Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal Output Distributions

In many real-world applications, from robotics to pedestrian trajectory prediction, there is a need to predict multiple real-valued outputs to represent several potential scenarios. Current deep learning techniques to address multiple-output problems are based on two main methodologies: (1) mixture density networks, which suffer from poor stability at high dimensions, or (2) multiple choice learning (MCL), an approach that uses $M$ single-output functions, each only producing a point estimate hypothesis. This paper presents a Mixture of Multiple-Output functions (MoM) approach using a novel variant of dropout, Multiple Hypothesis Dropout. Unlike traditional MCL-based approaches, each multiple-output function not only estimates the mean but also the variance for its hypothesis. This is achieved through a novel stochastic winner-take-all loss which allows each multiple-output function to estimate variance through the spread of its subnetwork predictions. Experiments on supervised learning problems illustrate that our approach outperforms existing solutions for reconstructing multimodal output distributions. Additional studies on unsupervised learning problems show that estimating the parameters of latent posterior distributions within a discrete autoencoder significantly improves codebook efficiency, sample quality, precision and recall.