Causal Intervention Modeling of Exercise--Sleep--Mental Health for College Students from Multimodal Wearable Data

Multimodal wearables reveal detailed links among physical activity, sleep, and psychological well-being, but learning whether a change in exercise would improve a student's subsequent distress requires a causal rather than predictive model. We formulate exercise--sleep--mental health intervention modeling as a sequential stochastic intervention problem with compositional activity budgets, lagged sleep mediation, temporally sparse outcome assessments, and observational treatment assignment. We introduce CISM, a Compositional Interventional State Model that represents physical-activity modifications as feasible reallocation operators, learns a shared stochastic response operator over next-night sleep and subsequent mental-health outcomes, and estimates population and individualized policy contrasts using g-computation and sequentially augmented estimators. Interventional mediation is expressed through randomized mediator kernels, avoiding cross-world interpretations. The empirical evaluation considers two student datasets, GLOBEM and the 2026 SSAQS Fitbit dataset, together with structural-model experiments for causal recovery. We assess factual prediction, intervention estimation, model components, policy support, and sensitivity. The manuscript provides theoretical identification conditions, seven tables, and eight vector figures; analytical diagnostics are distinguished from cohort-based evaluation.