CONTRA: Conformal Prediction Region via Normalizing Flow Transformation
Authors: Zhenhan Fang, Aixin Tan, Jian Huang
Summary
The authors present CONTRA, a method for generating multi-dimensional prediction regions with coverage guarantees using normalizing flows. Standard conformal prediction struggles with multi-dimensional outputs because it relies on one-dimensional scores. CONTRA instead trains a normalizing flow, defines nonconformity scores as distances from the center in the flow's latent space, and maps high-density latent regions back to sharp output-space prediction regions. They also extend it to work with any predictive model by training a flow on residuals.
Main takeaways:
- Conformal prediction gives coverage-guaranteed prediction regions but struggles in multiple dimensions because it uses one-dimensional nonconformity scores
- CONTRA uses normalizing flows to define nonconformity scores as latent-space distances, producing sharper regions than traditional hyperrectangles or ellipsoids
- For cases where you prefer a non-flow model, you can add CONTRA by training a simple flow on the residuals to get reliable prediction regions
- Both versions maintain guaranteed coverage probability and outperform existing methods across datasets
- CONTRA works for both conditional density estimation and delivering multi-dimensional prediction regions
Relevance
Not directly related to my persona/midtraining work—this is about uncertainty quantification and prediction regions in supervised learning, not about behavioral conditioning in language models.
Abstract
arXiv:2605.08561v1 Announce Type: new Abstract: Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.