Poisson reduced-rank regression (p-RRR) builds on a standard linear regression in three ways.
- Counts rather than continuous values. Spike counts are non-negative integers, so the noise model is Poisson rather than Gaussian.
- A non-negative rate. The linear term is passed through
softplus, which is smooth and never negative. - Neurons fitted jointly rather than independently. Neural populations often have low-dimensional shared structure, which is modeled with a rank constraint between predictors and targets.
Rank constraint
When the middle dimension equals the smaller of the predictor and target counts, the model is at full rank: a set of independent regressions, one per target.
A lower rank requires the targets' weights to be built from the same r patterns.
Rank selection demo Explore p-RRR on ground-truth simulated data
Rank selection in the data
Fitted models on the recorded data
Every neuron and every model is browsable in the V1 neuron explorer.