Bi-cross-validation: a data-driven method to evaluate dynamic functional connectivity models in fMRI

Dynamic functional connectivity (dFC) models have become increasingly popular over the past decade for characterising time-varying interactions between brain regions. However, assessing and comparing dFC models remains challenging. Here, we introduce bi-cross-validation as a general framework for evaluating dFC models and selecting key hyperparameters, such as the number of states. By jointly partitioning the data across subjects and brain regions, bi-cross-validation enables out-of-sample evaluation without re-estimating latent states on the same data used for testing, thereby avoiding circularity. Using simulated data with known ground-truth dynamics, we show that bi-cross-validation favours models that accurately capture the underlying state structure. Applying the framework to real resting-state fMRI data, we demonstrate that bi-cross-validation naturally balances goodness-of-fit against model complexity, with performance improving and then declining as model complexity increases. Finally, we use bi-cross-validation to directly compare static and dynamic FC models, showing that dynamic models underperform static models at low spatial dimensionality, but outperform static models at sufficiently high dimensionality. Together, these results establish bi-cross-validation as a principled tool for dFC model selection, evaluation, and comparison.