Conformal Calibration for Multi-Modal Regression with Missing Modalities

Multimodal fusion architectures typically assume all modalities are available at inference, yet sensor failures, acquisition variability, and cost constraints routinely produce incomplete observations. Existing work treats modality absence as a prediction-accuracy problem, leaving a more basic question unanswered: whether a model's confidence estimates remain calibrated when an entire input stream is removed. We argue that missing-modality robustness and calibrated uncertainty are a single coupled property, and introduce Modality-Conditioned Conformal Fusion (MCCF), an architecture that addresses both at once. MCCF combines a multimodal bottleneck fusion backbone trained with modality dropout, per-modality evidential heads producing modality-decomposed Dirichlet distributions, and a Dempster-Shafer combination rule that fuses the per-modality evidence into a joint predictive distribution; an absent modality contributes vacuous evidence that is structurally ignored, so the fused uncertainty automatically reflects the reduced information without test-time imputation. A Mondrian conformal calibration module keyed on the modality-presence mask then provides finite-sample group-conditional coverage for every non-empty modality subset. MCCF is, to our knowledge, the first method with formal coverage guarantees under arbitrary modality availability through architectural integration rather than post-hoc recalibration, and the evidential decomposition yields per-modality vacuity scores that localise uncertainty to the absent modality responsible. Across a synthetic problem and three real multimodal benchmarks, MCCF holds its target coverage on every modality-presence subset, substantially narrows the coverage gap between full and partial modalities relative to a marginal split-conformal baseline, and imposes no measurable accuracy cost relative to temperature-scaled and evidential baselines.

Multimodal learning often grapples with the challenge of low-quality data, which predominantly manifests as two facets: modality imbalance and noisy corruption. While these issues are often studied in isolation, we argue that they share a common root in the predictive uncertainty towards the reliability of individual modalities and instances during learning. In this paper, we propose a unified framework, termed Conformal Predictive Self-Calibration (CPSC), which leverages conformal prediction to equip the model with the ability to perform self-guided calibration on-the-fly. The core of our proposed CPSC lies in a novel self-calibrating training loop that seamlessly integrates two key modules: (1) Representation Self-Calibration, which decomposes unimodal features into components, and selectively fuses the most robust ones identified by a conformal predictor to enhance feature resilience. (2) Gradient Self-Calibration, which recalibrates the gradient flow during backpropagation based on instance-wise reliability scores, steering the optimization towards more trustworthy directions. Furthermore, we also devise a self-update strategy for the conformal predictor to ensure the entire system co-evolves consistently throughout the training process. Extensive experiments on six benchmark datasets under both imbalanced and noisy settings demonstrate that our CPSC framework consistently outperforms existing state-of-the-art methods. Our code is available at https://github.com/XunCHN/CPSC.

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates irreducible noise with uncertainty induced by heterogeneous training data (aleatoric), model limitations, or calibration mismatch (epistemic), offering little insight into why an interval is wide or whether it could be reduced. We introduce an uncertainty-aware explainability framework that analyses the reducibility of calibration-induced epistemic conformal uncertainty via progressive calibration localisation for regression tasks. The approach is diagnostic rather than causal: it does not estimate true aleatoric or epistemic uncertainty, but explains how conformal intervals contract and stabilise as calibration support is localised around a test instance. Across benchmarks and real-world data, absolute reducible uncertainty aligns with epistemic proxies, while its relative contribution varies by task, revealing regimes hidden by interval width. This instance-level view complements conformal uncertainty, enhancing interpretability without altering the predictor or coverage.