Convex conformal network improves multidimensional uncertainty regions
CoCoNet: Convex Conformal Network for Multi-Dimensional Uncertainty Regions
Machine Learning
Summary
Predicting uncertain outcomes in multiple related dimensions is hard because errors can depend on each other. The authors created CoCoNet, a method that learns how to draw uncertainty regions that fit the data well and stay mathematically nice and simple. Their approach guarantees reliable coverage, meaning the true value falls inside these regions often enough, without assuming specific data distributions. They tested CoCoNet in different scenarios and found it often creates more efficient (smaller, more informative) uncertainty regions than previous methods.
What this means in practice
- •For machine learning engineers: Generate reliable and tight uncertainty bounds for predictions involving multiple related outputs.
- •For financial risk analysts: Quantify complex joint uncertainties in multidimensional financial forecasts with guaranteed coverage.
Authors
Alireza Moradi, Thomas Bruys, Pascal Van Hentenryck, Reza Zandehshahvar
Abstract
Conformal prediction (CP) provides distribution-free coverage guarantees under exchangeability, but the efficiency of its prediction regions depends critically on the choice of the conformity score. This is particularly important in multivariate regression, where dependencies across output dimensions induce complex joint uncertainty structures. This paper introduces CoCoNet (Convex Conformal Network) for learning convex conformity scores that induce flexible, data-adaptive prediction regions. CoCoNet learns the score from held-out data by optimizing prediction-region efficiency while enforcing convexity with respect to the residual. CoCoNet then applies split-conformal calibration to retain finite-sample coverage guarantees. The paper presents two variants of the method: CoCoNet$_{\mathrm{Spline}}$, based on piecewise-linear scores, and CoCoNet$_{\mathrm{ICNN}}$, based on Input Convex Neural Networks. Experiments compare CoCoNet with other CP baselines over synthetic and real-world datasets with output dimensions ranging from 2 to 16. The results demonstrate the flexibility of CoCoNet in learning different response types. Across 8 models and 30 multi-dimensional regression tasks, CoCoNet$_\text{ICNN}$ and CoCoNet$_{\mathrm{Spline}\text{-}\ell_1}$ achieve the best efficiencies with average ranks of 1.45 and 2.75, respectively. In particular, CoCoNet$_\text{ICNN}$ ranks first on 22 tasks out of 30 in terms of efficiency.