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SUMMARY:Variational Inference for Lévy Process-Driven SDEs via Neural Til
 ting - Dr Yaman Kindap\, University of Cambridge
DTSTART:20251106T130000Z
DTEND:20251106T140000Z
UID:TALK240094@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:Modelling extreme events and heavy-tailed phenomena is central
  to building reliable predictive systems in domains such as finance\, clim
 ate science\, and safety-critical AI. While Lévy processes offer the natu
 ral mathematical foundation for capturing jumps and heavy tails\, Bayesian
  inference for Lévy-driven stochastic differential equations (SDEs) remai
 ns challenging. Monte Carlo approaches provide rigour and are well-establi
 shed for low-dimensional problems\, but scale poorly to high-dimensional s
 ettings. Neural variational inference frameworks achieve greater computati
 onal efficiency but typically rely on Gaussian assumptions that fail to ca
 pture discontinuities and heavy tails. We resolve this tension by introduc
 ing a neural exponential tilting framework for variational inference in L
 évy-driven SDEs. Our approach derives the optimal variational family as a
 n exponential reweighting of the Lévy measure\, parametrised by neural ne
 tworks. To ensure tractability\, we develop (i) a quadratic neural paramet
 risation that enables closed-form computation of normalising constants\, (
 ii) a conditionally Gaussian representation of stable processes for effici
 ent forward simulation\, and (iii) symmetry-exploiting Monte Carlo schemes
  for scalable loss approximation. The resulting tilted Lévy processes ret
 ain heavy-tailed behaviour while guaranteeing finite moments\, thus combin
 ing mathematical expressiveness with computational feasibility. We demonst
 rate the effectiveness of our method on synthetic datasets\, showing that 
 it accurately captures jump dynamics and provides reliable posterior infer
 ence where existing approaches struggle.
LOCATION:LT6\, Baker Building\, CUED
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