# Model Selection across Distributions

Hi all,

I´d have a question regarding model selection with different distributions.
When we want to decide the partition that best describes the data for a
given distribution we go with that that gives the smallest entropy. However
say we want to compare 2 different distributions d1 and d2 and the best fit
for d1 gives an entropy value of e1 and for d2 e2 respectively. If e1 < e2,
can we say that d1 describes better our data than d2?

Best Regards,
Enrique Castaneda

Could you be more specific about to which "distributions" you are
referring? Are you talking about edge covariates?

If so, model selection is explained here:

https://graph-tool.skewed.de/static/doc/demos/inference/inference.html#id28

In this case, the entropy* itself is not enough, you have to consider
also the derivative terms, as is explained in the above.

(The term "entropy" is actually misleading in this context, since the
value refers to a log-density rather than a log-probability.)

Best,
Tiago

Hi Tiago,

yes, I mean edge-covariates. In the example you referenced you compare
state.entropy() for two distributions, i.e. exponential and
log-normal, where for the log-normal model the covariates were scaled,
which is handled by subtracting log(g.ep.weight.a).sum().

In case I want to simply compare two models with unscaled discrete
covariates: one using a geometric distribution and one using a
binomial distribution. Can I perform model selection by simply
comparing their state.entropy() values?

Best Regards,
Enrique Castaneda

Yes, in the case of discrete distributions, the derivative term is not
applicable.

Best,
Tiago