Standard conformal prediction calibrates a single threshold to guarantee coverage, but this forces you to pick the shape of your prediction sets (e.g., ellipses) before calibration, typically requiring data splitting. The authors introduce multi-variable conformal prediction (MCP), which uses vector-valued score functions with multiple calibration variables, unifying shape design and calibration into one optimization problem without splitting data. They propose two variants: RemMCP (based on constraint removal, a clean generalization of split conformal) and RelMCP (handles non-convex scores via constraint relaxation). Both methods maintain finite-sample coverage guarantees while producing smaller, less variable prediction sets than split conformal.
Main takeaways:
- Classical conformal prediction is limited to a single threshold and scalar scores, forcing prediction set shapes to be fixed before calibration
- MCP extends to vector scores and multiple calibration variables, jointly optimizing shape and calibration without data splitting
- RemMCP uses constrained optimization with constraint removal; RelMCP handles non-convex scores via iterative relaxation
- Experiments show MCP achieves target coverage with smaller prediction sets and lower variance across calibration runs than split conformal baselines
- The approach uses scenario theory (a framework for certifying data-driven decisions) to maintain finite-sample coverage guarantees