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.

通过使用多假设 dropout 和一种新颖的随机分胜负损失函数，本文提出了一个混合多输出函数 (MoM) 方法，该方法不仅估计均值而且估计假设的方差，并在监督学习和无监督学习问题上实验验证了其性能优越性。

多假设丢弃：多模态输出分布参数估计

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

Ensemble methods are arguably the most trustworthy techniques for boosting
the performance of machine learning models. Popular independent ensembles (IE)
relying on naive averaging/voting scheme have been of typical choice for most
applications involving deep neural networks, but they do not consider advanced
collaboration among ensemble models. In this paper, we propose new ensemble
methods specialized for deep neural networks, called confident multiple choice
learning (CMCL): it is a variant of multiple choice learning (MCL) via
addressing its overconfidence issue.In particular, the proposed major
components of CMCL beyond the original MCL scheme are (i) new loss, i.e.,
confident oracle loss, (ii) new architecture, i.e., feature sharing and (iii)
new training method, i.e., stochastic labeling. We demonstrate the effect of
CMCL via experiments on the image classification on CIFAR and SVHN, and the
foreground-background segmentation on the iCoseg. In particular, CMCL using 5
residual networks provides 14.05% and 6.60% relative reductions in the top-1
error rates from the corresponding IE scheme for the classification task on
CIFAR and SVHN, respectively.

本研究提出一种针对深度神经网络的新型集成学习方法，名为自信多选学习（CMCL），通过解决其过度自信的问题来提高模型的性能，CMCL 比独立集成方法在图像分类和前景 - 背景分割等任务中提高了显著的准确率。