Probabilistic Forecasting and Information-Theoretic Analysis of Multivariate fMRI Dynamics

Functional magnetic resonance imaging (fMRI) signals exhibit complex temporal structure arising from multivariate neural dynamics, physiological variability, and measurement uncertainty. In this work, we formulate region-of-interest-level fMRI analysis as a probabilistic multi-step forecasting problem and investigate the predictability of blood-oxygen-level-dependent (BOLD) activity from an information-theoretic perspective. Using the Natural Scenes Dataset, we model multiregional BOLD activity as a stochastic process with finite memory and train multiple forecasting architectures, including linear regression, exponential smoothing, recurrent neural networks, and transformer-based models, to predict future BOLD samples from preceding temporal observations. Forecasting performance is analyzed together with entropy-based quantities, including marginal entropy, conditional entropy, and normalized predictive information measures estimated directly from model-derived predictive distributions without imposing restrictive Gaussian assumptions on the underlying BOLD dynamics. The transformer model achieved significant improvement over a naive persistence baseline (p=0.001) while yielding a high predictive information fraction (η=75.49%). Post hoc directed information analysis revealed that short-horizon prediction was dominated primarily by autoregressive, within-ROI, temporal structure. Overall, the proposed framework demonstrates how probabilistic forecasting and information-theoretic analysis can be integrated to characterize the predictability, uncertainty structure, and directional organization of large-scale fMRI dynamics and may support future downstream neuroengineering and neural-state inference applications.