Paper: A Effective Variance Change Detection Method under constantly Changing Mean (ICLR-2024)

Reviewer comment (Novelty):
This article lacks novelty and is an improvement on the Gao19 method. The mean estimation method and variance change point detection method, as well as the experimental design, are the same as the Gao19 method.

Author response:
The method presented in this paper focuses more on methods rather than theoretical. Besides, we integrated the dual control window structures into the method of Gao et al. (2019) to sufficiently narrow down the detection range of the variance change points. Therefore, all the theoretical properties of Gao et al. (2019) still apply to our method. To conduct a fair comparison, we reproduced the data analysis experiments in Gao19 to illustrate that our proposed method has obvious improvement in both simulation and application.

Reviewer comment (Evaluation):
Using the dual control window only speeds up the computation time by 40%, but incurs quite significant estimation bias compared to the result in Gao et al. (2019), as shown in the application section.

Author response:
The application is an unsupervised learning environment; we cannot tell which method provided more accurate results. However, as we have motioned in this paper, our proposed algorithm discovers more earlier deteriorated change points distributed around 12 hours than Gao19. Therefore, our detection results are more consistent with the biological and biomedical conclusions. page8.

Reviewer comment (Writing):
The algorithm for dual control windows is not well described and the details are a bit confusing, e.g. regarding the iterations over data profile index m and the iteration j in Algorithm 1.

Author response:
I have rearranged the expression of Algorithm 1. page4;

Reviewer comment (Theory):
The test statistic \Delta_n is shown in Gao et al. (2019) to asymptotically follow an extreme value distribution, which is how a rejection criterion can be chosen with control of the type I error. This is not included in this paper, and the proposed rejection criterion in section 2.4 could have a really high type I error.

Author response:
This is a very good question. We conducted additional simulation studies for type-I error, the results is updated in the Appendix-B. From Table-2, we see that the empirical sizes of the test are smaller than the levels of the test indicating that the test is a bit more conservative than expected in claiming a change point when there is no change point. The reason is that the asymptotic null distribution is a heavy-tailed extreme value distribution and may require a larger sample size to achieve the desired size of the hypothesis test.

Reviewer comment (Theory):
As discussed in section 2.1, the objective (1) doesn't have a global minimizer since \sigma and \delta can go all the way to infinity, so only a local minimizer is searched for. While I am aware that the same objective is used in Gao et al. (2019), I wonder why not to use the objective taking the form of penalized log-likelihood of a Gaussian model, such that \log\det(\Sigma) is added to the objective and global minimizers now exist?

Author response:
This is a very good question. My team is actually working on this direction. But it has not been done because the algorithm is more complex, and hopefully we can report this in the near future. On the other hand, we should also emphasize that the current results are already very good.

Reviewer comment (Presentation):
If there are other contributions, the authors should better highlight them.

Author response:
The method presented in this paper integrated the dual control window structures into the method of Gao et al. (2019). The proposed method sufficiently narrowed down the detection range of the variance change points, which significantly improved the change detection efficiency and accuracy.

Reviewer comment (Experiments):
Thanks to the proposed approach, the processing time of a thermal image of a porcine liver decreases from 1h to 30 minutes. I cannot tell if this improvement is significant as I am unfamiliar with this application. If 30 minutes is an acceptable execution time, could it be obtained by simply parallelizing the current algorithm? Since each pixel of the thermal video is processed independently, a 3x or 4x speed-up is expected on a personal laptop.

Author response:
As mentioned in the first paragraph of this paper, in an organ transplantation operation, both doctors and patients are racing against time. Even 30 seconds is a luxury, not to mention 30 minutes. If we run our proposed method and Gao19 method together on the same computer, ours is constantly faster than Gao 19.

Reviewer comment (Novelty):
It is not clear to me if the variance change point detection procedure (Section 2.4) is a contribution of this work. Can you clarify?

Author response:
The variance change point detection procedure is the step-A of our proposed algorithm, page4;

Reviewer comment (Experiments):
The new algorithm seems more accurate because the candidate change points are restricted to a window. This can prevent false detection on the edges of the signal. How is your method better than a post-processing of the change-points of Gao19 (e.g., by computing a window on the results of Gao19)?

Author response:
The method presented in this paper integrated the dual control window structures into the method of Gao et al. (2019). The proposed method sufficiently narrowed down the detection range of the variance change points, which significantly improved the change detection efficiency and accuracy.

Reviewer comment (Theory):
L124: "Large sample size will slow down the computational speed." This statement is vague. You could provide the computational complexity, for instance.

Author response:
Thanks for your question. 
1. The numerical studies in this paper (pape 7, Table-1) provided the evidence of high efficiency of our method. Generally our method reduced 40%~45% of computational time than Gao19. 
2. The computational complexity of the variance change detection procedure (Step-A in Algorithm-1) is O((log n)^4(log log n)^2), and is O(n^3) for the mean estimation procedure (Step-2.2 and Step-A in Algorithm-1) (For more details of the relative theoretical properties please see Kim&Gu 2004 and Gao et al. 2019). Sufficient reduction in sample size will increase the computational efficiency significantly.

Reviewer comment (Reproducibility):
How are the initial change-points estimated at the beginning of the algorithm (Step 1)?

Author response:
revised and marked in blue, page4;

Reviewer comment (Writing):
"Equation 1" instead of "equation 1".

Author response:
revised and marked in blue, second paragraph on page3;

Reviewer comment (Writing):
Typo L251.

Author response:
revised;

Reviewer comment (Writing):
Typo L178.

Author response:
revised;

Reviewer comment (Writing):
Typo L113.

Author response:
revised;

Reviewer comment (Writing):
Typo L116-117.

Author response:
revised;

Reviewer comment (Writing):
More typos.

Author response:
revised;