?? cpd_to_lambda_msg.m
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function lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p)
% CPD_TO_LAMBDA_MSG Compute lambda message (gaussian)
% lam_msg = compute_lambda_msg(CPD, msg_type, n, ps, msg, p)
% Pearl p183 eq 4.52
switch msg_type
case 'd',
error('gaussian_CPD can''t create discrete msgs')
case 'g',
self_size = CPD.sizes(end);
if all(msg{n}.lambda.precision == 0) % no info to send on
lam_msg.precision = zeros(self_size);
lam_msg.info_state = zeros(self_size, 1);
return;
end
cpsizes = CPD.sizes(CPD.cps);
dpval = 1;
Q = CPD.cov(:,:,dpval);
Sigmai = Q;
wmu = zeros(self_size, 1);
for k=1:length(ps)
pk = ps(k);
if pk ~= p
bk = block(k, cpsizes);
Bk = CPD.weights(:, bk, dpval);
m = msg{n}.pi_from_parent{k};
Sigmai = Sigmai + Bk * m.Sigma * Bk';
wmu = wmu + Bk * m.mu; % m.mu = u(k)
end
end
% Sigmai = Q + sum_{k \neq i} B_k Sigma_k B_k'
i = find_equiv_posns(p, ps);
bi = block(i, cpsizes);
Bi = CPD.weights(:,bi, dpval);
if 0
P = msg{n}.lambda.precision;
if isinf(P) % inv(P)=Sigma_lambda=0
precision_temp = inv(Sigmai);
lam_msg.precision = Bi' * precision_temp * Bi;
lam_msg.info_state = precision_temp * (msg{n}.lambda.mu - wmu);
else
A = inv(P + inv(Sigmai));
precision_temp = P + P*A*P;
lam_msg.precision = Bi' * precision_temp * Bi;
self_size = length(P);
C = eye(self_size) + P*A;
z = msg{n}.lambda.info_state;
lam_msg.info_state = C*z - C*P*wmu;
end
end
if isinf(msg{n}.lambda.precision)
Sigma_lambda = zeros(self_size, self_size); % infinite precision => 0 variance
mu_lambda = msg{n}.lambda.mu; % observed_value;
else
Sigma_lambda = inv(msg{n}.lambda.precision);
mu_lambda = Sigma_lambda * msg{n}.lambda.info_state;
end
precision_temp = inv(Sigma_lambda + Sigmai);
lam_msg.precision = Bi' * precision_temp * Bi;
lam_msg.info_state = Bi' * precision_temp * (mu_lambda - wmu);
end
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