Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper designs a generalized autoregression method (GAR) and its efficient implementation CIGAR to deal with non-structured high-dimensional outputs and non-subset multi-fidelity data. The result shows their method outperforms the baselines among several benchmarks at the highest fidelity level.
strengths_and_weaknesses: Strengths:
Well-written paper in general.
Include 5 experiments. 2 with real-world data.

Weaknesses: 
My main concern about the paper is its novelty. Although the author didn't overclaim their contributions "Generalization of the AR for arbitrary non-structured high-dimensional outputs" and "Generalization to non-subset multi-fidelity data for the AR", which are all for the classic autoregression model specifically. But there's existing non-AR work [1] that is able to handle both non-structured high-dimensional outputs and non-subset multi-fidelity data [1] besides MF-BNN.

[1] Wu, Dongxia, et al. "Multi-fidelity Hierarchical Neural Processes." arXiv preprint arXiv:2206.04872 (2022).

Besides, there's no big improvement between the proposed method and baselines (MF-BNN, ResGP) for some of the experiments. Only one metric RMSE is evaluated. 
questions: The paper mentioned uncertainty quantification. But why there's no evaluation of uncertainty quantification for experiments? It will be great if the author could include other metrics for accuracy (negative log-likelihood) and uncertainty quantification (Continuous Ranked Probability Score [1] or mean interval score [1,2]).

[1] Gneiting, Tilmann, and Adrian E. Raftery. "Strictly proper scoring rules, prediction, and estimation." Journal of the American statistical Association 102.477 (2007): 359-378.
[2] Wu, Dongxia, et al. "Quantifying uncertainty in deep spatiotemporal forecasting." arXiv preprint arXiv:2105.11982 (2021).

limitations: No potential negative societal impact I can see.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The authors here present a generalized autoregressive model to conduct multi-fidelity prediction on data with high-dimensional outputs via tensor decomposition. A different non-subset multi-fidelity data setting is explored. Based on autokrigeability, a more efficient implementation is proposed.
strengths_and_weaknesses: Strength:
1)	Problems are clearly stated and addressed. 
2)	The non-subset data scenario is addressed here for the first time.
3)	Tensor GP is applied here to reflect possible underlying structures of the data.
Weakness:
1)	The notations are a bit confusing, like Z, F and their subscripts.
2)	Sparse variational inference might further improve the inference efficiency here.

questions: 1. How do you decide the size of the tensor? 
limitations: N/A
review_title: null

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The authors proposed Generalized Autoregression (GAR) to handle high-dimensional outputs for multi-fidelity fusion problems. GAR is a GP-based approach that employed tensor algebra to efficiently model covariances across the high dimensions. To handle situations where high fidelity data is not a subset of low fidelity data, they propose a latent variable approach and with a simple trick they proposed CIGAR, which is a computational more efficient version of GAR.

Experiments of GAR and CIGAR showed promising results compared to SOTAs. 
strengths_and_weaknesses: Strengths:
- clear and thorough comparison of GAR with existing methods in sec.4 
- exact solutions are obtainable (when subset data exists)
- although tensor algebra papers tend to be tedious to read, the authors defined the notations clearly and communicated effectively between equations.
- the problem is clearly defined, and worthwhile contribution to handle high dim output multi fidelity fusion problem. 

Weakness:
- there are some typos around, e.g. line 38 there is a 1. after citation [9], or in line 55 the word "Problems" is capitalised, but these do not affect the reading experience at all.
- seems to only work for regression problems for now - if non-gaussian likelihood is needed, not sure how straight forward it is to translate the whole tensor algebra business to that. Worth mentioning in the paper a bit as well I guess? Nonetheless, focusing on regression data is a worthwhile contribution already in my opinion.

questions: The idea of using imaginary variables to match "missing" data seems very similar to the use of inducing variables in sparse GPs, can you comment a bit on that? 
limitations: Currently only works for Gaussian likelihood. Not sure how straight forward or not it might be to generalised to arbitrary likelihood in high dimensinoal output space.
review_title: null

Meta-review: metareview: This paper considers the problem of multi-fidelity fusion using generalized autoregression. The authors especially take on problems such as high-dimensionality and non-subsetness with this approach. The reviewers agree that the paper is well written and makes a significant contribution to MF-fusion. I recommend acceptance and strongly encourage the authors to take the reviewer comments into account in preparing the final manuscript. 
confidence: Certain
Decision: Accept