Modal Uncertainty Estimation via Discrete Latent Representations

Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we propose a novel deep learning based framework, named {\it modal uncertainty estimation} (MUE), to learn the one-to-many mappings between the inputs and outputs, together with faithful uncertainty estimation. Motivated by the multi-modal posterior collapse problem in current conditional generative models, MUE uses a set of discrete latent variables, each representing a latent mode hypothesis that explains one type of input-output relationship, to generate the one-to-many mappings. Benefit from the discrete nature of the latent representations, MUE can estimate any input the conditional probability distribution of the outputs effectively. Moreover, MUE is efficient during training since the discrete latent space and its uncertainty estimation are jointly learned. We also develop the theoretical background of MUE and extensively validate it on both synthetic and realistic tasks. MUE demonstrates (1) significantly more accurate uncertainty estimation than the current state-of-the-art, and (2) its informativeness for practical use.