  Uncertainty quantification for multi-view learning is motivated by the
increasing use of multi-view data in scientific problems. A common variant of
multi-view learning is late fusion: train separate predictors on individual
views and combine them after single-view predictions are available. Existing
methods for uncertainty quantification for late fusion often rely on
undesirable distributional assumptions for validity. Conformal prediction is
one approach that avoids such distributional assumptions. However, naively
applying conformal prediction to late-stage fusion pipelines often produces
overly conservative and uninformative prediction regions, limiting its
downstream utility. We propose a novel methodology, Multi-View Conformal
Prediction (MVCP), where conformal prediction is instead performed separately
on the single-view predictors and only fused subsequently. Our framework
extends the standard scalar formulation of a score function to a multivariate
score that produces more efficient downstream prediction regions in both
classification and regression settings. We then demonstrate that such
improvements can be realized in methods built atop conformalized regressors,
specifically in robust predict-then-optimize pipelines.
