Multimodal relational data analysis has become of increasing importance in recent years, for exploring across different domains of data, such as images and their text tags obtained from social networking services (e.g., Flickr). A variety of data analysis methods have been developed for visualization; to give an example, t-Stochastic Neighbor Embedding (t-SNE) computes low-dimensional feature vectors so that their similarities keep those of the observed data vectors. However, t-SNE is designed only for a single domain of data but not for multimodal data; this paper aims at visualizing multimodal relational data consisting of data vectors in multiple domains with relations across these vectors. By extending t-SNE, we herein propose Multimodal Relational Stochastic Neighbor Embedding (MR-SNE), that (1) first computes augmented relations, where we observe the relations across domains and compute those within each of domains via the observed data vectors, and (2) jointly embeds the augmented relations to a low-dimensional space. Through visualization of Flickr and Animal with Attributes 2 datasets, proposed MR-SNE is compared with other graph embedding-based approaches; MR-SNE demonstrates the promising performance.

Bayesian Neural Networks with Latent Variables (BNN+LV's) provide uncertainties in prediction estimates by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between model parameters and input noise while fitting the data equally well. We demonstrate that, as a result, traditional inference methods may yield parameters that reconstruct observed data well but generalize poorly. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real datasets.