Variational Inference for Lévy Process-Driven SDEs via Neural Tilting

Researchers have introduced a novel neural exponential tilting framework to address the challenges of Bayesian inference in Lévy-driven stochastic differential equations (SDEs). While Lévy processes are essential for modeling extreme events and heavy-tailed phenomena in fields like finance and climate science, existing inference methods struggle with scalability or fail to capture discontinuities due to Gaussian assumptions. This new approach constructs a flexible variational family by exponentially reweighting the Lévy measure using neural networks, preserving the jump structure while ensuring computational tractability. Key innovations include a quadratic neural parametrization for closed-form normalization, a conditional Gaussian representation for stable processes, and symmetry-aware Monte Carlo estimators. Empirical results on synthetic and real-world datasets demonstrate that the method accurately captures jump dynamics and provides reliable posterior inference in regimes where traditional Gaussian-based variational approaches fail. This advancement offers a scalable and rigorous solution for predictive systems requiring robust handling of rare, high-impact events.