Neural Causal Discovery with Learnable Input Noise
Learning causal relations from observational time series with nonlinear interactions and complex causal structures is a key component of human intelligence, and has a wide range of applications. Although neural nets have demonstrated their effectiveness in a variety of fields, their application in learning causal relations has been scarce. This is due to both a lack of theoretical results connecting risk minimization and causality (enabling function approximators like neural nets to apply), and a lack of scalability in prior causal measures to allow for expressive function approximators like neural nets to apply. In this work, we propose a novel causal measure and algorithm using risk minimization to infer causal relations from time series. We demonstrate the effectiveness and scalability of our algorithms to learn nonlinear causal models in synthetic datasets as comparing to other methods, and its effectiveness in inferring causal relations in a video game environment and real-world heart-rate vs. breath-rate and rat brain EEG datasets.
 In the manuscript entitled "Neural Causal Discovery with Learnable Input Noise" the authors describe a method for automated causal inference under the scenario of a stream of temporally structured random variables (with no missingness and a look-back window of given size). The proposed approach combines a novel measure of the importance of fidelty in each variable to predictive accuracy of the future system state ("learnable noise risk") with a flexible functional approximation (neural network). Although the setting (informative temporal data) is relatively restricted with respect to the general problem of causal inference, this is not unreasonable given the proposed direction of application to automated reasoning in machine learning. The simulation and real data experiments are interesting and seem well applied. A concern I have is that the manuscript as it stands is positioned somewhere between two distinct fields (sparse learning/feature selection, and causal inference for counterfactual estimation/decision making), but doesn*t entirely illustrate its relationship to either. In particular, the derived criterion is comparable to other sparsity-inducing penalities on variable inclusion in machine learning models; although it has motivation in causality it is not exclusively derived from this position, so one might wonder how alternative sparsity penalities might perform on the same challenge. Likewise, it is not well explained what is the value of the learnt relationships, and how uncertainty and errors in the causal learning are relevant to the downstream use of the learnt model. In the ordinary feature selection regime one is concerned simply with improving the predictive capacity of models: e.g. a non-linear model might be fit using just the causal variables that might out-perform both a linear model and a non-linear model fit using all variables. Here the end goal is less clear; this is understandable in the sense that the work is positioned as a piece in a grand objective, but it would seem valuable to nevertheless describe some concrete example(s) to elucidate this aspect of the algorithm (use case / error effects downstream).
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Neural Causal Discovery with Learnable Input Noise
Learning causal relations from observational time series with nonlinear interactions and complex causal structures is a key component of human intelligence, and has a wide range of applications. Although neural nets have demonstrated their effectiveness in a variety of fields, their application in learning causal relations has been scarce. This is due to both a lack of theoretical results connecting risk minimization and causality (enabling function approximators like neural nets to apply), and a lack of scalability in prior causal measures to allow for expressive function approximators like neural nets to apply. In this work, we propose a novel causal measure and algorithm using risk minimization to infer causal relations from time series. We demonstrate the effectiveness and scalability of our algorithms to learn nonlinear causal models in synthetic datasets as comparing to other methods, and its effectiveness in inferring causal relations in a video game environment and real-world heart-rate vs. breath-rate and rat brain EEG datasets.
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>



 In the manuscript entitled "Neural Causal Discovery with Learnable Input Noise" the authors describe a method for automated causal inference under the scenario of a stream of temporally structured random variables (with no missingness and a look-back window of given size). The proposed approach combines a novel measure of the importance of fidelty in each variable to predictive accuracy of the future system state ("learnable noise risk") with a flexible functional approximation (neural network). Although the setting (informative temporal data) is relatively restricted with respect to the general problem of causal inference, this is not unreasonable given the proposed direction of application to automated reasoning in machine learning. The simulation and real data experiments are interesting and seem well applied. A concern I have is that the manuscript as it stands is positioned somewhere between two distinct fields (sparse learning/feature selection, and causal inference for counterfactual estimation/decision making), but doesn*t entirely illustrate its relationship to either. In particular, the derived criterion is comparable to other sparsity-inducing penalities on variable inclusion in machine learning models; although it has motivation in causality it is not exclusively derived from this position, so one might wonder how alternative sparsity penalities might perform on the same challenge. Likewise, it is not well explained what is the value of the learnt relationships, and how uncertainty and errors in the causal learning are relevant to the downstream use of the learnt model. In the ordinary feature selection regime one is concerned simply with improving the predictive capacity of models: e.g. a non-linear model might be fit using just the causal variables that might out-perform both a linear model and a non-linear model fit using all variables. Here the end goal is less clear; this is understandable in the sense that the work is positioned as a piece in a grand objective, but it would seem valuable to nevertheless describe some concrete example(s) to elucidate this aspect of the algorithm (use case / error effects downstream).
assistant
 In the manuscript entitled "Neural Causal Discovery with Learnable Input Noise" the authors describe a method for automated causal inference under the scenario of a stream of temporally structured random variables (with no missingness and a look-back window of given size). The proposed approach combines a novel measure of the importance of fidelty in each variable to predictive accuracy of the future system state ("learnable noise risk") with a flexible functional approximation (neural network). Although the setting (informative temporal data) is relatively restricted with respect to the general problem of causal inference, this is not unreasonable given the proposed direction of application to automated reasoning in machine learning. The simulation and real data experiments are interesting and seem well applied. A concern I have is that the manuscript as it stands is positioned somewhere between two distinct fields (sparse learning/feature selection, and causal inference for counterfactual estimation/decision making), but doesn*t entirely illustrate its relationship to either. In particular, the derived criterion is comparable to other sparsity-inducing penalities on variable inclusion in machine learning models; although it has motivation in causality it is not exclusively derived from this position, so one might wonder how alternative sparsity penalities might perform on the same challenge. Likewise, it is not well explained what is the value of the learnt relationships, and how uncertainty and errors in the causal learning are relevant to the downstream use of the learnt model. In the ordinary feature selection regime one is concerned simply with improving the predictive capacity of models: e.g. a non-linear model might be fit using just the causal variables that might out-perform both a linear model and a non-linear model fit using all variables. Here the end goal is less clear; this is understandable in the sense that the work is positioned as a piece in a grand objective, but it would seem valuable to nevertheless describe some concrete example(s) to elucidate this aspect of the algorithm (use case / error effects downstream).