Title: Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables
Venue: NeurIPS 2025
Accepted: yes
Keywords: Causal Effect

Covariate Selection

Latent Variables

Local Learning

Causal Discovery
Abstract: Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global causal structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nCausal effect estimation is a fundamental problem in many domains, such as epidemiology, economics, and political science. One popular method for causal effect estimation is known as backdoor adjustment. The challenge with backdoor adjustment, however, is that it may not always be clear which variables constitute a valid backdoor adjustment set. The authors propose a new method known as LSAS that improves upon known methods in the literature, most notably in time complexity. Through synthetic simulations and an analysis on a real-world dataset, the authors demonstrate the effectiveness and improvements of their method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\nA major strength of this paper is its clarity of writing. The literature review is comprehensive, and it is easy to follow the authors’ claims and their examples. All major claims are supported by theoretical proofs and simulation studies.\n\nThe key insight of this paper is that, for the purposes of learning a valid covariate adjustment set, one only needs to look at the Markov blankets of $X$ and $Y$ because, as the authors prove, there is a valid adjustment set amongst all of the observed variables if and only if there is a valid adjustment set amongst the Markov blankets of $X$ and $Y$. When the number of potential confounders is large, reducing the search space to just the Markov blankets can result in huge improvements in efficiency. This insight is, to the best of my knowledge, not previously known in the literature. The rest of the paper then uses this insight and known methods, most notably an efficient algorithm for learning the Markov blanket of a variable, to develop their method and algorithm.\n\nThe simulation studies clearly show how the authors’ method improves upon current methods with respect to run-time without sacrificing accuracy with respect to estimation of the causal effect.\n\nWeaknesses\n\nI have no major complaints regarding this paper.\n\nQUESTIONS:\nIn your definition for a maximal ancestral graph, is that the same as an acyclic directed mixed graph (ADMG)? Further, what is an “almost directed cycle” in lines 90-91?\n\nTheorems 2,3, and 4 are nearly exactly the same as the inference rules and Theorems 2 and 3 presented in Entner et al. (2013). Is there a specific reason why the authors did not cite Entner et al. (2013) when presenting these three theorems? It seems to me that the proofs of Theorems 2, 3, and 4 should follow in a fairly straightforward manner from the proofs in Entner et al. (2013) once Theorem 1 is established. I believe that it is important to cite Entner et al. (2013) when presenting these three theorems as they are, at the very least, heavily inspired by the work of EHS.\n\nIs faithfulness implicit in the theorems of this paper? Line 257 is the first mention of the faithfulness assumption in the main paper. If the authors are assuming faithfulness throughout, then they should define faithfulness and state the assumption somewhere in Section 2.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-17"}

comments: SUMMARY:
* The paper seems to be placed the intersection of causal discovery and causal inference -- though more focused on causal identification. In particular, the authors focus on inferring if X has a potential causal effect on Y. To this goal, they learn an appropriate set of covariates to adjust to identify and estimate causal effect; what makes this work unique is that they do it in presence of latent features. 
* Relies on analyzing the testable conditional independence and dependence relationships

STRENGTHS AND WEAKNESSES:
Strength:
* The paper targets a relevant theoretical question -- given the causal dependencies, can we identify the causal effect and if yes, what are the set of covariates one needs to adjust for.
* The paper is very well written, with nice remarks, discussion and mix of formal and informal language

Weakness:
* The paper is notationally heavy. I am not sure there is much the authors can do.
* The work realies on stronger assumption about ordering of covariates and knowledge of MAG/DAG. I am not sure if it is realistic.

QUESTIONS:
* Can authors provide sensitivity analysis to violation of correct specification of MAG/DAG?
* In Algorithm 1, what if R1 or R2 is satisfied for multiple different combinations of S and Z? What if they result in different estimates?
* Typically, MB(Y) is always much larger than MB(X). In that case, their algorithm thats exponentially more time to run. How are authors claiming scalability?

LIMITATIONS:
The authors discuss limitations in appendix but I think it is worth moving to maintext. Further, it will be useful to discuss the reliance on assumptions and what happens when they are violated.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-06-20

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper focuses on causal effect estimation with latent variables. Existing methods often rely on learning the complete global causal structure, which can be computationally inefficient and unnecessary when the interest lies in a single causal effect of $X$ on $Y$. To overcome this limitation, the authors propose a novel and fully local algorithm called Local Search Adjustment Sets (LSAS). This approach leverages testable independence and dependence relationships among observed variables, specifically focusing on the Markov Blankets of $X$ and $Y$, to identify a valid adjustment set. The efficacy of the algorithm is validated through experiments on both synthetic and real-world datasets.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n\n1. This paper proposes a novel \"fully local\" learning approach for covariate selection in the presence of latent variables (i.e. LSAS), distinguishing itself from methods requiring learning a global causal structure that are computationally inefficient (e.g., EHS) or incomplete (e.g., CEELS, LDP).\n\n2. This paper proves that the proposed LSAS algorithm is both sound and complete under standard assumptions. Theorems 1, 2, 3, and 4, along with their proofs in Appendix D, establish a strong theoretical foundation for the method.\n\n3. This paper is well-structured and clearly explains complex concepts like MAGs, Markov blankets, and the generalized adjustment criterion. The examples provided (Figures 1, 2, 3) aid in understanding the theoretical concepts and the algorithm's intuition.\n\n4. This paper provides extensive experimental results on both synthetic and real-world datasets to demonstrate the effectiveness of the proposed LSAS.\n\n# Weaknesses\n\nI find no major weaknesses. Some minor questions are listed in Questions.\n\nQUESTIONS:\n1. I still cannot understand why the pretreatment assumption is realistic from the example \"every variable within the set $O$ is measured prior to the implementation of the treatment and before the outcome is observed\". Could you please provide more specific explanations?\n\n2. While the paper mentions experimental effectiveness even when the pretreatment assumption is violated, could the authors elaborate on the theoretical implications or provide a more detailed empirical analysis of LSAS's performance in such scenarios?\n\n3. The first step of LSAS is learning the Markov Blankets. What specific MB discovery algorithms are used? What are the computational complexities and known practical limitations of these MB discovery methods that might impact the overall efficiency of LSAS?\n\nLIMITATIONS:\nThis paper includes a section \"Limitations and Future Work\" in Appendix F, where they clearly state key assumptions such as the pretreatment assumption, discuss scenarios where these assumptions might be violated, and suggest future research directions to relax them, e.g., by leveraging background knowledge or data from multiple environments.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of identifying a valid adjustment set from observational data, opting to use a local, rather than global, causal discovery method. Assuming that the observed covariates O satisfy the pretreatment assumption, and additionally that Y is not a causal ancestor of X, the authors propose a local learning algorithm LSAS that identifies a valid adjustment set when possible (being both sound and complete). Their algorithm employs a two-stage procedure: first the Markov Blankets of X and Y are identified, then variables are added to the adjustment set if they satisfy the proposed rules R1 and R2. The authors then apply LSAS to both real and synthetic data, demonstrating that the VAS produced by LSAS attain the lowest relative error and lowest number of tests run when compared to some baselines.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nQuality - The work seems to me to be technically sound - although I did not inspect the proofs in the appendix closely, the high-level explanations given for the main results (such as Theorem 2 and Theorem 3) seem correct. The strategy of searching for conditions that allow one to conclude that there does exist a VAS, or that a VAS cannot be determined is intuitive. The work is complete in the sense that Theorem 5 (soundness/completeness) shows that LSAS is effective in the maximal number of cases in this setting.\n\nOriginality - It is clear the LSAS represents a step-forward from prior VAS identification methods, as the first one to satisfy both completeness and soundness without necessarily learning the strong graph (albeit under the strong pre-treatment assumption). The authors make this clear in both the second half of the introduction, as well as explicit remarks in Section 2.3. The reasoning behind the approach, i.e., identifying the necessary conditions for identifiability of VAS, then checking for whenever these conditions are satisfied, makes intuitive sense.\n\n\nWeaknesses:\n\nClarity - It is not really clear why the authors want to keep the pretreatment assumption. Its not clear what the challenge of non-pretreatment assumption is setting is, or why their current approach cannot be generalized to the non-pretreatment setting. Even under the pretreatment assumption, it is not clear to the reader what the main difficulty is that their algorithm tries to overcome. For example, without latent confounders the entire covariate set O constitutes a VAS under the pretreatment assumption, as there are no mediators or colliders. However, with pretreatment, one issue that arises are nodes that satisfy an m-structure induce a backdoor path when conditioned on - its not clear if this is really the only variables we want to exclude or if there other types of problematic variables  to exclude. Given these issues, it is difficult to ascertain exactly what insights researchers should derive about when local discovery approach of LSAS is intuitive, what are the major blockers, perhaps in some domains how it can be overcome.\n\n\nSignificance - Although LSAS is a local (rather than global) VAS identification method that does not relax the strong pretreatment assumption, it still retains a worst-case exponential (in dimension) runtime bound common to many global methods. This severely limits its applicability in practice, as it seems likely that LSAS would fall victim to a common practioner complaint, which is that many constraint-based discovery algorithms never converge outside small toy datasets. Although the experimental evaluation of LSAS presented in the main text seems to dispel those concerns, as LSAS seems to outperform other methods by large margins in both RE accuracy and nTests, I have strong concerns about whether these results honestly represent the capabilities of LSAS.\n\nThe authors note that the global VAS identification method EHS has already been shown to be sound and complete, but with time complexity exponential in the number of covariates. This excessive runtime motivates the local search approach of LSAS, and the authors show theoretically that LSAS achieves worst time complexity exponential in the Markov Blanket of $Y$, rather than all covariates, a definitive improvement. However, in their experiments, the authors use the number of tests ran nTests, rather than the absolute runtime of the algorithms (seconds), as an empirical measure of time complexity. This can be misleading, as the number of tests can diverge from absolute runtime, when the size of conditioning sets increases. It is not clear whether LSAS is prone to using smaller conditioning set sizes, therefore it is inappropriate to use nTest as a measure of time complexity, as it could mislead readers when a method runs fewer tests, but actually runs for a much longer time. The authors should take care to report runtime metrics alongside nTests for all baselines, to ensure fair comparison.\n\nFurther, the experimental results in the appendix present some additional worries. While experiments on synthetic data with randomly generated graphs (Figure 10) with increasing dimensionality ($d= 20,30,40,50) show that LSAS outperfoming baselines significantly, all settings use only sparse causal graphs, with a constant average degree 3 for all nodes. Given that the complexity of LSAS depends largely on its first step of Markov Blanket identification, if the MB of Y is small (which would be the case for sparse graphs), LSAS would enjoy a large improvement over baseline methods. However, this leaves the performance of LSAS in denser graphs entirely uncharacterized. This worry is further supported by the experimental results on the real-world INSURANCE and ANDES datasets in Figure 11; INSURANCE and ANDES have higher average degrees than the benchmarks commented on in the main text (3.03,3.85 vs 2.63,2.95), and here LSAS performs nearly identically to CEELS with respect to RE. Given a limited empirical analysis of LSAS's performance on dense graphs, and the few relevant experiments being relegated to the end of the appendix, this obscures the significance of LSAS to the broader community.\n\nQUESTIONS:\nQ1. I find it unclear why the pretreatment assumption is maintained and what specific challenges prevent generalization to non-pretreatment settings. Can you provide:\n- A concrete explanation of what algorithmic or theoretical barriers exist in the non-pretreatment case?\n- Specific examples showing how the LSAS approach would fail without this assumption?\n- A clear characterization of what types of problematic variables (beyond m-structures) LSAS aims to exclude?\n\nQ2. I am concerned that using nTests as a proxy for computational complexity may be misleading, since conditioning set sizes could vary significantly between methods. Can you:\n- Report actual wall-clock runtime comparisons alongside nTests for all baselines?\n- Analyze whether LSAS systematically uses smaller/larger conditioning sets than competitors?\n- Provide theoretical or empirical analysis of how conditioning set sizes scale with problem dimensions\n\nQ3. The experimental evaluation primarily focuses on sparse graphs (average degree 3), but limited results on denser graphs (INSURANCE/ANDES) show LSAS performing similarly to baselines. Can you:\n- Conduct systematic experiments on synthetic dense graphs with varying average degrees (5, 7, 10+)?\n- Provide theoretical analysis of how LSAS complexity scales with graph density?\n- If performance degrades on dense graphs, acknowledge this limitation and characterize the settings where LSAS provides advantages?\n\nIf the authors adequately address my concerns, in both the Strengths and Weaknesses and Questions sections, I am open to raising my score.\n\nLIMITATIONS:\nSee significance subsection of Strengths and Weaknesses section.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}