Cut Link Strength
I read Imme Ebert-Uphoff's link-strength work, which referred to the paper that Ann Nicholson and Nathalie Jitnah were finishing just as I arrive at Monash. After considering the two, I decided to use another measure that Nicholson and Jitnah had used, which I called Cut Link Strength.
Another approach is to compare with and without
the link . This was the “gold standard” that
Nicholson & Jitnah (1998) used to evaluate their (linkstrength-like) approximate inference. But we can afford to
use the gold standard itself.
When cutting the arc , we marginalize over X, which leaves unchanged the marginal distribution for Y. However, if the arc was not completely superfluous, the new P(Y|x) will differ from the old for at least some .
To control for possible back paths like , we use an intervention operator “||” rather than a regular
conditioning operator “|”. (An intervention operator, often
called “do(x)”, blocks backwards inference, effectively
cutting the links into X.) Let be the resulting
distribution in the original graph, and let be the
same in the new graph, with . The link strength is
the expected distance between these two distributions.
Thanks to Ebert-Uphoff for his Matlab code. I translated it for Quiddity and then added the Cut Link Strength method. I also worked on a Netica version.
Netica Quirks
When testing the method, I noticed that when you delete an arc in Netica , Netica marginalizes Y as if X were in its first state. This only makes sense if that is somehow a preferred default (as it might be in binary nodes). Otherwise it is quite arbitrary.Coda
The talks were nearly simultaneous, so we had to split up. Kathy, Kellen, & I went to Fort Leavenworth while Ed went to Montreal. To put a positive spin on it, we got the better conference center, by far. And Kathy & I did get to join him in Montreal the next day for the UAI conference. Alas, the cab ride out showed that I had missed the most interesting parts of the city. But PSA'2010 is in Montreal -- time to work on my paper!Thanks to our sponsors, both for funding the work and clearing the paper for publication.