Random graphical models

Causality in amongst confusion

Reading the The β€œIt’s really complicated and sad” theory of obesity put a question in my head about random structural models and what we can learn from them. I will be unlikely to return to and work through this right this minute, but it occurs to me that it is worth keeping around a list of models that sound like they are worth looking at

What is a good prior over causal graphs? With interactions? Good, in my current mode of thought, would mean, what classes of random causal graphs could e have that were intermediate in complexity between homogenous structure and maybe non-trivial structure. For example, monotonic, or multiplicative interactions with sparse links.

When we are concerned with sampling models over random graphs we might consider Exponential Random Graphs Model, a.k.a. ERGM models. I have some perfunctory notes on that theme under graph sampling. I wonder if that will subsume this idea or not?

I should read upon random graph theory and possible sparse random hypergraphs, e.g. Bapst and Coja-Oghlan (2016), as seen in theoretical analysis of message passing.


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