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1 function lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)
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2 % CPD_TO_LAMBDA_MSG Compute lambda message (gmux)
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3 % lam_msg = compute_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)
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4 % Pearl p183 eq 4.52
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5
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6 % Let Y be this node, X1..Xn be the cts parents and M the discrete switch node.
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7 % e.g., for n=3, M=1
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8 %
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9 % X1 X2 X3 M
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10 % \
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11 % \
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12 % Y
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13 %
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14 % So the only case in which we send an informative message is if p=1=M.
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15 % To the other cts parents, we send the "know nothing" message.
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16
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17 switch msg_type
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18 case 'd',
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19 error('gaussian_CPD can''t create discrete msgs')
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20 case 'g',
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21 cps = ps(CPD.cps);
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22 cpsizes = CPD.sizes(CPD.cps);
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23 self_size = CPD.sizes(end);
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24 i = find_equiv_posns(p, cps); % p is n's i'th cts parent
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25 psz = cpsizes(i);
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26 dps = ps(CPD.dps);
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27 M = evidence{dps};
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28 if isempty(M)
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29 error('gmux node must have observed discrete parent')
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30 end
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31 P = msg{n}.lambda.precision;
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32 if all(P == 0) | (cps(M) ~= p) % if we know nothing, or are sending to a disconnected parent
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33 lam_msg.precision = zeros(psz, psz);
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34 lam_msg.info_state = zeros(psz, 1);
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35 return;
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36 end
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37 % We are sending a message to the only effectively connected parent.
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38 % There are no other incoming pi messages.
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39 Bmu = CPD.mean(:,M);
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40 BSigma = CPD.cov(:,:,M);
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41 Bi = CPD.weights(:,:,M);
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42 if (det(P) > 0) | isinf(P)
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43 if isinf(P) % Y is observed
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44 Sigma_lambda = zeros(self_size, self_size); % infinite precision => 0 variance
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45 mu_lambda = msg{n}.lambda.mu; % observed_value;
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46 else
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47 Sigma_lambda = inv(P);
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48 mu_lambda = Sigma_lambda * msg{n}.lambda.info_state;
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49 end
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50 C = inv(Sigma_lambda + BSigma);
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51 lam_msg.precision = Bi' * C * Bi;
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52 lam_msg.info_state = Bi' * C * (mu_lambda - Bmu);
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53 else
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54 % method that uses matrix inversion lemma
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55 A = inv(P + inv(BSigma));
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56 C = P - P*A*P;
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57 lam_msg.precision = Bi' * C * Bi;
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58 D = eye(self_size) - P*A;
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59 z = msg{n}.lambda.info_state;
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60 lam_msg.info_state = Bi' * (D*z - D*P*Bmu);
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61 end
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62 end
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