Hi there,
I noticed that for MeasuredBlockState objects there are two functions get_p_posterior() and get_q_posterior() that are not available for MixedMeasuredBlockState. Do you think it would be possible to add them for future versions of graphtool?
Thanks,
Leo
Could you please open an issue at the issue tracker so this is forgotten? Issues · Tiago Peixoto / graph-tool · GitLab
Many thanks.
Hello,
I am trying to implement get_p_posterior() and get_q_posterior() for the MixedMeasuredBlockState (on the Python side).
I looked into the code for the same methods in MeasuredBlockState. The naming of the variables in there is not the same as the one in the paper, though I think I understood that the following conversion applies
N_c = \mathcal{M}_p = \sum_{i < j}{n_{ij}} \\ M_c = \mathcal{E}_p = \sum_{i < j}{n_{ij}A_{ij}} \\ X_c = \mathcal{X}_p = \sum_{i < j}{x_{ij}} \\ T_c = \mathcal{T}_p = \sum_{i < j}{x_{ij}A_{ij}} \\
where the subscript c means that the variable is from the code, p means that the variable is from the paper.
From the code of MeasuredBlockState.get_q_posterior
returns X-T+self.mu, N-X-(M-T) + self.nu
so what it is returning is basically
\sum_{i < j}{x_{ij}} - \sum_{i < j}{x_{ij}A_{ij}} + \mu, \sum_{i < j}{n_{ij}} - \sum_{i < j}{x_{ij}} - (\sum_{i < j}{n_{ij}A_{ij}} - \sum_{i < j}{x_{ij}A_{ij}}) + \nu
which simplifies to
\sum_{i < j}{x_{ij}(1-A_{ij})} + \mu, \sum_{i < j}{(n_{ij} - x_{ij})(1-A_{ij})} + \nu
I assume that a version of this function for the MixedMeasuredBlockState should simply split the sum and return a vector of tuples, in the form
({x_{ij}(1-A_{ij})} + \mu, {(n_{ij} - x_{ij})(1-A_{ij})} + \nu)
where n_{ij} and x_{ij} are defined on the original graph, while A_{ij} is the edge probability from the graph obtained from collect_marginal.
In an analogous manner, I guess MixedMeasuredBlockState.get_p_posterior should return a vector of tuples in the form
((n_{ij} - x_{ij})A_{ij} + \alpha, x_{ij}A_{ij} + \beta)
I hope I didn’t completely botch the maths.
Questions: