From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper11/Authors
comment: As per the recommendations, in the future iteration we are very interested in making the connection with the state-of-the-art machine learning research, such as convolutional neural network architectures. As we mentioned, the graph signal stationarity testing is an interesting avenue of research that we plan to continue in a future iteration of this article, including both further theoretical research and experiments. 

For the camera ready workshop version we:
- included a sensitivity analysis and recommendations for frame length selection.
- moved paragraph 32 to the conclusion as suggested.
- included (in Section 1) the suggested expansion on motivation from reviewers comments 1 and 2, as well as a reference to learning convolutional neural networks as suggested in the last paragraph. We however plan to expand on this last topic in a future version of the article, including experiments.

Next we are providing a response to the question regarding why we have decided to use the second order to derive the test and if we considered using the trispectrum.

In this article we are using the 2nd order cumulant spectrum to derive a test for strict stationarity. In the ’94 referenced article “Higher order cumulants and cumulant spectra” the relationship between higher order cumulant spectra and polyspectra under strict stationarity was derived as: Cum(f/N)=delta(f1+f2+..+fN)S(f(N-1)), where delta(f) is the Dirac delta function and the cumulant spectra and polyspectra definitions are given in the same article. In our article we use the case with N=2 and the relationship between the second order cumulant spectrum Cum(f/2) or Cum2 and the first order polyspectrum, or the spectrum, S(f). The spectrum is assumed 1 at all frequencies after whitening of the series, which leads to further simplifications (the standard error of the Cum2 estimate assumes a convenient form). With N=4, one can presumably use the relationship between the 4th order cumulant spectrum Cum(f/4) and the third order polyspectrum, the trispectrum, S(f(4-1)). However, the theoretical derivation and computational complexity would be higher than in the Cum2 case and we do not plan to include an N=4 derivation at this time. 

We again thank the reviewer for their helpful remarks.
title: From the authors: we thank you the reviewer for the very helpful comments and excellent recommendations.

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper11/AnonReviewer1
evaluation: The authors present a rigorous approach to test strict sense stationarity with interesting results. While relevance to this workshop may be a little low, it will be quite interesting for the general NIPS audience.

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper11/AnonReviewer1
relevance: 2: low
impact: 4: high
novelty: 4: high

From: ~Ransalu_Senanayake1
comment: This paper proposes a test to determine the strict stationary of a discrete-time stochastic process in the frequency domain with the aim of extending to graph signals. To do this, the second-order cumulant spectrum is used (the time series is strictly stationary, if this value is zero for all pairs of frequencies). The paper also provides an analysis of the statistical power/sample size. Indicating the potential to use in practice, the paper concludes with an application.

Although the paper is well-written, it should be well-motivated in order to be accessible for the NIPS community. Specifically,
1. Why determining the strict stationary is useful and why it is a hard problem should be discussed.
2. What is graph signal processing and why is it important? It is always a good idea to start the paper with a broad motivation and then narrow down to highlight the specific problem at hand.

This reviewer is wondering how the length L affects the test and how it is determined. I would like to see a sensitivity analysis. 

It is not clear why the 2nd order is particularly important in this case. Isn't the 3rd order easier to compute? Do you have any plans to use trispectrum?

Authors might consider moving the paragraph in line 32 to the conclusion. It is not clear how the method would extend to graph signals. The paper should be extended with more experiments.

As a general comment, considering the fact that the majority of the young researchers in the NIPS community is less familiar with the DSP techniques and frequentists hypothesis testing, in order to better engage, I would highly recommend making connections with the state-of-the-art machine learning research whether it is of something interest of the authors or not. In particular, the convolution (and convolutional neural network architectures) and RKHS literature on graphs and manifolds is abundant. On the other hand, since the nonstationarity has various notions in the machine learning literature (nonstationarity of data in deep learning, nonstationary RKHS kernels, etc.) the community might confuse with some of the terminologies. These are just recommendations. 
title: From: NIPS 2018 Workshop Spatiotemporal Paper11 AnonReviewer3