MatLab BayesNetToolbox parameter learning

Question

My question is specific to the "learn_params()" function of the BayesNetToolbox in MatLab. In the user manual, "learn_params()" is stated to be suitable for use only if the input data is fully observed. I have tried it with a partially observed dataset where I represented unobserved values as NaN's.

It seems like "learn_params()" can deal with NaNs and the node state combinations that do not occur in the dataset. When I apply dirichlet priors to smoothen the 0 values, I get 'sensible' MLE distributions for all nodes. I have copied the script where I do this.

Can someone clarify whether what I am doing makes sense or if I am missing something, i.e. the reason why "learn_params()" cannot be used with partially observed data.

The MatLab Script where I test this is here:

% Incomplete dataset (where NaN's are unobserved)
Age = [1,2,2,NaN,3,3,2,1,NaN,2,1,1,3,NaN,2,2,1,NaN,3,1]; 
TNMStage = [2,4,2,3,NaN,1,NaN,3,1,4,3,NaN,2,4,3,4,1,NaN,2,4];
Treatment = [2,3,3,NaN,2,NaN,4,4,3,3,NaN,2,NaN,NaN,4,2,NaN,3,NaN,4];
Survival = [1,2,1,2,2,1,1,1,1,2,2,1,2,2,1,2,1,2,2,1];
matrixdata = [Age;TNMStage;Treatment;Survival];
node_sizes =[3,4,4,2];

% Enter the variablesmap
keys = {'Age', 'TNM','Treatment', 'Survival'};
v= 1:1:length(keys);
VariablesMap = containers.Map(keys,v);

% create the dag and the bnet
N = length(node_sizes); % Instead of entering it manually
dag2 = zeros(N,N);
dag2(VariablesMap('Treatment'),VariablesMap('Survival')) = 1;
bnet21 = mk_bnet(dag2, node_sizes);
draw_graph(bnet21.dag);
dirichletweight=1;

% define the CPD priors you want to use
bnet23.CPD{VariablesMap('Age')} = tabular_CPD(bnet23, VariablesMap('Age'), 'prior_type', 'dirichlet','dirichlet_type', 'unif', 'dirichlet_weight', dirichletweight);
bnet23.CPD{VariablesMap('TNM')} = tabular_CPD(bnet23, VariablesMap('TNM'), 'prior_type', 'dirichlet','dirichlet_type', 'unif', 'dirichlet_weight', dirichletweight);
bnet23.CPD{VariablesMap('Treatment')} = tabular_CPD(bnet23, VariablesMap('Treatment'), 'prior_type', 'dirichlet','dirichlet_type', 'unif','dirichlet_weight', dirichletweight);
bnet23.CPD{VariablesMap('Survival')} = tabular_CPD(bnet23, VariablesMap('Survival'), 'prior_type', 'dirichlet','dirichlet_type', 'unif','dirichlet_weight', dirichletweight);

% Find MLEs from incomplete data with Dirichlet prior CPDs
bnet24 = learn_params(bnet23, matrixdata);

% Look at the new CPT values after parameter estimation has been carried out
CPT24 = cell(1,N);
for i=1:N
s=struct(bnet24.CPD{i}); % violate object privacy
CPT24{i}=s.CPT;
end

Answer 1

According to my understanding of the BNT documentation, you need to make a couple of changes:

1. Missing values should be represented as empty cells instead of NaN values.
2. The learn_params_em function is the only one that supports missing values.

My previous response was incorrect, as I mis-recalled which of the BNT learning functions had support for missing values.