I'm trying out the 'factor' model for a project where we're interested in low-rank structure in noise correlations. I implemented a grid search over alpha and rank rather than use your pattern search so that I could get an estimate of the likelihood over a broad parameter space. First, I'd just like to confirm that cove.vloss can be treated as a negative log likelihood. Second, I inspected the mean cross-validated loss results over the grid expecting to find a relatively sharp distribution. I was surprised to find that the alpha parameter seemed to make no difference, and that a rank of 0 or 1 nearly always dominated, despite eigenspectra that typically suggest on the order of 5 dimensions of large variance (and dozens more of significantly > 0 variance).
Please let me know if you have any insights, and thank you for sharing your code!
I'm trying out the 'factor' model for a project where we're interested in low-rank structure in noise correlations. I implemented a grid search over
alphaandrankrather than use your pattern search so that I could get an estimate of the likelihood over a broad parameter space. First, I'd just like to confirm thatcove.vlosscan be treated as a negative log likelihood. Second, I inspected the mean cross-validated loss results over the grid expecting to find a relatively sharp distribution. I was surprised to find that thealphaparameter seemed to make no difference, and that a rank of 0 or 1 nearly always dominated, despite eigenspectra that typically suggest on the order of 5 dimensions of large variance (and dozens more of significantly > 0 variance).Please let me know if you have any insights, and thank you for sharing your code!