We are trying to figure out intrinsic dimensionality of the activity of population of spiking neurons and to avoid having to use arbitrary smoothing kernels to infer firing rate, we decided to use gaussian process factor analysis. But unlike PCA it doesn’t give us an measure of explained variance. What would be the best way to infer latent dimensionality?
One method we explored is Crossvalidation across different numbers of latent dimensions and finding maximum likelihood. But considering our initial space is ~100 dimensional, checking all possible intermediate is too expensive. Is there a better way? Eg. Does log likelihood vs dimensions necessarily have structure that can help us use other search algorithms?
Finally if we want to compare seperation of decisions on the activity space across populations using a classification method after running GPFA, is it necessary or better to have same number of latent dimensions?