Multiple modalities often co-occur when describing natural phenomena. Learning a joint representation of these modalities should yield deeper and more useful representations. Previous work have proposed generative models to handle multi-modal input. However, these models either do not learn a joint distribution or require complex additional computations to handle missing data. Here, we introduce a multimodal variational autoencoder that uses a product-of-experts inference network and a sub-sampled training paradigm to solve the multi-modal inference problem. Notably, our model shares parameters to efficiently learn under any combination of missing modalities, thereby enabling weakly-supervised learning. We apply our method on four datasets and show that we match state-of-the-art performance using many fewer parameters. In each case our approach yields strong weakly-supervised results. We then consider a case study of learning image transformations---edge detection, colorization, facial landmark segmentation, etc.---as a set of modalities. We find appealing results across this range of tasks.
It is easy for people to imagine what a man with pink hair looks like, even if they have never seen such a person before. We call the ability to create images of novel semantic concepts visually grounded imagination. In this paper, we show how we can modify variational auto-encoders to perform this task. Our method uses a novel training objective, and a novel product-of-experts inference network, which can handle partially specified (abstract) concepts in a principled and efficient way. We also propose a set of easy-to-compute evaluation metrics that capture our intuitive notions of what it means to have good visual imagination, namely correctness, coverage, and compositionality (the 3 C's). Finally, we perform a detailed comparison of our method with two existing joint image-attribute VAE methods (the JMVAE method of Suzuki this http URL. and the BiVCCA method of Wang this http URL.) by applying them to two datasets: the MNIST-with-attributes dataset (which we introduce here), and the CelebA dataset.