Conformal Prediction for Time-Series and Flow-Based Generative Models
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Xu, Chen NMI
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Abstract
This thesis addresses two key areas: quantifying uncertainty in point prediction models (Chapters 1 and 2) and modeling data distributions with flow-based generative models (Chapters 3 and 4). Chapter 1 extends conformal prediction to time-series data, providing prediction intervals with bounded conditional coverage gaps and demonstrating superior empirical performance. Chapter 2 builds on this by sequentially updating non-conformity quantiles to better capture time-series dependencies and introducing ellipsoidal prediction regions for multivariate time-series. On the other hand, Chapter 3 develops flow-based models using ordinary differential equations, enabling novel sample generation and likelihood estimation via a framework based on the Jordan-Kinderlehrer-Otto scheme for stage-wise training. Finally, Chapter 4 enhances the scalability of ODE-based models by introducing a local flow matching approach, improving training efficiency and distillation performance.
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2025-01-10
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Dissertation