnet.intra);
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28 pot = engine.CPDpot{i,t};
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29 c = engine.obschild(i);
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30 pot = multiply_by_pot(pot, engine.CPDpot{c,t});
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31 pot = multiply_by_pot(pot, engine.back{i,t});
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32 ps = parents(bnet.dag, i+ss);
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33 for p=ps(:)'
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34 pot = multiply_by_pot(pot, engine.fwd{p,t-1});
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35 end
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36 marginal = pot_to_marginal(normalize_pot(pot));
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37
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38
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