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Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation
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Proposes ccGPFA, a conditionally-conjugate GPFA for spike count data using Pólya-gamma and Pólya-inverse-gamma data augmentation, enabling closed-form variational EM with sparse GPs and natural gradients.
Problem
Inference in GPFA models for spike count data (negative binomial / binomial likelihoods) is intractable because the likelihood is non-conjugate, and prior methods rely on black-box VI, numerical integration, or polynomial approximations that are unstable, non-fully-Bayesian, or non-scalable.
Approach
Augment the negative binomial likelihood with Pólya-gamma variables and Pólya-inverse-gamma/gamma auxiliary variables so that the model is conditionally conjugate, including the dispersion parameters, yielding closed-form CAVI/variational EM updates, with sparse GP inducing points and natural-gradient stochastic updates for scalability.
Key results
- Ours (NegBinomial) achieved the lowest test NLL of 0.3333 ± 0.0010 per bin, versus 0.3407 for the best baseline (PAL-like method) and 0.3504 for bGPFA.
- Ours (NegBinomial) ran in 7.67 seconds, about 1/7 the run time of the fastest baseline, which took 62.95 seconds.
- The binomial variant of ccGPFA reached test NLL 0.3390 in 9.25 seconds, also outperforming all baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ccGPFA with a negative binomial observation model instead of PAL | GPFA for spike count data · Allen Brain Observatory Visual Coding Neuropixels held-out trials | test negative log likelihood: 0.3407 -> 0.3333 | Helped |
| Use ccGPFA with a negative binomial observation model instead of PAL | GPFA for spike count data · Allen Brain Observatory Visual Coding Neuropixels held-out trials | run time: 62.95 -> 7.67 | Helped |
| Use ccGPFA with a binomial observation model instead of PAL | GPFA for spike count data · Allen Brain Observatory Visual Coding Neuropixels held-out trials | test negative log likelihood: 0.3407 -> 0.3390 | Helped |
| Use ccGPFA with a binomial observation model instead of PAL | GPFA for spike count data · Allen Brain Observatory Visual Coding Neuropixels held-out trials | run time: 62.95 -> 9.25 | Helped |
| Use a negative binomial rather than a binomial observation model | ccGPFA · Allen Brain Observatory Visual Coding Neuropixels held-out trials | test negative log likelihood: 0.3390 -> 0.3333 | Helped |
| Use a negative binomial rather than a binomial observation model | ccGPFA · Allen Brain Observatory Visual Coding Neuropixels held-out trials | run time: 9.25 -> 7.67 | Helped |
Limitations
- Sparse GP inducing-point and natural-gradient extensions were not evaluated in the experiments because trials were short.
- Experiments are on a single dataset (one recording session of drifting gratings), with a limited set of baselines.
- Requires clipping of latent mean values to handle non-identifiability between dispersion and latent function.
Experimental setup
Datasets: Allen Brain Observatory Visual Coding Neuropixels dataset
Benchmarks: Allen Brain Observatory Visual Coding Neuropixels (drifting gratings, V1)
Metrics: test negative log likelihood per bin run time (seconds)
Baselines: GPFA PAL bGPFA
Builds on: GPFA Polya-gamma augmentation bGPFA PAL
Closest papers by meaning
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