This was really Kris and Marcelo's problem, and their solution; but they let me kibbitz. Still, since it's mostly their work (by a large margin), I feel like I can say that it's very nice, without tooting my own horn too much. Existing methods, like cross-correlation or joint peristimulus time histograms, can handle certain kinds of coordination between neurons, but basically they do it by making really restrictive assumptions about what patterns of activity the neurons might be using, and how they're related. If you look at cross-correlation, for instance, you're sticking to linear relationships between what happens at one time to one neuron and to another neuron after some time-lag, and ignoring non-linear relationships or relationships between extended patterns (rather than just momentary activity). What Kris and Marcelo realized is that you don't have to make this kind of assumption. If we had a way to discover each neuron's characteristic patterns of behavior, we could just look at the moment-to-moment coordination of those patterns. But reconstructing the effective state space, which is something we know how to do, is the same thing as discovering those patterns; and there we are.
Another nice feature of this approach is that, as we say in the abstract, it lets us get at global coordination in a way which goes beyond just averaging pairwise measurements. Since we use mutual information between states, it would be nice to look at the global mutual information — essentially how far the joint distribution of all the neurons' states departs from statistical indepdence. Estimating that global distribution directly is really hard, but it turns out one can use Chow-Liu trees to put a very reasonable lower bound on the global information, while only having to estimate the joint distribution of each pair of neurons. This is like ignoring higher-order interactions in statistical mechanics, except when they can be decomposed into pairwise interactions, and it's actually (see Amari) a kind of maximum-entropy approximation. Nothing like this would work for, say, correlation coefficients. — We learned about Chow-Liu trees from a cool paper by Kirshner, Smyth and Robertson at UAI last year; I'm surprised they're not better known.
There is no reason why informational coherence should measure coordination only between neurons. But that will be another story.
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Posted by crshalizi at June 10, 2005 13:54 | permanent link