Hi Tiago, thanks, this is already quite helpful. Short follow-up:
Our final aim is to sample from the fitted model, also according to the inferred edge covariate distributions between groups. Is this somehow possible with graph-tool? (Up to now we were not able to do this.) Would it, in any case, be valid to retrieve the empirical distributions between each group from the fitted model and to fit a non-microcanonical version of the distributions (like binomial) to the covariates for each group combination, which could then be used to sample a weighted SBM e.g. with graspy? Or do you see a more direct way? Best, Dominik > On Jun 4, 2020, at 11:37, Tiago de Paula Peixoto <[email protected] > <mailto:[email protected]>> wrote: > > Am 04.06.20 um 10:09 schrieb kicasta: > > Hi Tiago, > > I have a short question regarding your implementation of the weighted > SBM > described here: > > https://arxiv.org/pdf/1708.01432.pdf > > https://graph-tool.skewed.de/static/doc/demos/inference/inference.html#edge-weights-and-covariates > > Does your implementation fit one distribution to sample edges per > block > combination or one global distribution? > > > One distribution per pair of groups (otherwise the covariates and the > group structure would be completely decoupled, which would be the same > as ignoring them altogether.) > > And how to retrieve the parameters > of the distribution from a fitted model? > > > The distributions are "microcanonical", i.e. the parameters are > quantities like the total sum of covariates, which is not allowed to > fluctuate. For example the "exponential" distribution for nonegative > covariates assumes that they are uniformly distributed among all > possibilities that have the exact same sum. This means that the > parameters need not be explicitly encoded. So, in this case, if you want > to extract the parameter of the distribution, you just get the sum of > covariates between any two pairs of groups. > > We were trying to fit a model similar to the SBM in graspy used for > simulation: > > https://graspy.neurodata.io/tutorials/simulations/sbm.html > > There you can choose one distribution per block combination for > simulation. > I was figuring that this should also be possible when fitting the > model. > > > Yes, this exactly what is described in the above paper, and what is > implemented in graph-tool. > > Best, > Tiago >
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