Dear Tiago, I am trying to understand each value of NestedBlockState.level_entropy that contributes to the entropy of a hierarchical SBM (hSBM). In particular, I am focusing on the “prior for the edge counts“. In PRE 95, 012317 (2017), we have used the multigraph entropy for _all levels_ of the hSBM because of the dominance of parallel edges at higher levels. Nevertheless, for each level (l=k; 1 <= k < L), we assume its connectivity pattern is generated by some NDC-SBM at a higher level (l=k+1), rendering the sum of the entropy terms of all levels smaller than that of a flat prior, avoiding under-fitting. There will be 2 questions along with the thread. To see what arguments BlockState.entropy() uses, I added,
print("eargs.###: {}".format(eargs.###))
before the return line of the entropy() function in the graph_tool/inference/blockmodel.py file, where ### can be _degree_dl_, _edges_dl_, and _multigraph_, etc. Taking the “lesmis” dataset as an example, if we run minimize_nested_blockmodel_dl() on it, we (may) obtain two levels, i.e. [(77, 6), (6, 1)]. Now using this commands,
nested_state.level_entropy(0)
which outputs: eargs.dense: False eargs.edges_dl: False eargs.multigraph: True Out[•]: 630.133156768878 And, with this command,
nested_state.level_entropy(1)
It outputs: eargs.dense: True eargs.edges_dl: True eargs.multigraph: True Out[•]: 71.0082133080805 Which constitute the two levels of entropies that sum up to nested_state.entropy(). Here is my 1st question: 🧐 Why is `edges_dl` excluded except the highest level? I expected `edges_dl` at the lowest to be something nonzero, but _less_ than `69.21645383885243`, i.e. the exact negative logarithm of Eq. (40) of the PRE paper, using B=6 and e=254 (the number of edges of the “lesmis” dataset). Am I thinking it the right way? 🧐 <— this is the 2nd question. Sincerely thanks, Tzu-Chi -- Sent from: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/