SMURF: Statistical Modality Uniqueness and Redundancy Factorization.

Multimodal late fusion is a well-performing fusion method that sums the outputs of separately processed modalities, so-called modality contributions, to create a prediction; for example, summing contributions from vision, acoustic, and language to predict affective states. In this paper, our primary goal is to improve the interpretability of what modalities contribute to the prediction in late fusion models. More specifically, we want to factorize modality contributions into what is consistently shared by at least two modalities (pairwise redundant contributions) and what the remaining modality-specific contributions are (unique contributions). Our secondary goal is to improve robustness to missing modalities by encouraging the model to learn redundant contributions. To achieve our two goals, we propose SMURF (Statistical Modality Uniqueness and Redundancy Factorization), a late fusion method that factorizes its outputs into a) unique contributions that are uncorrelated with all other modalities and b) pairwise redundant contributions that are maximally correlated between two modalities. For our primary goal, we 1) verify SMURF's factorization on a synthetic dataset, 2) ensure that its factorization does not degrade predictive performance on eight affective datasets, and 3) observe significant relationships between its factorization and human judgments on three datasets. For our secondary goal, we demonstrate that SMURF leads to more robustness to missing modalities at test time compared to three late fusion baselines.