This is an implementation of Gaussian Process Factor Analysis, an analysis tool for simultaneous dimensionality reduction and smoothing. The model was developed by Byron Yu and John Cunningham. My implementation builds heavily on their original code, which can be found here:

https://users.ece.cmu.edu/~byronyu/software.shtml

Details about the model can be found in the following paper:

Yu, B.M. et al., 2009. Gaussian-Process Factor Analysis for Low-Dimensional Single-Trial Analysis of Neural Population Activity. Journal of Neurophysiology, 102(1), pp.614-635.

I used this model in the following paper:

A.S. Ecker, P. Berens, R.J. Cotton, M. Subramaniyan, G.H. Denfield, C.R. Cadwell, S.M. Smirnakis, M. Bethge, A.S. Tolias (2014): State dependence of noise correlations in macaque primary visual cortex. Neuron.

For more information go to: https://toliaslab.org/publications/ecker-et-al-2014/

I used the model in a slightly different context, whichrequired some additions but also allowed me to simplify some aspects:

• Fixed trial length. In contrast to the original implementation, my code does not allow for variable trial length (fixed T).

• Known regressors. I added the option to include a number of known regressors. This can be useful if you want to include an external signal as a predictor into the model. Examples of such signals could be the local field potential or a stimulus with known temporal dynamics.

• Estimation of residual covariance. I added the option to estimate the residual covariance that remains after a certain number of latent factors have been accounted for. This can be useful if you want to estimate the covariance in the presence of some confounder, which is modeled by the latent factor.