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Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions
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Builds a linear dynamical system (Markovian state-space form) that exactly mirrors a multi-output complex-valued GP with a separable multi-region kernel, enabling linear-time inference for discovering frequency-specific directional communication across brain regions.
Problem
Existing GP-based multi-region methods capture frequencies and communication directions but scale cubically in time points, while LDS-based methods are linear-time but lack expressive latent representations; a GP-to-LDS conversion for complex-valued multi-output kernels was unknown.
Approach
Converts a complex-valued separable multi-region kernel (frequency and phase delay) into an LDS via spectral factorization of a polynomial approximation of the temporal spectral density, then uses Kronecker structure to add spatial phase delays, yielding a linear-cost state-space model; extended with HMM switching states.
Key results
- On LFP data, MRM-GP achieves test log-likelihood similar to CSM-GPFA and higher than DLAG across 16 datasets.
- Inference time of MRM-GP grows linearly with time points, whereas CSM-GPFA and DLAG grow cubically (over 50-200 time points).
- On V1-V2 spike trains, MRM-GP with Z=2 states achieves the highest test LL among MRM-GP (Z=1), CSM-GPFA and DLAG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the multi-region kernel instead of the Squared Exponential kernel | MRM-GP versus DLAG · LFP recordings | test log-likelihood | Helped |
| Use MRM-GP instead of CSM-GPFA | MRM-GP · LFP recordings | test log-likelihood | No clear effect |
| Use linear-time MRM-GP inference instead of cubic-time inference | MRM-GP versus CSM-GPFA and DLAG · LFP recordings, varying time points | inference time growth | Helped |
| Set the number of states to 2 instead of 1 (ablation) | MRM-GP · Synthetic data | test log-likelihood | Helped |
| Set the number of states to 3 instead of 1 (ablation) | MRM-GP · Synthetic data | test log-likelihood | Helped |
| Set the number of states to 3 instead of 2 (ablation) | MRM-GP · Synthetic data | test log-likelihood | No clear effect |
| Increase the number of derivatives from 2 to 3 (ablation) | MRM-GP latent dynamics · Generated latent variables | smoothness | Helped |
| Increase the number of derivatives from 2 to 4 (ablation) | MRM-GP latent dynamics · Generated latent variables | smoothness | Helped |
| Set the number of states to 2 instead of 1 (ablation) | MRM-GP · Neural spike trains | test log-likelihood | Helped |
| Set the number of states to 1 instead of 2 (ablation) | MRM-GP · Neural spike trains | test log-likelihood | No clear effect |
Surprising findings
- The LFP across-region latent variable from DLAG shows three frequency peaks while MRM-GP's shows a single dominant peak, and the learned phase delay (8.2 ms) differs from DLAG's time delay (1.1 ms) despite matching direction.
Limitations
- Relies on separability of multi-output kernels, restricting kernel choice.
- Cannot capture phase resetting or phase variability across trials.
Experimental setup
Datasets: synthetic data mouse V1-VISam local field potential recordings monkey V1-V2 spike trains
Benchmarks: mouse V1-VISam LFP recordings monkey V1-V2 spike trains synthetic data
Metrics: test log-likelihood on held-out neurons inference time
Baselines: DLAG CSM-GPFA Factor Analysis
Builds on: CSM-GPFA DLAG spectral factorization GP-LDS conversion switching linear dynamical system recurrent state space framework for decision-making
Closest papers by meaning
- Learning Time-Varying Multi-Region Brain Communications via Scalable Markovian Gaussian Processes (ICML 2025 · similarity 0.93)
- Accurate Identification of Communication Between Multiple Interacting Neural Populations (ICML 2025 · similarity 0.88)
- Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems (NeurIPS 2024 · similarity 0.88)
- One-hot Generalized Linear Model for Switching Brain State Discovery (ICLR 2024 · similarity 0.88)
- Wavelet Canonical Coherence for Nonstationary Signals (NeurIPS 2025 · similarity 0.87)
- Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics (NeurIPS 2024 · similarity 0.86)
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