Mauch MIREX 2010

function lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)

% CPD_TO_LAMBDA_MSG Compute lambda message (gmux)

% lam_msg = compute_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)

% Pearl p183 eq 4.52

% Let Y be this node, X1..Xn be the cts parents and M the discrete switch node.

% e.g., for n=3, M=1

%

%  X1 X2 X3 M

%   \

%    \

%      Y

%

% So the only case in which we send an informative message is if p=1=M.

% To the other cts parents, we send the "know nothing" message.

switch msg_type

 case 'd',

  error('gaussian_CPD can''t create discrete msgs')

 case 'g',

  cps = ps(CPD.cps);

  cpsizes = CPD.sizes(CPD.cps);

  self_size = CPD.sizes(end);

  i = find_equiv_posns(p, cps); % p is n's i'th cts parent

  psz = cpsizes(i);

  dps = ps(CPD.dps);

  M = evidence{dps};

  if isempty(M)

    error('gmux node must have observed discrete parent')

  end

  P = msg{n}.lambda.precision;

  if all(P == 0) | (cps(M) ~= p) % if we know nothing, or are sending to a disconnected parent

    lam_msg.precision = zeros(psz, psz);

    lam_msg.info_state = zeros(psz, 1);

    return;

  end

  % We are sending a message to the only effectively connected parent.

  % There are no other incoming pi messages.

  Bmu = CPD.mean(:,M);

  BSigma = CPD.cov(:,:,M);

  Bi = CPD.weights(:,:,M);

  if (det(P) > 0) | isinf(P) 

    if isinf(P) % Y is observed

      Sigma_lambda = zeros(self_size, self_size); % infinite precision => 0 variance

      mu_lambda = msg{n}.lambda.mu; % observed_value;

    else

      Sigma_lambda = inv(P);

      mu_lambda = Sigma_lambda * msg{n}.lambda.info_state;

    end

    C = inv(Sigma_lambda + BSigma);

    lam_msg.precision = Bi' * C * Bi;

    lam_msg.info_state = Bi' * C * (mu_lambda - Bmu);

  else

    % method that uses matrix inversion lemma

    A = inv(P + inv(BSigma));

    C = P - P*A*P;

    lam_msg.precision = Bi' * C * Bi;

    D = eye(self_size) - P*A;

    z = msg{n}.lambda.info_state;

    lam_msg.info_state = Bi' * (D*z - D*P*Bmu);

  end

end