Conformal prediction delivers finite-sample, distribution-free coverage guarantees, but its classical formulation is largely confined to univariate outputs and exchangeable observations. In this seminar I present two contributions that extend the framework along these axes.
The first concerns multi-output conformal regression. I introduce a unified comparative study of nine methods - marginal, density-based, and sample-based - that clarifies their theoretical relationships and reveals that several sample-based methods are special cases of density-based ones. Within this framework I propose two novel classes of conformity scores: CDF-based scores, yielding a method (C-PCP) that achieves asymptotic conditional coverage using only samples from a generative model; and latent-based scores, yielding a computationally efficient method (L-CP) for invertible generative models. A large-scale empirical study across thirteen datasets confirms the predicted ordering of methods on conditional coverage, region size, and computational cost.
The second contribution addresses multi-step forecasting under temporal dependence. I introduce JANET, which extends generalised conformal prediction from the transductive to the inductive setting and constructs joint prediction regions controlling the K-familywise error rate - a more flexible criterion than FWER for long horizons. The framework provides exact validity for independent series and approximate validity for single series under weak ergodicity, matching bootstrap alternatives at a fraction of the cost.