Scalable probabilistic inference for sequential stochastic models

Many real-world systems evolve over time under uncertainty. Examples include financial markets, climate systems, and autonomous technologies, where the underlying dynamics are only partially observed and measurements are often noisy. In such settings, it is necessary to infer hidden variables and predict future behavior while accounting for uncertainty in both data and models. Probabilistic inference provides a principled framework for addressing these challenges by estimating probability distributions over unknown variables. However, exact inference is often computationally infeasible for models involving nonlinear dynamics, high-dimensional latent variables, or complex temporal dependencies. Developing scalable and robust inference methods for such sequential stochastic systems therefore remains an important challenge. This thesis develops scalable approximate inference methods for sequential stochastic models within a Bayesian framework. The central goal is to design inference methods that remain computationally tractable as models become increasingly complex. The contributions address inference and learning in progressively more complex settings. First, scalable methods are developed for models that describe systems evolving continuously over time, enabling efficient reasoning about uncertain dynamical processes. Second, a memory-efficient framework for sequential learning is introduced for settings where data arrive over time and storing all past observations is impractical, allowing models to update their predictions while retaining the most informative past information. Third, new inference methods are developed for generative models with complex stochastic dynamics, enabling efficient learning in models with rich latent structure. Finally, a Bayesian framework for causal discovery integrates information from language models as uncertain prior knowledge, enabling robust identification of cause–effect relationships even when both data and prior information may be imperfect. A central insight of this thesis is that structured approximations combined with Bayesian inference enable scalable learning and uncertainty quantification across a wide range of sequential stochastic models. Together, these contributions provide a coherent framework for scalable probabilistic inference in sequential stochastic models. The proposed methods enable efficient and reliable inference across diverse applications, including continuous-time dynamical systems, sequential learning, generative modeling, and causal discovery.