  Fusing data from multiple modalities provides more information to train
machine learning systems. However, it is prohibitively expensive and
time-consuming to label each modality with a large amount of data, which leads
to a crucial problem of semi-supervised multi-modal learning. Existing methods
suffer from either ineffective fusion across modalities or lack of theoretical
guarantees under proper assumptions. In this paper, we propose a novel
information-theoretic approach, namely \textbf{T}otal \textbf{C}orrelation
\textbf{G}ain \textbf{M}aximization (TCGM), for semi-supervised multi-modal
learning, which is endowed with promising properties: (i) it can utilize
effectively the information across different modalities of unlabeled data
points to facilitate training classifiers of each modality (ii) it has
theoretical guarantee to identify Bayesian classifiers, i.e., the ground truth
posteriors of all modalities. Specifically, by maximizing TC-induced loss
(namely TC gain) over classifiers of all modalities, these classifiers can
cooperatively discover the equivalent class of ground-truth classifiers; and
identify the unique ones by leveraging limited percentage of labeled data. We
apply our method to various tasks and achieve state-of-the-art results,
including news classification, emotion recognition and disease prediction.
