Reviews: Learning a latent manifold of odor representations from neural responses in piriform cortex

The authors develop a dimensionality reduction method to identify a low-dimensional representation of olfactory responses in Piriform cortex. Each trial is embedded in a low-dimensional space, and for each neuron a different nonlinear mapping is learned to predict firing rate from this low-dimensional embedding. The nonlinear mapping is parameterized by a Gaussian Process with a relatively smooth prior, which aids in interpretability. The authors assume and exploit Kronecker structure in the noise covariance matrix of the learned model, and describe efficient methods for variational inference. I think this method could be very useful in other experimental systems--not just piriform cortex.