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ABSTRACT Advances in digital phenotyping have opened the door to continuous, individualised monitoring of mental health, but realising the full potential of these data demands machine learning models that can operate effectively in ‘small‐data’ regimes—where per‐user data are sparse, irregular and noisy. This article explores the feasibility, challenges and opportunities of small‐data machine learning approaches for forecasting individual‐level mental health trajectories. We examine the limitations of traditional clinical tools and population‐level models and argue that fine‐grained time‐series forecasting, powered by models such as tabular prior‐data fitted networks (TabPFN), Gaussian processes, Kalman filters and meta‐learning strategies, offers a path towards personalised, proactive psychiatry. Emphasis is placed on key clinical requirements: real‐time adaptation, uncertainty quantification, feature‐level interpretability and respect for interindividual variability. We discuss implementation barriers including data quality, model transparency and ethical considerations and propose practical pathways for deployment—such as integrated biosensor platforms and just‐in‐time adaptive interventions (JITAIs). We highlight the emerging convergence of small‐data ML, mobile sensing and clinical insight as a transformative force in mental healthcare. With interdisciplinary collaboration and prospective validation, these technologies have the potential to shift psychiatry from reactive symptom management to anticipatory, personalised intervention. 

Abstract In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization withnon-Lipschitzianvalue functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient is a new type of cuts based on generalized conjugacy. Several interesting classes of MS-MINLP are identified, where the new algorithms are guaranteed to obtain the global optimum without the assumption of complete recourse. This significantly generalizes the classic SDDP algorithms. We also characterize the iteration complexity of the proposed algorithms. In particular, for a$$(T+1)$$ $(T+1)$-stage stochastic MINLP satisfyingL-exact Lipschitz regularization withd-dimensional state spaces, to obtain an$$\varepsilon $$ $\epsilon$-optimal root node solution, we prove that the number of iterations of the proposed deterministic sampling algorithm is upper bounded by$${\mathcal {O}}((\frac{2LT}{\varepsilon })^d)$$ $O\left({\left(\frac{2LT}{\epsilon }\right)}^d\right)$, and is lower bounded by$${\mathcal {O}}((\frac{LT}{4\varepsilon })^d)$$ $O\left({\left(\frac{\mathrm{LT}}{4\epsilon }\right)}^d\right)$for the general case or by$${\mathcal {O}}((\frac{LT}{8\varepsilon })^{d/2-1})$$ $O\left({\left(\frac{\mathrm{LT}}{8\epsilon }\right)}^{d/2-1}\right)$for the convex case. This shows that the obtained complexity bounds are rather sharp. It also reveals that the iteration complexity dependspolynomiallyon the number of stages. We further show that the iteration complexity dependslinearlyonT, if all the state spaces are finite sets, or if we seek a$$(T\varepsilon )$$ $\left(T\epsilon \right)$-optimal solution when the state spaces are infinite sets, i.e. allowing the optimality gap to scale withT. To the best of our knowledge, this is the first work that reports global optimization algorithms as well as iteration complexity results for solving such a large class of multistage stochastic programs. The iteration complexity study resolves a conjecture by the late Prof. Shabbir Ahmed in the general setting of multistage stochastic mixed-integer optimization.