{"id":"1ba45fc6-6586-4830-a974-85e601df039f","arxiv_id":"2508.20259","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Latent DML fits a parametric latent variable model to DML residuals and adjusts the outcome residual before the final effect regression, yielding consistent estimates under well-specified unobserved confounding.","lead":"The paper adds a latent variable model to the second stage of double machine learning, using EM to fit the residual noise structure and an adjusted outcome residual to estimate causal effects when unobserved factors are present. It shows improved bias and variance on synthetic data and two real world examples, though the real data evidence has gaps.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Neyman orthogonality proof omits the dependence of the adjustment E[f_u|R,V] on the estimated first-stage residuals, so the stated consistency/normality guarantees do not cover Algorithm 2.","rationale":"The reader's weakest assumption (identifiability of γ0) is a plausible concern, and Proposition B.2 indeed asserts rather than verifies the needed condition; I agree it should be checked. But the more direct threat to the central claim is that the estimator analyzed in the appendix is not the estimator implemented in Algorithm 2. The adjustment E[f_u(Z)|R,V,γ] depends on h,m through the residuals, and Lemma A.5's orthogonality proof treats q_γ(W) as nuisance-free. In the confounder scenario the omitted derivative terms are generically nonzero, so the proof of consistency/asymptotic normality does not go through. This does not prove the estimator is inconsistent—finite-sample bias from the nuisance term is o_p(1) under n^{1/4}-consistent first-stage fits, so θ̂ may still be consistent at a slower rate—but it invalidates the root-n normality and variance-reduction claims and the 'unbiased' phrasing in Section 3.1. The same flaw would also affect the outcome-latent model if V and U were dependent, but there the independence makes the extra terms vanish; the damage is concentrated in the unobserved-confounder case, which is the paper's main selling point. The reader's conditional verdict remains appropriate: the issue is addressable by either proving orthogonality for the true moment (e.g., by cross-fitting the residual-based q) or by deriving the correct higher-order distribution, but the current text does not support the stated guarantees.","tokens_in":20812,"tokens_out":26789,"duration_ms":269915,"concrete_test":"On data simulated from the confounder model (§3.3) with known h0,m0 and (θ,a,b,q,σu,σv)=(0.5,2,2,0.5,1,1), compute the empirical moment M(s) = (1/n)Σ [(Y−h0−sξ −θ(D−m0) − E_{γ0}[aZ|Y−h0−sξ, D−m0]) (D−m0)] for ξ=1 and s ∈ {0, ±0.01, ±0.05}. If dM/ds|_{s=0} is statistically nonzero, the moment implemented in Algorithm 2 is not Neyman orthogonal. As a second check, run latent DML with a deliberately biased root-n-consistent first-stage learner (e.g., Ridge with a small fixed penalty) versus an oracle-residual version; if the difference in θ̂ does not vanish at the rate predicted by Theorem A.7, the proof's orthogonality assumption is violated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Algorithm 2 (lines 10–13) computes the adjusted residual Rz_i = R_hat_i − E[f_u(Z)|R_hat_i,V_hat_i,γ_hat], where R_hat = Y − ĥ(X) and V_hat = D − m̂(X). Thus the adjustment term is a function of the estimated nuisance functions ĥ,m̂. The theoretical moment in Lemma A.5, however, is φ = (Y−h−θ(D−m)−q_γ(W))(D−m−r_γ(W)) with q_γ(W) written as a function of raw W, and the orthogonality calculation differentiates only the explicit h,m terms appearing in Y−h and D−m. Under a nuisance perturbation h→h+sξ_h, m→m+sξ_m, the implemented q also changes through its residual arguments: q' = (∂q/∂R)(−ξ_h) + (∂q/∂V)(−ξ_m). The derivative of E[φ] then contains −E[(∂q/∂R)V ξ_h] − E[(∂q/∂V)V ξ_m] in addition to the direct terms that conditions (19)–(20) kill. In the confounder model of §3.3, V = bZ + W_v is informative about Z, so ∂q/∂V and ∂q/∂R are generically nonzero and these extra terms do not vanish. Therefore Neyman orthogonality (18) is not established for the moment actually solved by Algorithm 2; Theorem A.6 and Theorem A.7 rely on it. The 'unbiased estimate' statement after Eq. (12) holds only when R,V,γ are oracle quantities, not for the plug-in residuals used in the algorithm. The first-order nuisance error contaminates θ̂ at the DML inference level.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes 'latent double machine learning' (latent DML), a modification of the double machine learning framework in which a latent variable model is fitted to the first-stage residuals and the outcome residual is adjusted by the conditional expectation of the latent contribution before the causal parameter is estimated via a score equation. Two instantiations are given: an outcome-only model with a shifted exponential latent variable, and a confounder model with a shifted Bernoulli latent variable affecting both treatment and outcome. The authors claim consistency and asymptotic normality of the resulting estimator under Neyman orthogonality, and support the method with synthetic experiments, a BIC-based model-selection procedure, and two real-data applications (401(k) participation and advertisement timing). The central theoretical claim is that, under correct specification, fitting the latent structure to the residuals removes the bias caused by unobserved confounding while retaining the computational decoupling of DML.","tokens_in":21212,"tokens_out":12460,"duration_ms":115056,"significance":"If the theoretical claims were established, the paper would offer a practically useful extension of DML to settings with latent structure: the second-stage-only modification is computationally attractive, the two parametric models are transparent and easy to interpret, and the synthetic results show clear bias reduction relative to ordinary DML in the confounded scenarios. The paper also deserves credit for spelling out the score equation, providing EM-based algorithms, including an explicit model-selection heuristic, and reporting replication-oriented experimental details. However, the theoretical guarantees are the main advertised contribution, and they are currently not connected to the algorithm that is actually implemented: the Neyman orthogonality proof does not account for the dependence of the adjustment term on the estimated residuals. In addition, two displayed formulas in Sections 3.2 and 3.3 appear to be incorrect as written, and the identifiability assumption that the theoretical results rely on is asserted rather than verified. These issues are load-bearing for the paper's central claims, although they are potentially fixable.","major_comments":[{"comment":"The Neyman orthogonality proof does not cover the estimator actually implemented. Lemma A.5 treats q_gamma(W)=E[f_u(Z)|W,gamma] as a function of the raw observation W, and the derivative with respect to s differentiates only the explicit h and m terms in Y-h and D-m. In Algorithm 2, however, the adjustment is computed as E[f_u(Z)|R_hat_i,V_hat_i,gamma_hat] with R_hat=Y-h_hat(X) and V_hat=D-m_hat(X), so q depends on the estimated nuisance functions through its arguments. Under a perturbation h->h+s xi_h, m->m+s xi_m, the derivative of E[phi] contains the additional terms -E[(partial q/partial R) V xi_h] and -E[(partial q/partial V) V xi_m]. In the confounder model of Section 3.3 these partial derivatives are generically nonzero, and conditions (19)-(20) do not make the extra terms vanish. Therefore Lemma A.5, and with it the consistency and asymptotic normality of Theorems A.6 and A.7, do not apply to Algorithm 2. The unbiasedness statement after Eq. (12) holds for oracle residuals R,V and the true gamma0, not for the plug-in residuals used in the algorithm.","section":"§3.1, Eq. (12); Algorithm 2; §A.2 Lemma A.5"},{"comment":"The displayed posterior probability pi_i = P(Z_i=1-q | R_hat_i,V_hat_i,theta,a,b,q,sigma_u,sigma_v) is not the posterior under the stated model. For q=1/2, the correct posterior log-odds for Z=1-q is [a(R-theta V)]/sigma_u^2 + [b V]/sigma_v^2, whereas the displayed exponential has the opposite sign. For q != 1/2, the term log(q/(1-q)) is also missing from the logistic argument. Since the adjusted residual R^z_i = R_hat_i - a(pi_i - q) uses pi_i, implementing this formula as written would not remove E[aZ|R,V] under the stated model. Please correct the formula or clarify the parametrization.","section":"§3.3, formula for pi_i"},{"comment":"The conditional expectation formula for the outcome latent model appears to be shifted. Under Eq. (15), Z has support [-beta, infinity), or equivalently T=Z+beta has support [0, infinity). The text states that E[Z_i | R_i,V_i,theta,beta,sigma] is the mean of a truncated normal N(m_i,sigma^2) truncated on [0, infinity), with m_i := R_i - theta V_i + beta - sigma^2/beta. This is at best a formula for a mean of T, not for the mean of Z; as written the adjustment in Eq. (12) is offset by beta and uses the wrong truncation point for Z. Please restate the formula with the correct support and offset.","section":"§3.2, Eq. (15) and following"},{"comment":"Identification of the latent-variable parameters is load-bearing but is not actually verified. Proposition B.2 restates a standard local-identification result, but the application to the shifted exponential model and the shifted Bernoulli model is dismissed with the sentence that verification is 'straightforward' and no proof or computation is provided. Since the EM algorithm converges only to local maxima and Assumption A.4(a) requires the moment condition to vanish only at the true gamma0, the paper should show non-singularity of the relevant Fisher information (or otherwise establish local identification) for the specific models in Sections 3.2 and 3.3.","section":"Assumption A.4(a); Proposition B.2"}],"minor_comments":[{"comment":"The sentence 'the the nuisance components are estimated' contains a duplicated article; also the phrase 'unbiased estimate' is used where the argument establishes a conditional-moment property at the true parameter, not finite-sample unbiasedness for the implemented estimator.","section":"§3.1"},{"comment":"The text refers to 'late model parameters' where 'latent model parameters' is intended, and the second theorem in Section B.2.2 is labeled 'Theorem A.5 (Asymptotic Normality)' although it should be Theorem A.7.","section":"§A.2"},{"comment":"The table caption says the effect is 'percentage per 10 days' while the text reports 'per 100 days'; the units should be harmonized.","section":"§5.2.2 and Table 2"},{"comment":"The latent parameter gamma in Eq. (10) is said to include theta, yet Algorithm 2 first estimates gamma by minimizing L(gamma) and then solves Eq. (11) for theta separately; the relationship between the EM estimate of theta and the score-equation estimate should be clarified.","section":"Algorithm 2 and Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"The empirical results in Figures 2-4 are plausible, but the apparent discrepancy between the printed formulas in Sections 3.2 and 3.3 and the reported successful performance suggests that the implementation may differ from the text. It would be useful to ask the authors to release the code or to confirm which formulas were actually used. The main theoretical gap (Neyman orthogonality for the plug-in residual adjustment) is substantial and should be addressed head-on; if it cannot be repaired, the claims of consistency and asymptotic normality should be weakened accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. The paper has a genuinely useful idea: instead of trying to fit latent variables jointly with the first-stage ML models in DML, move the latent structure entirely into the second stage and adjust the outcome residual by the conditional mean of the latent component. That keeps computation cheap, and the score equation is correct if the residuals were oracle quantities. The empirical vignettes, especially the 401(k) missing-covariate experiments, show the method can reduce bias in settings where unobserved confounders are only partially encoded in the covariates.\n\nThe soft spot is in the theory section, and it is not cosmetic. The Neyman orthogonality proof in Lemma A.5 treats the adjustment term q_gamma(W) as independent of the nuisance functions. But the algorithm in Section 3.1 computes q from the estimated residuals R_hat = Y - h_hat(X) and V_hat = D - m_hat(X). When you perturb h and m, q changes through its own arguments, and that dependence is not accounted for in the derivative used to establish orthogonality. The extra terms E[(∂q/∂R)V ξ_h] and E[(∂q/∂V)V ξ_m] are generically nonzero in the confounder latent model, so the moment condition solved by Algorithm 2 is not the one whose orthogonality is proved. That means the consistency and asymptotic normality theorems apply to the oracle moment, not to the implemented estimator. This is a serious gap, though I think it is fixable with additional assumptions or a more careful treatment of q as a function of the residuals.\n\nThe identification section is also thinner than it looks. Proposition B.2 quotes Rothenberg and then asserts that verifying non-singular Fisher information for the shifted exponential and shifted Bernoulli models is straightforward. That might be true, but no actual check is provided, and for finite mixtures identifiability can fail on measure-zero subsets. A short calculation would settle it.\n\nEmpirically, the synthetic data come from the same family as the fitted models, so the close-to-oracle performance is not surprising. The advertisement experiment has no error bars, and the BIC model selection is done on the same data used to report the effect, which is fine as an illustration but not as a rigorous evaluation. No code or data artifacts are provided, which limits reproducibility.\n\nAll of this is addressable. The core idea is real, the writing is clear, and the method deserves serious peer review. If the orthogonality gap is fixed—either by proving the extra terms vanish or by modifying the estimator to match the proof—this would be a reasonable contribution to the causal inference and DML literature. I would not rely on the current theoretical guarantees, but I would definitely send this to referees.","headline":"A useful second-stage latent-variable extension to DML with a real theoretical gap: the Neyman orthogonality proof ignores that the adjustment term depends on the estimated residuals.","tokens_in":21762,"tokens_out":3097,"would_cite":false,"duration_ms":28920,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62D20","62F12"],"pacs":[],"model":"deepseek-v4-flash","headline":"A second-stage latent adjustment — subtracting the fitted expected latent contribution from the outcome residual — makes the causal-effect estimate consistent even when an unobserved confounder drives both treatment and outcome.","keywords":["latent DML","double machine learning","unobserved confounding","causal effect estimation","latent variable models","EM algorithm","Neyman orthogonality","BIC model selection"],"falsifier":"Simulate data from the confounder latent model with the Bernoulli probability $q$ near the boundary ($q \\approx 0.01$) and with noise variances large relative to the loadings $a$ and $b$; fit latent DML across many EM restarts and check whether the fitted latent parameters recover their generating values and whether the empirical Fisher information at the EM solution stays well conditioned. If the latent parameters drift across restarts while $\\hat{\\theta}$ stays near the truth, the identification condition is failing and the paper's stated mechanism is not what is carrying the estimate; if $\\hat{\\theta}$ itself drifts, the consistency claim fails exactly in the regime the paper does not test.","tokens_in":20601,"feed_emoji":"🎯","tokens_out":19940,"duration_ms":151325,"temperature":0.7,"pith_summary":"Double machine learning (DML) isolates a causal effect by regressing the outcome residual on the treatment residual, but that regression is biased whenever an unobserved factor moves both residuals. The paper claims this bias can be removed without altering the first-stage machine learning at all: fit a parametric latent-variable model to the paired residuals, then subtract the posterior expectation of the latent contribution to the outcome residual before solving the usual score equation. The paper calls the result latent DML, gives two concrete latent families — a shifted exponential for outcome-only hidden noise and a shifted Bernoulli for a hidden confounder affecting both treatment and outcome — and proves consistency and asymptotic normality ($\\sqrt{n}$-rate) under the standard DML regularity conditions, including Neyman orthogonality of the score. If the latent model is well specified, the computational decoupling that makes DML practical is preserved, because the latent inference runs once in the second stage. Synthetic experiments and two real-data applications (401(k) wealth and advertising ROAS) show the adjustment reducing bias relative to ordinary DML.","feed_headline":"Latent DML strips hidden-confounder bias out of causal estimates","feed_subtitle":"A second-stage latent adjustment recovers unbiased treatment effects where ordinary DML goes biased.","key_machinery":"The load-bearing object is the adjusted score equation and its Neyman-orthogonal moment function. The paper defines $\\varphi(W, \\gamma, \\nu) = (Y - h(X) - \\theta(D - m(X)) - q_\\gamma(W))\\,(D - m(X) - r_\\gamma(W))$ with $q_\\gamma(W) = E[f_u(Z)\\mid W, \\gamma]$ and $r_\\gamma(W) = 0$; once residuals are plugged in, this is exactly the estimating equation $\\sum_i (R^z_i - \\hat{\\theta} V_i) V_i = 0$. The trailing factor $D - m(X)$ is the treatment residual, which acts as the noisy window onto $Z$; the leading factor is the latent-adjusted outcome residual. Neyman orthogonality — the derivative of the moment with respect to perturbations of the nuisance functions $h$ and $m$ vanishes — is what lets the second-stage latent fit ignore first-stage estimation error, and Lemma A.5 derives it from two conditional mean-zero restrictions, Equations (19)-(20). The posterior expectation $E[f_u(Z)\\mid R, V, \\hat{\\gamma}]$ is the mechanism that removes the bias: it projects the latent part of the outcome noise onto what the treatment residual reveals about $Z$. EM computes that posterior — a truncated-normal mean in the outcome-only model, a success-probability-weighted average in the Bernoulli confounder model — and BIC selects between the two latent structures.","core_discovery":"On the paper's own terms, the central claim is an unbiasedness identity. The outcome residual in DML decomposes as $R = \\theta V + U$; writing the noise as $U = f_u(Z) + W_u$ and $V = f_v(Z) + W_v$ with mutually independent $Z, W_u, W_v$, subtracting $E[f_u(Z)\\mid R, V, \\gamma_0]$ from $R$ leaves an error that is mean-independent of $V$, so a well-specified latent model replaces the unconfoundedness condition $E[UV\\mid X] = 0$ with a distributional assumption on the residual pair. The estimator solves the score equation $\\sum_i (R^z_i - \\hat{\\theta} V_i) V_i = 0$ with adjusted residual $R^z_i = R_i - E[f_u(Z)\\mid R_i, V_i, \\hat{\\gamma}]$, and the paper proves this score is Neyman-orthogonal to first-stage nuisance estimation error, yielding consistency and asymptotic normality under the usual $n^{1/4}$ rate condition on the nuisance fits. The claim is not that the latent variable itself is identified in an absolute sense, but that the finite-dimensional parameters are identified from the residual likelihood; Proposition B.2 ties this to non-singular Fisher information, and the paper asserts it holds 'straightforwardly' for the shifted exponential and shifted Bernoulli models without giving the verification (end of Appendix B.2.1). Two instantiations implement the framework — an outcome-only latent model and a confounder latent model — with EM supplying the posterior moments and BIC choosing between the two structures.","pith_inferences":["Editorial inference: the adjusted-residual construction is structurally a control-function estimator — the treatment residual acts as a noisy measurement of the hidden confounder — so latent DML should be directly comparable to econometric control-function and measurement-error estimators; the paper does not draw that connection or run that comparison.","The variance-reduction argument points to a use the paper only mentions in passing: applying the latent second stage in settings with no confounding at all as a pure precision booster, for instance in randomized trials where unconfoundedness holds by design.","A testable extension the paper does not run: generate the confounder as continuous but fit the shifted-Bernoulli model, and trace the bias of the causal estimate as the deviation grows; the paper's misspecification argument predicts gradual degradation, but its experiments cover only Laplace noise in the outcome-only setting, not misspecification of the confounder's support.","Editorial flag: the main text reports the ROAS advertising effect at 'per 100 days' scales (positive 29.5%, negative 60.4%) while Table 2 labels its unit as 'per 10 days'; the scaling of the signed effects should be checked before the direction claim is used."],"forward_implications":["With a well-specified latent model, the unconfoundedness condition $E[UV\\mid X] = 0$ is no longer required: latent DML is consistent for $\\theta$ even when a hidden factor drives both treatment and outcome, a regime where ordinary DML is inconsistent.","Because the latent fit runs in the second stage only, the first-stage ML models are trained exactly once; latent DML inherits DML's computational decoupling and adds a single EM run on the residuals.","The asymptotic variance formula of Theorem A.7 implies the latent adjustment narrows confidence intervals even when no confounding is present, since conditioning on the posterior of $Z$ reduces the variance of the estimating equation by the law of total variance.","BIC selection between the outcome-latent and confounder-latent structures is claimed to stay reliable under misspecification, for instance with Laplace-distributed outcome noise, so the method can be applied without prior knowledge of the latent structure.","In the real-data analyses, omitting covariates such as IRA participation (a treatment-outcome confounder) yields less bias than ordinary DML or coordinated DML, and the ad-timing effect on ROAS flips from an implausible positive value to the domain-expected negative value once the latent adjustment is applied."],"supporting_citations":[{"why":"supplies the double-machine-learning paradigm (cross-fitting, Neyman orthogonality, and the fourth-root nuisance convergence rate) that latent DML extends and whose regularity assumptions the theorems reuse.","marker":"[15]"},{"why":"the partially linear model whose residual structure — outcome residual equals the causal effect times the treatment residual plus noise — is the substrate of the second-stage score equation.","marker":"[50]"},{"why":"the identification criterion of non-singular Fisher information that Proposition B.2 invokes to justify Assumption A.4(a) for the latent models.","marker":"[51]"},{"why":"maximum-likelihood consistency under misspecification, the argument the paper cites for latent DML remaining valid when the residual model is approximate.","marker":"[32]"},{"why":"maximum likelihood under misspecified models, cited alongside [32] to support validity when the underlying distribution is approximated.","marker":"[59]"},{"why":"the coordinated DML baseline that latent DML is compared against in the 401(k) experiment.","marker":"[25]"},{"why":"ElasticNet, the model used for first-stage nuisance estimation and as the direct regression baseline in the synthetic and real-data experiments.","marker":"[30]"}],"fun_headline_variants":["Latent DML tames hidden confounders for unbiased effects","Robust causal estimates via latent-variable double ML","Latent factors wipe out DML's hidden-bias blind spot","Hidden confounders? Latent DML has the remedy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The adjusting term $E[f_u(Z)\\mid R, V, \\hat{\\gamma}]$ only removes the confounding if the latent parameters are identified from the residual likelihood alone: the paper assumes the moment condition vanishes only at the true $\\gamma_0$ (Assumption A.4(a)) and asserts, with the verification left as 'straightforward', that its shifted exponential and shifted Bernoulli models satisfy this (Appendix B.2.1), so a near-singular Fisher information would let the EM fit settle on the wrong adjustment and the bias would return.","fun_headline_variants_meta":{"raw":{"variants":["Latent DML tames hidden confounders for unbiased effects","Robust causal estimates via latent-variable double ML","Latent factors wipe out DML's hidden-bias blind spot","Hidden confounders? Latent DML has the remedy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000203,"raw_usage":{"total_tokens":1418,"prompt_tokens":1011,"completion_tokens":407,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":627,"completion_tokens_details":{"reasoning_tokens":336}},"tokens_in":627,"tokens_out":407,"duration_ms":4283,"temperature":1.0,"reasoning_tokens":336,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:48:24.176352+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate data from the confounder latent model with the Bernoulli probability $q$ near the boundary ($q \\approx 0.01$) and with noise variances large relative to the loadings $a$ and $b$; fit latent DML across many EM restarts and check whether the fitted latent parameters recover their generating values and whether the empirical Fisher information at the EM solution stays well conditioned. If the latent parameters drift across restarts while $\\hat{\\theta}$ stays near the truth, the identification condition is failing and the paper's stated mechanism is not what is carrying the estimate; if $\\hat{\\theta}$ itself drifts, the consistency claim fails exactly in the regime the paper does not test.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the double-machine-learning paradigm (cross-fitting, Neyman orthogonality, and the fourth-root nuisance convergence rate) that latent DML extends and whose regularity assumptions the theorems reuse."},{"cited_title":"Robinson","cited_arxiv_id":null,"evidence_quote":"the partially linear model whose residual structure — outcome residual equals the causal effect times the treatment residual plus noise — is the substrate of the second-stage score equation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the identification criterion of non-singular Fisher information that Proposition B.2 invokes to justify Assumption A.4(a) for the latent models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"maximum-likelihood consistency under misspecification, the argument the paper cites for latent DML remaining valid when the residual model is approximate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"maximum likelihood under misspecified models, cited alongside [32] to support validity when the underlying distribution is approximated."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the coordinated DML baseline that latent DML is compared against in the 401(k) experiment."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"ElasticNet, the model used for first-stage nuisance estimation and as the direct regression baseline in the synthetic and real-data experiments."}],"review_version":1}