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