  Multimodal regression is a fundamental task, which integrates the information
from different sources to improve the performance of follow-up applications.
However, existing methods mainly focus on improving the performance and often
ignore the confidence of prediction for diverse situations. In this study, we
are devoted to trustworthy multimodal regression which is critical in
cost-sensitive domains. To this end, we introduce a novel Mixture of
Normal-Inverse Gamma distributions (MoNIG) algorithm, which efficiently
estimates uncertainty in principle for adaptive integration of different
modalities and produces a trustworthy regression result. Our model can be
dynamically aware of uncertainty for each modality, and also robust for
corrupted modalities. Furthermore, the proposed MoNIG ensures explicitly
representation of (modality-specific/global) epistemic and aleatoric
uncertainties, respectively. Experimental results on both synthetic and
different real-world data demonstrate the effectiveness and trustworthiness of
our method on various multimodal regression tasks (e.g., temperature prediction
for superconductivity, relative location prediction for CT slices, and
multimodal sentiment analysis).
