This paper proposes a new GP-based method to handle real-world signals that are non-stationary, multi-task, multi-fidelity, and multi-resolution. The main proposals are two versions based on a shallow-GP and deep-GPs. The idea is to use a composite likelihood based approach to be able to handle such signals. All reviewers find the problem relevant and the solutions also useful. Experiments are done reasonably well, although there are some recommendations (eg from R3). There is a serious concern from R4 on the effectiveness of the composite likelihood. The paper is not written for non-experts, e.g., I consider myself an expert on GPs but not very familiar with GP-RN, and I am unable to follow the papers. It takes a few iterations to understand the details. This has also been pointed out by R1. The opinion of the paper has generally improved after the rebuttal and reviewers have increased their scores. The paper is still borderline but can be acceptable. I will encourage the authors to improve aspects of the paper to have a bigger impact, otherwise this paper might only be accessible to a narrow audience. I will give an accept to this paper for now, and hope that the authors will improve the paper taking the reviewers feedback into account.