All reviewers are positive or very positive about the paper and most reviewers were satisfied by the authors reponse. This is a clear accept. I however encourage the authors to take into account the reviewers comments to improve their paper, especially the (unanswered) issues raised by reviewer 4.

Stigma has emerged as one of the major obstacles to effectively diagnosing depression, as it prevents users from open conversations about their struggles. This requires advanced questioning skills to carefully probe the presence of specific symptoms in an unobtrusive manner. While recent efforts have been made on depression-diagnosis-oriented dialogue systems, they largely ignore this problem, ultimately hampering their practical utility. To this end, we propose a novel and effective method, UPSD$^{4}$, developing a series of strategies to promote a sense of unobtrusiveness within the dialogue system and assessing depression disorder by probing symptoms. We experimentally show that UPSD$^{4}$ demonstrates a significant improvement over current baselines, including unobtrusiveness evaluation of dialogue content and diagnostic accuracy. We believe our work contributes to developing more accessible and user-friendly tools for addressing the widespread need for depression diagnosis.

Additional Feedback: The paper is not interesting enough for a competitive conference. It is good to have these results in the literature, but I suggest to send it to a journal. Having read the reviews, and following the discussion, I still think that this does not below in a competitive conference. Indeed, as the authors stress in their response, the power of the result is due to the specific algorithm developed here. Nevertheless, I cannot be excited by it, given the monotonicity assumption and the fact that it applies only to the uniform distribution setting. I agree that it's an interesting result, but I think that it's not interesting enough nor important enough for a top conference.

The submission got four reviews that were quite polarised in their recommendations, with two against accepting and two strongly in favour. The disagreement did not concern the technical quality of the paper. The reviewers agree that the theoretical work in this paper has been very competently performed and in the context of the problem the authors consider, the results are interesting and advance the state of the art. The disagreement is over whether the results are significant enough for NeurIPS or would be more appropriate for a specialised theory conference. The main objections against accepting are (i) the results are not surprising, (ii) the assumptions (monotonicity and uniform distribution) are strong and (iii) the overall computational complexity is high.

UPDATE: Thank you for the thoughtful response, those changes should improve the things that were unclear to me. There is a rich recent literature on identification criteria for linear structural causal models, but most of the recently proposed criteria largely ignore the question of efficient computability. This paper answers important questions in this area by given efficient algorithms for some criteria, while showing others to be NP-complete. The paper is original and generally clear and of high quality. Minor comments: l100: double "a" l104: the equation you refer to is in the supplement, which should be mentioned here.

The paper proposes a method to efficiently find instrumental subsets for identification in linear acyclic SCMs. The reviewers think that the method is interesting and relevant. An improvement to its evaluation would be the addition of an experimental section -- the authors indicated that they will add it in the revised version of the paper.

Clarity: The main paper is mostly written fairly well, the Appendix less so (lots of typos at least). The work nevertheless lacks clarity because several relevant details are moved to the Supplementary part, and some aspects are not mentioned at all (at least in the main paper). The Appendix even contains a section regarding categorical features that is not even hinted at in the main paper. Clarification is needed, e.g., at the following points: - p.2, l.70-73 is too vague, the meaning is unclear - pls. clarify - p.2, l. 85f: clarify what "[...] i enters leaf node l " means (i.e., that data pt. If \hat{y}_i denotes a predicted label, then why is it real-valued and not in [Y]? (Also regarding the description on p.3, l.96f: why should y_i - \hat{y}_i \geq 1 here -- \hat{y}_i is in R, so couldn't it be, say, y_i - delta for some small delta?) - p.3, l.92: perhaps clarify "tree sparsity" -- actually here this means sparsity of the decision hyperplanes, no the tree itself - The 1-norm is used in the MIP (1) and several times in the text later called "linear" (e.g., p.4, l.136), but this is technically incorrect.

This paper is about employing advances in computational efficiency of mixed integer programming methods towards decision tree construction problems. While locally optimal methods can achieve an upper bound on the minimization problem efficiently, closing the optimality gap requires tight lower bounds. The authors use an interval relaxation and a support-vector machine procedure to tighten the lower bound. To scale the algorithm, the authors use a LP-based data selection procedure, and perform all experiments using this procedure. It is not clear whether the global optimality properties of the MIP formulation carry through with the data-selection procedure.

POST REBUTTAL -- I have read the authors' responses and other reviewers' comments. Unfortunately, some of my primary concerns have not been addressed, which I will elaborate on below. This paper studies the implementation of Pearl's in a SCM, where each of its functions is represented as a neural network. The authors claim that the proposed approaches "are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals giving rise to a powerful new approach for answering causal questions in imaging applications and beyond." However, I believe the significance of its contributions to the causal inference literature is a bit overstated. In particular, the authors assume that detailed parameterization of the target SCM is *precisely known*.

The reviewers agree on the whole that this work addresses an important problem and that the paper makes sound, well-supported claims. The rebuttal did a good job at clarifying the scope of their work, largely improving the scores of the reviewers. I urge the authors to carefully update the paper to address the reviewers concerns in the final version. Examples of what to improve include: - Description of the "intervention vs counterfactual" distinction. One reviewer recommends: "since it is key for the paper's novelty claim I think this distinction needs a little more explanation, perhaps through a simple example" - Engage with the existing literature on causal inference.