  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.
