The paper introduces MEGPODE, a Bayesian nonparametric mixed‑effect ODE framework that models each subject’s dynamics as a combination of a shared population component and a subject‑specific deviation, both governed by Gaussian process priors. It avoids repeated ODE solves by representing latent trajectories with state‑space GP priors and penalizing derivative discrepancies on a finite time grid, enabling a single variational objective for joint inference of trajectories and vector fields. Experiments on heterogeneous oscillatory and biomedical ODE benchmarks show that MEGPODE outperforms strong baselines in recovering population‑level fields and predicting subject‑level trajectories.
arXiv:2606. 06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics.
The paper introduces Neural ODE-LMM, a hybrid model that integrates a Neural Ordinary Differential Equation into a linear mixed‑effects framework to flexibly learn time‑varying associations between exposures and outcomes. By encoding covariate trajectories into a continuous‑time latent state, the method preserves standard likelihood inference while capturing complex, potentially cumulative effects without pre‑specifying functional forms. Simulations demonstrate accurate recovery of instantaneous and cumulative effects, and application to the 3C cohort uncovers BMI and fasting glucose trajectories linked to cognitive decline.
arXiv:2610.07383v1 Announce Type: cross Abstract: Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learni...
arXiv:2606. 14313v1 Announce Type: cross Abstract: Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification.
arXiv:2606. 16138v1 Announce Type: cross Abstract: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics.
arXiv:2607. 13984v1 Announce Type: cross Abstract: Longitudinal tumor measurements, dropout information, and genetic covariates provide complementary information about treatment response, but integrating these data sources within a single population modeling framework remains challenging.
Simulation-based inference is challenging when many heterogeneous observations must be composed, hierarchical latent structure must be preserved, and the simulator is misspecified relative to observed...
arXiv:2505. 07068v2 Announce Type: replace-cross Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data.
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
arXiv:2606. 15458v1 Announce Type: cross Abstract: Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models.
The paper introduces a scalable variational inference framework for latent field models with non‑Gaussian likelihoods. It mirrors the sparse nearest‑neighbor autoregressive structure of the Gaussian process prior in the variational family, employs normalizing‑flow conditionals for expressiveness, and amortizes all variational parameters through a single shared neural conditioner. The method achieves polylogarithmic per‑iteration complexity via doubly stochastic optimization with reduced ancestor sets.
arXiv:2609.36950v1 Announce Type: new Abstract: Simulation-based inference is challenging when many heterogeneous observations must be composed, hierarchical latent structure must be preserved, and t...