Diachronic Sample Integration: Robust Tail-Risk Estimation with Generative Models

Abstract

Deep generative models are increasingly used as simulators for downstream decision-making under data scarcity, but in risk-sensitive applications their usefulness depends on rare adverse scenarios rather than typical samples. Standard generative objectives prioritize bulk distributional fidelity, leaving low-probability tails vulnerable to localized optimization noise and making tail-dependent functionals unstable under finite simulation budgets. We introduce Diachronic Sample Integration (DSI), a test-time inference framework that ensembles generated samples across checkpoints from a stochastic training trajectory. DSI targets a checkpoint-mixture distribution that averages checkpoint-specific tail fluctuations rather than relying on a single brittle endpoint. We formalize this mechanism through a finite-budget bias-variance theory. Empirically, across multivariate synthetic processes and high-frequency trading data, DSI substantially reduces tail-estimation error compared to single-checkpoint baselines under fixed simulation budgets, outperforming standard diffusion and state-of-the-art tail-aware baselines without modifying the generative objective.

Shuning Zhao (赵舒宁）

Ph.D. Candidate - Department of Computer Science and Technology, Tsinghua University

My research interests include the application of Artificial Intelligence and Machine Learning in Finance, Insurance, Speech, and Audio domains.

Patrick Wong

Lecturer (Assistant Professor) - Department of Econometrics and Business Statistics, Monash University

My research focuses on actuarial science, financial mathematics, AI, Machine Learning and commodity market dynamics, including the evaluation and valuation of variable annuities in general stochastic environments, jump-diffusion processes in crude oil markets, and higher-order risk-neutral moments.

Xiaolin Hu

Associate Professor - Department of Computer Science and Technology, Tsinghua University

Faculty member of Department of Computer Science and Technology, Tsinghua University, working in the TSAIL group directed by Prof. Bo Zhang and Prof. Jun Zhu. My current research interests include artificial neural networks and computational neuroscience. I’m an Associate Editor of IEEE Transactions on Pattern Analysis and Machine Intelligence, IEEE Transactions on Image Processing and Cognitive Neurodynamics. Previously I was an Associate Editor of IEEE Transactions on Neural Networks and Learning Systems. I’m a Senior Member of IEEE.