function CPD = linear_gaussian_CPD(bnet, self, theta, sigma, theta0, n0, alpha0, beta0)% LINEAR_GAUSSIAN_CPD Make a linear Gaussian distrib.%% CPD = linear_gaussian_CPD(bnet, self, theta, lambda)% This defines the distribution P(Y|X) =  N(y | theta'*x, sigma),% where y (self) is a scalar, theta is a regression vector, and sigma is the variance.% Pass in [] to generate a default random value for a parameter.%% CPD = linear_gaussian_CPD(bnet, self, [], [], theta0, n0, alpha0, beta0)% defines a Normal-Gamma prior over the parameters:%   P(theta | lambda) = N(theta | theta0, n0*lambda)%   P(lambda) = Gamma(lambda | alpha0, beta0)% where lambda = 1/sigma is the precision for y.% n0 is a precision matrix, beta0 is a scale factor.% Pass in [] to generate a default value for a hyperparameter.% theta and sigma will be set to their prior expected values.% See "Bayesian Theory", Bernardo and Smith (2000), p442.if nargin==0  % This occurs if we are trying to load an object from a file.  CPD = init_fields;  CPD = class(CPD, 'linear_gaussian_CPD', generic_CPD(0));  return;elseif isa(bnet, 'linear_gaussian_CPD')  % This might occur if we are copying an object.  CPD = bnet;  return;endCPD = init_fields;ns = bnet.node_sizes;ps = parents(bnet.dag, self);d = sum(ns(ps));assert(ns(self)==1);if nargin < 5,  prior = [];  if isempty(theta), theta = randn(d, 1); end  if isempty(sigma), sigma = 1; endelse    %if isempty(theta0), theta0 = zeros(d, 1); end  %if isempty(n0), n0 = 0.1*eye(d); end  %if isempty(alpha0), alpha0 = 0.1; end  %if isempty(beta0), beta0 = 0.1; end     % use non-informative priors  if isempty(theta0), theta0 = zeros(d, 1); end  if isempty(n0), n0 = 0.001*ones(d); end  if isempty(alpha0), alpha0 = -d/2 + 0.001; end  if isempty(beta0), beta0 = 0.001; end  prior.theta = theta0;  prior.n = n0;  prior.alpha = alpha0;  prior.beta = beta0;    % set params to their mean  theta = prior.theta;  %sigma = prior.beta/prior.alpha; % mean of Gamma is E[lambda] = alpha/beta endCPD.self = self;CPD.theta = theta;CPD.sigma = sigma;CPD.prior = prior;clamped = 0;CPD = class(CPD, 'linear_gaussian_CPD', generic_CPD(clamped));%%%%%%%%%%%function CPD = init_fields()% This ensures we define the fields in the same order % no matter whether we load an object from a file,% or create it from scratch. (Matlab requires this.)CPD.self = [];CPD.theta = [];CPD.sigma = [];CPD.prior = [];