Gaussian-process factor analysis (GPFA)

GPFA extracts smooth, low-dimensional single-trial neural trajectories by combining two operations that were traditionally done separately. Factor analysis reduces the high-dimensional binned firing rates to a few latent factors while explicitly modelling per-neuron private variance, and a Gaussian-process prior on each latent dimension imposes temporal smoothness with a timescale learned from the data. Because reduction and smoothing are fitted jointly, GPFA can recover a clean trajectory on a single trial where naive bin-then-PCA would either over-smooth or leave the low-dimensional signal buried in noise.

GPFA became a standard first look at population dynamics because it needs no behavioural labels and lets each latent dimension have its own smoothness. Its assumptions bound its use: the observation model is linear-Gaussian applied to (often square-root transformed) binned counts, the latents are modelled as independent a priori, and inference is offline and non-causal, so GPFA is an analysis and visualization tool rather than a real-time decoder. Nonlinear and dynamical successors relax these assumptions when the goal is causal, closed-loop estimation.