{"id":"81d9e04d-42b1-460e-9a90-9efb9cb4ffce","arxiv_id":"2411.09639","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"MCCE builds pseudo-concepts from a model's hidden states, orthogonal to observed concepts, to reduce bias in causal concept effect estimates when some concepts are unobserved.","lead":"This paper introduces a method called MCCE that estimates how much human-readable concepts, such as food quality or service, causally affect a model's predictions even when some concepts are not annotated in the data. It matters because real-world explanations often have incomplete labels, and the method aims to keep causal explanations reliable under this missingness.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Orthogonalized pseudo-concepts do not change observed-concept OLS coefficients; the bias-correction mechanism is mathematically inert.","rationale":"The reader's weakest assumption concerned whether H encodes unobserved concepts. My analysis shows a stronger, more direct problem: even if H encodes all unobserved concepts perfectly, the orthogonalization in Equation (7) projects away the component of H that is correlated with the observed concepts, and only that correlated component could correct omitted-variable bias in β_ob. Because C_ob^T Cpseud = 0, the joint least-squares coefficient for β_ob is identical to the coefficient from regressing the output on Cob alone. Therefore the proposed pseudo-concepts cannot reduce the residual bias that the paper derives in Section 3, and the paper's own reduction of ICaCE-Error to coefficient error (Equation 5) implies the headline empirical metric should be unaffected by the pseudo-concept term. This is not merely an untested modeling assumption but an internal mathematical inconsistency in the central mechanism. The empirical results may still show useful predictive properties of the architecture, but they do not support the paper's causal bias-correction claim. Because the central contribution is the pseudo-concept construction for missingness-aware causal effect estimation, and that construction is ineffective for its stated purpose, the appropriate verdict is REJECT rather than CONDITIONAL. I agree with the reader that the representation-sufficiency assumption is untested, but the more decisive issue is that the orthogonalization actively removes the information needed for bias correction.","tokens_in":10363,"tokens_out":6700,"duration_ms":70722,"concrete_test":"Run a synthetic omitted-variable simulation: draw one observed concept C1, one unobserved concept C2 correlated with C1, and y = β1 C1 + β2 C2 + noise. Set H = C2 (so H contains the unobserved concept perfectly), construct Cpseud = (I-P)H, and fit OLS of y on C1 and Cpseud. Check whether the estimated coefficient on C1 is numerically identical to the OLS coefficient from y ~ C1 alone; if it is, the pseudo-concept construction cannot reduce omitted-variable bias, contradicting the paper's central claim. As a complementary check, rerun Table 1 with MCCE's pseudo-concepts removed but the same linear estimator to see whether the reported gains persist.","verdict_should_be":"REJECT","load_bearing_attack":"Equations (7)-(10) define Cpseud = (I-P)H with P the projection onto the column space of Cob, so C_ob^T Cpseud = 0. In the joint OLS for N(X) = C_ob β_ob + Cpseud β_pseud, the normal equations decouple: C_ob^T C_ob β_ob_hat = C_ob^T N(X), which is exactly the coefficient obtained by regressing N(X) on Cob alone. Thus β_ob_hat is independent of H, of the number of pseudo-concepts j, and of β_pseud. Omitted-variable bias for β_ob arises from correlation between Cob and Cun; any component of H that carries that correlated information is removed by the projection (I-P), while the retained orthogonal component is uncorrelated with Cob and cannot adjust β_ob. Consequently, the pseudo-concepts do not mitigate the residual bias analyzed in Section 3, and by the paper's own Equation (5), ICaCE-Error is unchanged. The empirical improvement over S-Learner therefore cannot be attributed to the proposed mechanism: S-Learner is a logistic regression, MCCE is linear, and the comparison in Table 1 is between different estimators rather than a demonstration that pseudo-concepts reduce bias.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses causal concept effect estimation when some human-annotated concepts are missing. It first shows, using a linear model, that omitting unobserved concepts biases the estimated coefficients of observed concepts. It then proposes MCCE, which extracts a hidden representation H from the black-box model's input and constructs pseudo-concepts Cpseud = (I - P)H, where P projects onto the observed concepts. These pseudo-concepts are concatenated with the observed concepts in a linear predictor of the black-box output, and the resulting coefficients are used to estimate individual causal concept effects on the CEBaB dataset with BERT, RoBERTa, and Llama-3 backbones. The paper reports ICaCE-Error comparisons against approximate counterfactuals, S-Learner, and Causal Proxy Models, and also presents global interpretation coefficients and predictive performance of MCCE as an interpretable model.","tokens_in":10633,"tokens_out":6004,"duration_ms":60908,"significance":"If the proposed mechanism worked, MCCE would fill a real gap: current concept-based causal explainers assume complete concept annotations, which is unrealistic in practice. The paper's empirical setup is relevant: it uses a benchmark with human-verified counterfactual texts, evaluates multiple transformer backbones, and includes one- and two-concept missingness scenarios. The formal demonstration that omitted unobserved concepts bias observed-concept effect estimates is standard but clearly presented. However, the central claimed mechanism—that orthogonalized pseudo-concepts reduce this bias—is mathematically inert under the paper's own equations, and the empirical comparison does not isolate the effect of the pseudo-concepts. The paper also provides no theorem or formal condition under which (I - P)H captures the effect of unobserved concepts. Because the main contribution is not supported, the manuscript cannot be accepted in its current form.","major_comments":[{"comment":"The proposed pseudo-concepts cannot change the estimated coefficients of the observed concepts. Because Eq. (8) establishes C_ob^T Cpseud = 0, the normal equations for the joint OLS in Eq. (10) decouple, giving \\hat\\beta_ob = (C_ob^T C_ob)^{-1} C_ob^T N(X), which is exactly the estimate obtained by regressing N(X) on C_ob alone. Thus \\hat\\beta_ob is independent of H, of the number of pseudo-concepts j, and of \\hat\\beta_pseud. Consequently, the omitted-variable bias analyzed around Eq. (6) is unchanged, and by the paper's own Eq. (5) the ICaCE-Error for observed concepts is unchanged. The orthogonality property prevents collinearity but does not address the source of the bias, which is correlation between C_ob and C_un; any component of H carrying that correlated information is removed by the projection (I - P), while the retained orthogonal component is uncorrelated with C_ob and cannot adjust \\hat\\beta_ob. The paper's central claim that pseudo-concepts 'effectively mitigate the residue bias' is therefore not supported by the estimator defined in Eq. (10).","section":"§3, Eq. (7)–(10)"},{"comment":"The intervention formula E_MCCE(c, c'|x) is not a clean swap of the observed concept value while holding all other concepts fixed. In Eq. (11), the pseudo-concept term contains the projection matrix I - C_{x,ob}(C_{x,ob}^T C_{x,ob})^{-1} C_{x,ob}^T, which depends on the observed concept vector itself. Replacing C_{x,ob} by C_{x,ob}^{c→c'} therefore changes not only the observed-concept term but also the value of the pseudo-concept term, even though the raw input x is unchanged. The paper does not define what intervention is being applied to the pseudo-concepts or why this corresponds to the counterfactual in Eq. (4), where all remaining concepts are unchanged. This makes the causal interpretation of the reported estimates ambiguous and needs to be resolved for the main empirical claims to be meaningful.","section":"§3, Eq. (11)–(12)"},{"comment":"The empirical comparison between MCCE and S-Learner does not demonstrate that pseudo-concepts reduce bias. S-Learner is a logistic regression, whereas MCCE uses a linear MSE predictor on hidden representations, so the comparison in Table 1 varies both the model class and the feature representation. A controlled ablation would compare a linear regression on the observed concepts alone against a linear regression on observed concepts plus pseudo-concepts, using the same extractor and training procedure. The paper instead calls S-Learner a 'special case of MCCE that removed the components of the pseudo-concepts,' which is not literally true because the two estimators have different loss functions and model classes. Given the mathematical inertness of the pseudo-concepts for \\hat\\beta_ob shown in Eq. (7)–(10), any observed ICaCE-Error improvement cannot be attributed to the proposed bias-correction mechanism without this ablation.","section":"§5, Table 1"},{"comment":"No formal conditions are given under which the residual (I - P)H captures the effect of the unobserved concepts. The paper states, 'We hypothesize that H contains all necessary information about all concepts, including unobserved ones,' but this sufficiency assumption is never tested or formalized. If H encodes the unobserved concepts only along directions already collinear with the observed concepts, then (I - P)H contains no useful information about C_un. The paper needs either a theorem with explicit identification conditions or a direct diagnostic that the orthogonalized residuals carry information about the held-out concepts in the CEBaB experiments. As written, the theoretical contribution reduces to a demonstration of routine omitted-variable bias plus an untested representation-sufficiency assumption.","section":"§3, text before Eq. (7)"}],"minor_comments":[{"comment":"Equation (10) uses 'arg max' when minimizing a squared-error objective; it should be 'arg min.'","section":"Eq. (10)"},{"comment":"The phrase 'identification matrix' should read 'identity matrix.'","section":"Eq. (7)"},{"comment":"There is a typo in 'summerizing' and another in 'Cconcept Credible Models'; both should be corrected.","section":"§2"},{"comment":"The sentence 'A positive Ambiance has a peaking impact at the 5-star rating instead of the 5-star rating' contains a repeated rating value and should be clarified.","section":"§5, Figure 3"},{"comment":"The acronym 'MCEE' appears where 'MCCE' is intended.","section":"§5, Table 2 paragraph"},{"comment":"The statement that S-Learner is 'a special case of MCCE that removed the components of the pseudo-concepts' is misleading because S-Learner uses logistic regression; please specify the linear-regression variant used as the ablation.","section":"§5, first paragraph"}],"recommendation":"reject","confidential_remarks":"The central mechanism of the paper is contradicted by its own equations: the orthogonalized pseudo-concepts are mathematically inert for the observed-concept coefficients, and the intervention formula changes the pseudo-concepts when only the observed concept is intervened upon. The empirical results, while interesting on CEBaB, cannot be attributed to the proposed bias-correction mechanism without a controlled linear ablation. In my view, these are load-bearing issues that cannot be fixed within the scope of the current manuscript; rejection is appropriate, though the authors could consider reframing the pseudo-concepts as auxiliary prediction features rather than as a bias-correction device."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The stress-test note is right, and it lands hard. The core of the paper is the construction C_pseud = (I - P)H, where P projects onto the observed concepts. Because C_ob^T C_pseud = 0, the OLS normal equations for beta_ob decouple from C_pseud. Regressing N(X) on both C_ob and C_pseud gives exactly the same beta_ob as regressing on C_ob alone. Pseudo-concepts cannot adjust the observed-concept coefficients, and by the paper's own Equation (5) the ICaCE-Error is unchanged. The claimed bias correction is not just unproven; it is algebraically impossible.\n\nWhat is genuinely new is the problem framing. Existing causal concept effect methods do assume complete observation, and the paper is the first to point at missing concepts as a practical failure mode. The omitted-variable bias analysis in Section 3 is correct as far as it goes, and the paper is honest about its limitations: a single dataset, a hand-wavy hyperparameter, and the untested hypothesis that H contains all necessary concept information. The writing is clear and the construction is simple enough to probe.\n\nThe soft spots are not minor. Besides the inert mechanism, the intervention formula in Equation (12) is underspecified—it is unclear whether the projection is recomputed after swapping the concept values—and no code or full hyperparameter details are provided. The empirical comparison to S-Learner confounds estimator class (logistic vs linear) with the pseudo-concept mechanism, so the reported gains cannot be attributed to the paper's idea.\n\nThis paper is for a reader interested in concept-based interpretability who wants to see the missing-concepts problem stated cleanly. But the proposed solution does not work, and the central claim is contradicted by the paper's own equations. I would not send this to peer review in its current form; the main contribution is a well-posed problem without a valid method. A revision that actually uses H to estimate the omitted variable direction—rather than an orthogonalized residual—might deserve a second look.","headline":"The paper targets a real gap—missing concepts in causal concept effect estimation—but its pseudo-concept mechanism is mathematically inert: adding orthogonalized residuals does not change the observed-concept coefficients, so the claimed bias correction does not happen.","tokens_in":690,"tokens_out":1407,"would_cite":false,"duration_ms":52343,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that missing concept annotations bias causal concept effect estimates, and that orthogonalizing a hidden representation against observed concepts removes most of that bias.","keywords":["causal concept effect","concept-based explainability","missing concepts","pseudo-concepts","orthogonal projection","interpretable machine learning","ICaCE","CEBaB"],"falsifier":"Construct a synthetic benchmark where a known unobserved concept is included in the true data-generating process, then explicitly remove all information about it from the feature extractor's hidden representation H (for example, by orthogonalizing H against the unobserved concept); if MCCE's ICaCE-Error on the observed concepts is then no better than an S-Learner that ignores missing concepts, the central claim that pseudo-concepts compensate for unobserved concepts is falsified.","tokens_in":10138,"feed_emoji":"🧩","tokens_out":5795,"duration_ms":50704,"temperature":0.7,"pith_summary":"Causal concept effect explanations estimate how much a human-interpretable concept moves a model's prediction, but existing methods assume every relevant concept is annotated. This paper shows that when concepts are missing, ordinary linear estimates of the observed concepts' causal effects are biased, so the resulting explanations are wrong. Its proposed MCCE builds pseudo-concepts, residuals of a learned representation after removing the projection onto the observed concepts, and adds them to a linear predictor of the black-box output. On the CEBaB restaurant-review benchmark, MCCE reports ICaCE-Error at or below the strongest baseline even when one or two of the four concepts are hidden, while needing only factual data. The paper also notes that validation is limited to CEBaB and that the number of pseudo-concepts is chosen empirically.","feed_headline":"Missing concepts no longer break causal effect estimates","feed_subtitle":"Adding orthogonal residuals from a hidden representation keeps linear concept explanations accurate on partially annotated data.","key_machinery":"The load-bearing object is the pseudo-concept matrix $C_\\text{pseud} = (I-P)H$, where $H$ is the hidden representation extracted from the input, $P = C_\\text{ob}(C_\\text{ob}^T C_\\text{ob})^{-1} C_\\text{ob}^T$ is the least-squares projection matrix onto the observed concept columns, and $I$ is the identity. This is an orthogonalization: it removes from $H$ every direction already explainable by the observed concepts, leaving residual directions that are outside the observed concept span. The paper uses this residual as a proxy for the information that unobserved concepts would have contributed, and fits a linear model on the concatenated observed and pseudo concepts to approximate the black-box model's logits. The identity $C_\\text{ob}^T C_\\text{pseud} = 0$ is what prevents the pseudo-concepts from being a collinear duplicate of the observed concepts.","core_discovery":"The central claim is that missing concept annotations need not be fatal. The authors analyze the linear concept-effect model $N(X) = C_\\text{ob}^T \\beta^*_\\text{ob} + C_\\text{un}^T \\beta^*_\\text{un}$ and observe that fitting only $C_\\text{ob}$ leaves a residual $C_\\text{un}^T \\beta^*_\\text{un} - C_\\text{un}^T \\hat{\\beta}_\\text{un}$ that moves the estimated $\\hat{\\beta}_\\text{ob}$ away from $\\beta^*_\\text{ob}$; consequently the individual concept causal effect estimate is biased. They propose to recover the missing subspace information from a hidden representation $H$ by computing $C_\\text{pseud} = (I-P)H$, with $P$ the projection onto the observed concept columns. Because $C_\\text{ob}^T C_\\text{pseud}=0$, the added pseudo-concepts cannot create collinearity with the observed concepts and, assuming $H$ contains the unobserved concepts' information, their inclusion compensates for the omitted variables. MCCE then trains a linear predictor on observed concepts plus pseudo-concepts and uses its coefficients to estimate causal effects both locally and globally. On CEBaB with BERT, RoBERTa, and Llama-3 extractors, the method's reported ICaCE-Error is lower than S-Learner in all reported settings and on par with or lower than the input-based Causal Proxy Model.","pith_inferences":["If the orthogonalization is doing the work, then deliberately removing unobserved-concept information from H (for example, by projecting H onto a subspace uncorrelated with the missing concept) should make MCCE's bias reduction disappear; this is a testable isolation of the mechanism.","The success of pseudo-concepts suggests a rank condition: the number of pseudo-concepts should roughly match the dimension of the unobserved-concept space, which would explain the paper's empirical observation that setting it comparable to or slightly larger than the number of observed concepts works best.","Because MCCE is representation-agnostic, the same missingness-aware correction could extend to image, tabular, or multimodal encoders, although the paper only demonstrates it on text."],"forward_implications":["If the hidden representation captures the unobserved concepts, MCCE removes the main obstacle to using concept-based causal explanation on partially annotated data.","MCCE requires only factual samples, whereas the strongest baseline it compares with needs labeled counterfactual texts.","The linear coefficients returned by MCCE give a direct global summary of how each concept affects the model's outputs.","The same pipeline can be used as an interpretable predictor, with macro-F1 comparable to the black-box model on CEBaB."],"supporting_citations":[{"why":"Supplies the CEBaB dataset with human-validated counterfactuals and the ICaCE/ICaCE-Error metrics used to evaluate MCCE.","marker":"Abraham et al. (2022)"},{"why":"Introduces the Causal Proxy Model, the state-of-the-art baseline MCCE must match or beat; it is the main comparison method in the experiments.","marker":"Wu et al. (2023)"},{"why":"Provides the factor-analysis-style latent regression construction that motivates writing pseudo-concepts as $(I-P)H$.","marker":"Fan et al. (2024)"},{"why":"Gives the backdoor-path argument used to explain why unobserved concepts confound observed-concept causal effects.","marker":"Pearl (2009)"},{"why":"Defines the S-Learner baseline that MCCE outperforms, isolating the contribution of the pseudo-concepts.","marker":"Künzel et al. (2019)"}],"fun_headline_variants":["Missing concepts no longer bias causal concept effects","Causal concept effect estimates stay accurate with missing data","MCCE recovers missing concept influence from hidden representations","Hidden representation pseudo-concepts fix missing annotation bias"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework assumes the internal representation produced by the feature extractor still contains everything that would have been in the unobserved concepts; if it does not, the orthogonal residuals add nothing useful and the bias remains.","fun_headline_variants_meta":{"raw":{"variants":["Missing concepts no longer bias causal concept effects","Causal concept effect estimates stay accurate with missing data","MCCE recovers missing concept influence from hidden representations","Hidden representation pseudo-concepts fix missing annotation bias"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000783,"raw_usage":{"total_tokens":3504,"prompt_tokens":1041,"completion_tokens":2463,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":657,"completion_tokens_details":{"reasoning_tokens":2411}},"tokens_in":657,"tokens_out":2463,"duration_ms":18059,"temperature":1.0,"reasoning_tokens":2411,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:26:21.016934+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a synthetic benchmark where a known unobserved concept is included in the true data-generating process, then explicitly remove all information about it from the feature extractor's hidden representation H (for example, by orthogonalizing H against the unobserved concept); if MCCE's ICaCE-Error on the observed concepts is then no better than an S-Learner that ignores missing concepts, the central claim that pseudo-concepts compensate for unobserved concepts is falsified.","supporting_citations":[{"cited_title":"Cebab: Estimating the causal effects of real-world concepts on nlp model behavior","cited_arxiv_id":null,"evidence_quote":"Supplies the CEBaB dataset with human-validated counterfactuals and the ICaCE/ICaCE-Error metrics used to evaluate MCCE."},{"cited_title":"Causality","cited_arxiv_id":null,"evidence_quote":"Gives the backdoor-path argument used to explain why unobserved concepts confound observed-concept causal effects."}],"review_version":1}