On 08.08.2017 01:10, Valery Topinsky wrote: > > I work on my own network in exact same way, trying to perform sampling to > estimate > some metrics. But the results are in some way replicates the behaviour from > the cookbook example: > For both cases (simple and nested SBM) the marginal distributions for > vertices most of the times has too many non-zero values for different > clusters, hence the colouring is so fine granular. Only few (1-2) clusters > obey some explicit dominant group membership. But the rest of clusters > exhibit very distributed marginals. > Do you have any explanation for this?

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This means that the posterior distribution is broad, i.e. not concentrated on any particular distribution. This implies either that the model is mispecified, i.e. your network does not have well-defined groups, or that it is very noisy. > In case of my network I also have only 1-3 groups of nodes with some > explicit dominant group membership. And the rest of vertices has too many > non-zero, almost uniformly distributed marginals. I was thinking that for > the simple cookbook example it's not natural that some vertices has more > than 10 non-zero marginal values. > May be it's just the result of independent launches of mcmc algorithm and > random nature of groups labelling? Or there is some intuition behind this > high marginal variance in group membership? > I launched several times the optimisation, and drew the results. > Topologically the outputs were very close to each other, although colouring > was always different except a few kind of "stable" vertices. Hence, I guess, > the resulted marginals for them have the same properties. But labels are not > informative it selves. May be there is some trick how to force some > deterministic labelling policies to stabilise it ? There is no trick; this variance in the posterior reflects the nature of your data. You if you want a single partition to represent it, you have to choose between two extremes of the bias-variance trade-off: 1. Choose the most likely partition, i.e. the one that minimizes the description length. (more bias, less variance) 2. Choose the maximum a posteriori estimate for each node, i.e., the most likely node label according to the node marginals. (less bias, more variance) Option 2 averages over the noise, but might not be representative of any particular fit (specially if the number of groups is fluctuating). Option 1 usually underfits, but may also overfit, depending on your data. There is a discussion on this here: https://arxiv.org/abs/1705.10225 Best, Tiago -- Tiago de Paula Peixoto <ti...@skewed.de>

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