Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal
  Output Distributions
David D. Nguyen David Liebowitz Surya Nepal Salil S. Kanhere
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.