Measuring causal influence with back-to-back regression: the linear case
Identifying causes from observations can be particularly challenging when i) potential factors are difficult to manipulate individually and ii) observations are complex and multi-dimensional. To address this issue, we introduce “Back-to-Back” regression (B2B), a method designed to efficiently measure, from a set of co-varying factors, the causal influences that most plausibly account for multidimensional observations. After proving the consistency of B2B and its links to other linear approaches, we show that our method outperforms least-squares regression and cross-decomposition techniques (e.g. canonical correlation analysis and partial least squares) on causal identification. Finally, we apply B2B to neuroimaging recordings of 102 subjects reading word sequences. The results show that the early and late brain representations, caused by low- and high-level word features respectively, are more reliably detected with B2B than with other standard techniques.
This paper proposes *Back-to-Back* regression for estimating the causal influence between X and Y in the linear model Y=(XE+N)F, where the E denotes a diagonal matrix of causal influences. Furthermore, this work theoretically shows the consistency of B2B and the experiments also verify the effectiveness of this approach. The writing is well and clear and there are some minors issues: - Further analysis and explanation for using hat{E}=Diag(H)to estimate the causal influence might be needed. - The model defined in Fig. 1 seems the influence E should have a sparse diagonal vector. It is possible to introduce an L1 regulation in E? ############## After reading the author*s feedback and the comments from other reviewers, I keep the current rating but tend to a borderline score and it is ok if it must be rejected because of the concerns of limited applicability and the experimental.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Measuring causal influence with back-to-back regression: the linear case
Identifying causes from observations can be particularly challenging when i) potential factors are difficult to manipulate individually and ii) observations are complex and multi-dimensional. To address this issue, we introduce “Back-to-Back” regression (B2B), a method designed to efficiently measure, from a set of co-varying factors, the causal influences that most plausibly account for multidimensional observations. After proving the consistency of B2B and its links to other linear approaches, we show that our method outperforms least-squares regression and cross-decomposition techniques (e.g. canonical correlation analysis and partial least squares) on causal identification. Finally, we apply B2B to neuroimaging recordings of 102 subjects reading word sequences. The results show that the early and late brain representations, caused by low- and high-level word features respectively, are more reliably detected with B2B than with other standard techniques.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper proposes *Back-to-Back* regression for estimating the causal influence between X and Y in the linear model Y=(XE+N)F, where the E denotes a diagonal matrix of causal influences. Furthermore, this work theoretically shows the consistency of B2B and the experiments also verify the effectiveness of this approach. The writing is well and clear and there are some minors issues: - Further analysis and explanation for using hat{E}=Diag(H)to estimate the causal influence might be needed. - The model defined in Fig. 1 seems the influence E should have a sparse diagonal vector. It is possible to introduce an L1 regulation in E? ############## After reading the author*s feedback and the comments from other reviewers, I keep the current rating but tend to a borderline score and it is ok if it must be rejected because of the concerns of limited applicability and the experimental.
assistant
This paper proposes *Back-to-Back* regression for estimating the causal influence between X and Y in the linear model Y=(XE+N)F, where the E denotes a diagonal matrix of causal influences. Furthermore, this work theoretically shows the consistency of B2B and the experiments also verify the effectiveness of this approach. The writing is well and clear and there are some minors issues: - Further analysis and explanation for using hat{E}=Diag(H)to estimate the causal influence might be needed. - The model defined in Fig. 1 seems the influence E should have a sparse diagonal vector. It is possible to introduce an L1 regulation in E? ############## After reading the author*s feedback and the comments from other reviewers, I keep the current rating but tend to a borderline score and it is ok if it must be rejected because of the concerns of limited applicability and the experimental.