jtmatterer
commented
9 years ago I proposed the following model after class:
The sample space is (A,Y,X) \in {0,1}^{n\times n} \times {0,1}^n \times [-\pi,\pi]^{n\times n \times n}.
Here, A is the adjacency matrix for the graph, Y is whether the neuron is excitatory or inhibatory, and X is a difference between two orientation preferences. Specifically, we can define the model so that
X_{uvw} = z_u - z_v if u~w, v~w, u and v are excitatory and w is inhibatory 0 otherwise,
where z_u is the orientation preference for neuron u. By conditioning on the graph and neuron type, we can decompose the model
F{A,Y,X} = F{X|A,Y} F_{A,Y}.
Then making the assumption that the differences in orientation preference are independent for such occurrences in the graph, we can factor the model
F{A,Y,X} = \prod F{X{uvw}|A,Y} F{A,Y}.
Phrased in terms of this model, the statistical test from Bock is whether F{X{uvw}|A,Y} is the uniform distribution or not.
I apologize to anyone who had difficulty reading the LaTeX. Sidenote: does anyone know if there is a good way to embed LaTeX code into github comments? I googled the question, but couldn't find anything satisfactory.
imichaelnorris
Has anyone tried using a non-categorical model for Z for the Bock paper assignment? Although we discussed that SBM doesn't work - I want to get a sense of what other models can be used for Z other than merely categorizing Z as 8 or "x" number of categories.