Paper:
In recent work, it was shown that combining multi-kernel based support vector machines (SVMs) can lead to near state-of-the-art performance on an action recognition dataset (HMDB-51 dataset). In the present work, we show that combining distributed Gaussian Processes with multi-stream deep convolutional neural networks (CNN) alleviate the need to augment a neural network with handcrafted features. In contrast to prior work, we treat each deep neural convolutional network as an expert wherein the individual predictions (and their respective uncertainties) are combined into a Product of Experts (PoE) framework.

Review:
This paper, although titled "Distributed Non-Parametric Deep and Wide Networks", is mostly about fusion of existing models for action recognition on the HMDB51 dataset. The fusion is performed with Gaussian Processes, where each of the i=1,..,4 inspected models (TSN-Inception RGB, TSN-Inception Flow, ResNet-LSTM RGB, ResNet-LSTM Flow) returns a (\mu_i, \sigma_i), which are then combined in a product of experts formulation, optimized w.r.t. maximum likelihood.
At its current form this paper is unfit for submission. First, the novelty of the paper is not clear. It is stated that a framework is introduced for independent deep neural networks. However, this framework, the Gaussian Processes, already exists. Also, it is stated that the method can classify video snippets that have heterogeneity regarding camera angle, video quality, pose, etc. This is something characterizes also all other methods that report similar results on the same dataset. The third claim is that deep networks are combined with non-parameteric Bayesian models. That is a good claim, which is also shared between papers at http://bayesiandeeplearning.org/. The last claim is that model averaging taking into account uncertainty is shown to be useful. That is not true, the only result are the final accuracies per GP model, there is no experiment that directly reports any results regarding uncertainty and its contribution to the final accuracy.
Second, it is not clear that the proposed method is the one responsible for the reported improvements in the experiments. Currently, the training set is split into 7 sets, and each set is used to train 4 models, totalling 28 GP experts. It is unclear what new is learned by the 7 GP expert models for the 7 splits. Why is this better than training a single model on the whole dataset? Also, why is difference bigger between ResNet Fusion-1 and Resnet SVM-SingleKernel?
Third, the method reports results only on a single dataset, HMDB51, which is also rather small. Deriving conclusions from results on a single dataset is suboptimal. Other datasets that can be considered are (mini) Kinetics or Charades.
Forth,  the paper does not have the structure of a scientific publication. It rather looks like an unofficial technical report. There is no related work. The methodology section reads more like a tutorial of existing methods. And the discussion section is larger than any other section in the paper.
All in all, there might be some interesting ideas in the paper, specifically how to integrate GPs with deep nets. However, at the current stage the submission is not ready for publication.