Information flow in causal networks: directed acyclic graphs

[edunnwe1]

Just wanted to toss this paper out there that I thought was interesting. It's a way to potentially use a graph structure to evaluate causality in a network. What do people think?

http://www.santafe.edu/media/workingpapers/06-05-014.pdf

[DSP137]

Thanks for sharing. Looks like it will be an interesting read.

[dlee138]

So a directed acyclic graph is basically a graph where you cannot "loop back" to the same node by following its directed edges? Can you give any examples where this kind of system is found in nature or social networks? In the case of social networks, the idea that you can only be connected (have a directed edge towards you) with someone you don't "know" (someone you don't have a directed edge towards) is kind of odd. Based on the title of the paper, I'm assuming these graphs would be of some use in analyzing causal relationships.

[yaxigeigei]

Seems interesting. I'm going to read it during this weekend. (answer+1)

[whock]

This is a really cool idea, I like the analogy of intervention in the Bayesian network as a tracer injected into a flowing river. Although I've far from digested each equation, I have a conceptual question: wouldn't the injection of uncorrelated noise and subsequent tracking of its "progress" through the network have a similar problem as the correlative measures they mention. I.e., two regions could have the same signal not because it flowed from one to another put because, as the authors say, they "share a common past." I'm not sure how injecting noise solves this problem because as I see it the same thing could happen. Then again, they address the additive vs non-additive nature of material flow vs information flow so does this address the issue? Either way, very cool stuff I've always liked the SFI.

[yaxigeigei]

I've read 6 pages of this paper and been able to understand it since the Youtube Machine Learning course introduced such kind of graph and blocking, d-seperation, etc. The later part of the paper is too hard for me to understand and I gave up.

[edunnwe1]

@dlee138 I'm struggling to give you an example within a social network because the idea that social network graphs should be directed is counterintuitive to me. Perhaps you could explain that concept? In so far as an example where this could be found in nature, consider a graph where nodes are neurons that encode the animal's spatial position, and edges are directed synapses. Then, if you remember what Will H. described in his presentation, sometimes during what's called replay you have sequential activation of these so called place cells which is thought to be a recollection or planning of a path the animal will take. So that could be a directed graph that is acyclic.

[edunnwe1]

@whock does example 6 in the paper get at your question at all, conceptually?

[dlee138]

@edunnwe1 What I meant by a social network graph that could be directed is if there is a particular "flow" of something between two or more people. For example, flow of information from on person to another would be directed from the sender to the receiver. Or flow of goods from the buyer to the seller.

[whock]

@edunnwe1 it does help conceptually with the material / info flow distinction. thanks :)

[edunnwe1]

@dlee138 thanks for the example that you gave. In that case, though, it still seems it could be acyclic to me in the sense that you could have a directed edge between the seller and the buyer and not between the buyer and the seller. Consider when you order something off of ebay: they get all of your personal info including address and payment information, but you don't get any of that from them in return. I guess it depends on how you define edges.