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Spectral Learning of Shared Dynamics Between Generalized-Linear Processes
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Proposes PGLDM, a multi-stage covariance-based subspace identification method that learns a generalized-linear dynamical model dissociating shared from private dynamics between two generalized-linear time series, and shows better decoding with lower-dimensional latents in simulations and two NHP datasets.
Problem
Existing generalized-linear dynamical model (GLDM) learning methods model a single time series and cannot jointly model two generalized-linear observation sources while dissociating their shared and private dynamics.
Approach
Extends covariance-based subspace identification with a prioritized multi-stage procedure: first learn shared latent dynamics from a cross-covariance Hankel matrix between secondary and primary observations, then private primary dynamics from a residual Hankel matrix, and optionally private secondary dynamics; moment conversions (e.g., log-link for Poisson) make it applicable to non-Gaussian obser
Key results
- In simulations, PGLDM stage 1 achieved mode identification error of about -2.76 log10 for Gaussian/Gaussian versus -1.32 for Laplace-EM, and it reached accurate shared modes at latent dimension 4.
- In Sabes NHP data, PGLDM gave better cursor kinematic decoding than PLDSID and Laplace-EM at all latent dimensions, including the maximum shared dimension of 8.
- In V1/V2 data, PGLDM improved V1 decoding from V2 spiking activity while keeping comparable V2 self-prediction AUC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PGLDM instead of PSID | Gaussian/Gaussian simulation · Gaussian/Gaussian simulation | shared mode identification error (log10): -2.985 ± 0.102 -> -2.757 ± 0.070 | Hurt |
| Use PGLDM instead of PLDSID | Poisson/Gaussian simulation · Poisson/Gaussian simulation | shared mode identification error (log10): -1.319 ± 0.132 -> -2.707 ± 0.091 | Helped |
| Use PGLDM instead of PLDSID | Poisson/Poisson simulation · Poisson/Poisson simulation | shared mode identification error (log10): -1.203 ± 0.112 -> -1.969 ± 0.079 | Helped |
| Use PGLDM instead of bestLDS | Bernoulli/Gaussian simulation · Bernoulli/Gaussian simulation | shared mode identification error (log10): -1.209 ± 0.117 -> -2.864 ± 0.072 | Helped |
| Prioritize shared latent dynamics | PGLDM · Poisson-to-Gaussian simulation, low-dimensional regimes | Gaussian observation prediction CC | Helped |
| Add stage 2 to model private Poisson dynamics (ablation) | PGLDM · Sabes lab NHP neural data | neural self-prediction AUC | Helped |
| Use PGLDM instead of PLDSID and Laplace-EM | NHP movement decoding from population spiking · Sabes lab NHP dataset | kinematic prediction CC | Helped |
| Use PGLDM instead of PLDSID and Laplace-EM | V1 activity decoding from V2 spiking · Zandvakili and Kohn NHP dataset | V1 decoding AUC | Helped |
Limitations
- Time-invariant model; may not suit non-stationary data such as chronic recordings.
- Sensitive to accuracy of empirical moment estimates; can occasionally learn unstable modes in small-data regimes.
- Linear latent dynamics may not capture nonlinearly evolving states.
Experimental setup
Datasets: Sabes lab NHP cursor movement dataset Zandvakili and Kohn V1/V2 population recordings
Benchmarks: Sabes NHP cursor decoding Zandvakili and Kohn V1/V2 decoding simulated GLDMs
Metrics: normalized eigenvalue identification error correlation coefficient AUC Wilcoxon signed-rank test
Baselines: PLDSID Laplace-EM PSID Covariance SSID bestLDS
Builds on: PSID PLDSID covariance-based SSID
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