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Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions

Weihan Li, Chengrui Li, Yule Wang, Anqi Wu

TL;DR

Addressing directional inter-areal communication in multi-region neural recordings, the paper introduces MR-MGP, a Linear Dynamical System that mirrors a multi-output Gaussian Process with a complex-valued, frequency-aware kernel. It derives continuous-time and discrete-time Markovian representations for within- and across-region latents and supports switching states, enabling linear-time inference with cost $O(T)$ while capturing frequencies and phase delays. On synthetic data and real neural recordings (LFPs and spikes), MR-MGP yields interpretable latent trajectories and improved log-likelihood relative to baselines (DLAG, CSM-GPFA). The work provides a scalable framework for dissecting inter-areal communication and offers potential implications for neural decoding and neuroengineering.

Abstract

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process (GP) and Linear Dynamical System (LDS), each with unique strengths. The GP-based approach effectively discovers latent variables with frequency bands and communication directions. Conversely, the LDS-based approach is computationally efficient but lacks powerful expressiveness in latent representation. In this study, we merge both methodologies by creating an LDS mirroring a multi-output GP, termed Multi-Region Markovian Gaussian Process (MRM-GP). Our work establishes a connection between an LDS and a multi-output GP that explicitly models frequencies and phase delays within the latent space of neural recordings. Consequently, the model achieves a linear inference cost over time points and provides an interpretable low-dimensional representation, revealing communication directions across brain regions and separating oscillatory communications into different frequency bands.

Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions

TL;DR

Addressing directional inter-areal communication in multi-region neural recordings, the paper introduces MR-MGP, a Linear Dynamical System that mirrors a multi-output Gaussian Process with a complex-valued, frequency-aware kernel. It derives continuous-time and discrete-time Markovian representations for within- and across-region latents and supports switching states, enabling linear-time inference with cost while capturing frequencies and phase delays. On synthetic data and real neural recordings (LFPs and spikes), MR-MGP yields interpretable latent trajectories and improved log-likelihood relative to baselines (DLAG, CSM-GPFA). The work provides a scalable framework for dissecting inter-areal communication and offers potential implications for neural decoding and neuroengineering.

Abstract

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process (GP) and Linear Dynamical System (LDS), each with unique strengths. The GP-based approach effectively discovers latent variables with frequency bands and communication directions. Conversely, the LDS-based approach is computationally efficient but lacks powerful expressiveness in latent representation. In this study, we merge both methodologies by creating an LDS mirroring a multi-output GP, termed Multi-Region Markovian Gaussian Process (MRM-GP). Our work establishes a connection between an LDS and a multi-output GP that explicitly models frequencies and phase delays within the latent space of neural recordings. Consequently, the model achieves a linear inference cost over time points and provides an interpretable low-dimensional representation, revealing communication directions across brain regions and separating oscillatory communications into different frequency bands.
Paper Structure (38 sections, 18 equations, 14 figures)

This paper contains 38 sections, 18 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Multi-Region Kernel
  4. Multi-Region Gaussian Process Factor Analysis
  5. Method
  6. Markovian Within-Region Latent Variables
  7. Forming a continuous-time LDS.
  8. Forming a discrete-time LDS.
  9. Markovian Across-Region Latent Variables
  10. Multi-Region Markovian Gaussian Process
  11. Multi-Region Markovian Gaussian Process with Switching States
  12. Inference
  13. Experiments
  14. Datasets.
  15. Baselines for comparison.
  16. ...and 23 more sections

Figures (14)

  • Figure 1: An example of two dimensions across-region latent variables and one dimension within-region latent variable. Brain region A and region B have bidirectional communications within different frequency bands. Each region also has a one-dimensional neural activity unrelated to the other region.
  • Figure 2: Approximate $S(\omega)$ with $\eta=0.5$ rad/s, $\sigma=4.5$ when varying the number of derivatives $k=2,3,4$. $k=2$ could provide a satisfactory approximation.
  • Figure 3: Applying MRM-GP to synthetic data. (A): Compare the estimated latent variables and discrete states with the ground truth. MRM-GP accurately identifies two states with time-varying frequencies and phase delays, aligning with the ground truth. (B): Compare learned parameters with the ground truth indicated by dashed lines. (C): Examine the test LL with varying numbers of discrete states $Z$. The findings indicate that $Z=2$ and $Z=3$ exhibit similar LL, both larger than $Z=1$.
  • Figure 4: Applying MRM-GP to LFP recordings. A: Compare the across-region latent variables with DLAG. B-C: Visualize the learned phase delays and frequencies from V1-VISam and V1a-V1b. D: Compare the test LL with other multi-region methods: DLAG and CSM-GPFA. E: The power spectrum of across-region latent variables in A. The latent variable from DLAG exhibits three frequency peaks, while MRM-GP's latent variable has only one peak. F: Inference time comparison: MRM-GP has a linear time cost.
  • Figure 5: Applying MRM-GP to neural spike trains. A: Visualize across-region latent variables with state $z_1$ (in red) and state $z_2$ (in blue). The results suggest forward and feedback communications between V1 and V2, along with time-varying delays. B-C: Visualize estimated parameters through phase delays on the x-axis and frequencies on the y-axis. D: Depict phase delays and frequencies learned in the V1a-V1b control experiment, with their representation on the x-axis and y-axis, respectively. E: Compare the test LL with discrete states $Z=1,2$ and other multi-region methods: DLAG and CSM-GPFA.
  • ...and 9 more figures