Skip to content
 

Bayesian inference for network links

A colleague writes:

I’m working with a doctoral student on a latent affinity network problem and we keep hitting challenges in sampling, in our case using Metropolis-Hastings, for the network links. As you can imagine, lots of local modes, things get stuck, etc . . .

Any suggestions on how to sample network links?

My reply: Hi, yes, these are tough, with no general solution. One idea is to start with a reasonable approx and then use the Metropolis sampling to perturb it. You’re not getting the full posterior but you’re getting some sense of a range of possible soutions. Another approach is to change into a continuous-parameter model (instead of links being either there or not there, you can have a continuous parameter defined on the range (0,1) for each link), then you can fit it in Stan.

One Comment

  1. Till says:

    Yes, sampling adjacency matrices is extremely difficult. Xi’an recently provided me with some good pointers in his stats.stackexchange.com answer (see http://stats.stackexchange.com/questions/200377/sampling-a-random-binary-matrix-with-gaussian-probability-distribution). Andrew’s advice on converting the binary edges to continuous edges is also great. I have not tried to use Stan to fit network models but variational methods have worked very well for me.

Leave a Reply