Sparse Multimodal Switching State-Space Models for Regime-Dependent Neural Connectivity under Partial Observations

Multimodal electrophysiological recordings provide noisy, partially observed measurements of latent neural dynamics critical for tasks like brain state estimation and neurological diagnosis. In joint EEG-intracranial EEG (iEEG) recordings, scalp EEG offers broad but spatially mixed coverage, whereas iEEG provides high-fidelity but spatially sparse measurements. This creates a partial-observation problem: directed source-level interactions must be inferred from heterogeneous sensors with incomplete coverage. A second challenge is nonstationarity: latent neural dynamics and directed interactions among brain regions can change abruptly across distinct regimes (e.g., pre-seizure, ictal, and post-seizure states). The third challenge is sparsity of significant source-level interactions compared to the high-dimensionality of the brain networks. Standard models that assume single-mode, fully observed, or stationary may therefore fail to capture regime-specific activity or spurious couplings. We propose the Sparse Multimodal Switching State-Space Model (S$^4$M$^3$), which fuses EEG and iEEG as complementary observations of a shared source-space latent process. Dynamics switch between regimes governed by separate sparse directed transition matrices, jointly addressing multimodal fusion, nonstationarity, and sparse network estimation. The estimation of the model uses the expectation-maximization (EM) algorithm, where the E-step applies the Kim filter-RTS smoother to estimate latent states and regime probabilities, and the M-step imposes elastic-net penalization on off-diagonal elements, promoting sparse inter-regional couplings while preserving self-dynamics. The learned transition matrices facilitates the assessment of regime-dependent edge changes. To address the estimation bias of elastic-net sparsity penalty, we separate edge selection from edge assessment: selected edges are refit by regime-weighted least squares, followed by Wald tests with Benjamini-Hochberg correction. On synthetic benchmarks, S$^4$M$^3$ improves Edge F1 by approximately 25\% over the strongest stationary baseline and 64\% over two-stage source-connectivity pipelines. On a real EEG-iEEG epilepsy case study, S$^4$M$^3$ identifies sparse hippocampal and parahippocampal outgoing pathways concordant with the clinician-confirmed seizure-onset zone, without using clinical labels.