{"id":"e3566f66-5c36-4b5e-a5eb-91873928d517","arxiv_id":"2505.07180","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"The paper adapts nonlinear-ICA identifiability to time series imputation and claims separable latent states and missing-cause variables are identifiable under MAR and MNAR, but the missing-cause proof omits the missingness mask.","lead":"This paper builds separate time series imputation models for data missing at random versus missing not at random, and claims a mathematical guarantee that hidden states and missing-cause variables can be recovered. A generalist might read it because matching the right missing-data mechanism matters for health and sensor data, but the guarantee for missing-cause variables is not actually tied to the observed missingness.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorems 1 and 2 assert component-wise identifiability of the missing-cause variable c_t, but the proof never connects c_t to observed data: the ELBOs in Eqs. (5) and (13) contain no term for the observed missingness mask, so c_t is a latent variable with no modeled observed descendant.","rationale":"The reader's weakest assumption is exactly the missing-cause identifiability step: c_t is not connected to the missingness mask in the model, and the proof asserts rather than derives p(h_c(c_hat_t)) = p(c_t). My stress-test pass confirms that this is the load-bearing gap. Theorems 1 and 2 are the paper's main theoretical contribution, and the abstract explicitly claims latent variables are identifiable; if the c_t half of that claim is unsupported, the central claim collapses. I do not see an alternative reading that rescues the proof: the ELBOs in Eqs. (5) and (13) optimize reconstruction of x^m_t given z_t and c_t, and the KL terms regularize encoders for z_t and c_t, but the observed missingness mask that should reveal c_t's causal role is absent from all factors. Without a p(mask | c_t, ...) term or an equivalent observed-descendant condition, any two priors over c_t related by an invertible transformation are observationally equivalent. The experimental sections are extensive and the method may perform well as an imputation heuristic, but strong empirical numbers do not fix a missing derivation in the identification proof. The reader's REJECT verdict is therefore appropriate: the paper overclaims its identification results as stated. I am not raising a dispute with the nonlinear-ICA framework or with the z_t argument; the concern is specifically that the c_t identification theorem lacks a necessary observable link.","tokens_in":43320,"tokens_out":4443,"duration_ms":49434,"concrete_test":"Write the observed-data likelihood for the MAR model with the mask explicitly included: L = ∫ p(x^o_t) p(z_t|x^o_t) p(c_t|x^o_t) p(mask_t | x^m_t) p(x^m_t | z_t, c_t, x^o_t) dz_t dc_t dx^m_t, and check whether L is invariant under any smooth invertible reparameterization c_t → h(c_t) whenever the model contains no factor p(mask_t | c_t, ...). A direct analytical check is to re-derive the sentence \"Similarly, we have p(h_c(c_hat_t)) = p(c_t)\" from first principles: identify the observed marginal from which this equality follows. If no such marginal can be exhibited, the theorem is unproven.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim is that, under MAR and MNAR, both temporal latent states z_t and missing-cause variables c_t are component-wise identifiable. The load-bearing condition for the c_t part is that c_t must influence the observed distribution. In the imputation m-graph of Figure 1, c_t feeds into the missing values x^m_t, but those values are exactly what is unobserved. The observed data are x^o_t and the missingness mask. However, none of the generative factorizations in Eqs. (3)-(4) or the ELBOs in Eqs. (5) and (13) contains a factor p(mask_t | c_t, ...), and the mask never appears as a modeled random variable. In the proof of Theorem 1 (Appendix C), the c_t argument begins with the assertion \"Similarly, we have p(h_c(\\hat c_t)) = p(c_t)\" and then proceeds with derivatives. No step derives this equality from any observed marginal. For z_t the proof at least starts from a matched marginal p(\\hat x_t) = p(x_t); for c_t there is no analogue because the only variable c_t is claimed to generate is missing. An arbitrary smooth invertible reparameterization of c_t therefore leaves the observed-data likelihood and the training objective unchanged, so component-wise identification of c_t cannot hold as stated. This is not a question of extra assumptions being strong or weak: the stated theorem's proof omits the essential link between c_t and the observations. The empirical imputation results in Tables 1-16 may still demonstrate a useful method, but they do not supply the missing identification guarantee, and the abstract's claim that latent variables are identifiable is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DMM, a variational framework for time series imputation that treats MAR and MNAR missing mechanisms separately. It models data generation through temporal latent states z_t and missing-cause variables c_t, estimates their priors with normalizing-flow architectures, and claims component-wise identifiability of both z_t and c_t under nonlinear ICA assumptions (Theorems 1 and 2). The authors support the framework with extensive experiments on simulated and real-world datasets, including ablation, sensitivity, mixed-mechanism, and healthcare (MIMIC-III) evaluations.","tokens_in":43711,"tokens_out":7184,"duration_ms":66784,"significance":"If the central identifiability claim were valid, the paper would make a useful contribution by linking missing-data mechanisms to causal representation learning and providing mechanism-specific imputation guarantees. The empirical study is broad and includes useful checks (simulation MCC, sensitivity analysis, ablation, mixed mechanisms). However, the claimed identifiability of the missing-cause variable c_t is not established: the proof simply asserts a distributional equality for c_t without deriving it from any observed marginal, and the missingness mask, which is the natural observed consequence of c_t, is absent from the model. This gap affects the main theoretical contribution of the paper. The z_t part follows the standard nonlinear-ICA argument of Yao et al. (2022) and is likely sound under the stated assumptions, but the c_t part is not. On balance, the results as presented do not support the advertised guarantees.","major_comments":[{"comment":"The proof of Theorem 1 (Appendix C, after Eq. (30)) begins the c_t argument with the assertion 'Similarly, we have p(h_c(\\hat c_t)) = p(c_t)', and Theorem 2 (after Eq. (41)) repeats this for p(\\hat c_t|x_{t-1}). This equality is not derived from any observed marginal. For z_t, the proof starts from the matched marginal p(\\hat x_t) = p(x_t); for c_t, the only variable it is claimed to generate, x^m_t, is missing by definition, and the missingness mask is absent from the generative factorizations (Eqs. (3)-(4)) and from the ELBOs (Eqs. (5) and (13)). Consequently, an arbitrary smooth invertible reparameterization c'_t = h(c_t), with the prior p(c'_t|x^o_t) adjusted accordingly, leaves every term in the training objective unchanged. The linear independence condition in A2 (and A3) is stated in terms of derivatives of p(c_t|x^o_t), which is a quantity involving an unobserved variable; the condition cannot be checked or exploited without an observed variable that depends on c_t. Component-wise identifiability of c_t therefore does not follow from the stated proof. This is load-bearing because the abstract and Section 4 claim identifiability of both z_t and c_t.","section":"Section 4, Appendix C"},{"comment":"The imputation m-graph in Figure 1(a,b) includes c_t -> x^m_t, but x^m_t is the missing part of the data. The standard missing-data machinery uses the mask indicator as the observed consequence of the missingness mechanism; here the mask is used to create training data (Section B.2) but never appears as a modeled random variable in the factorizations or the ELBOs. To identify c_t, one would need a likelihood term p(mask_t | c_t, ...) or p(mask_t | x^o_t, x^m_t) and a corresponding observed marginal to match. The ELBOs contain only the reconstruction term p(x^m_{1:T}|z_{1:T},c_{1:T}) (evaluated on partially observed or imputed targets) and KL terms for z and c. Since c_t has no observed descendant in the model, the observed-data likelihood is invariant to reparameterizations of c_t. The paper never states which observed quantity identifies p(c_t|x^o_t) in Eq. (3) or p(c_t|x_{t-1}) in Eq. (4).","section":"Eqs. (5), (13); Figure 1"},{"comment":"There is an inconsistency between the generative process used for identification and the ELBO actually optimized. The identification proof for c_t in Theorem 1 targets p(c_t|x^o_t), and Theorem 2 targets p(c_t|x_{t-1}); these conditional distributions appear in the joint factorizations (3) and (4). However, the ELBO derivation in Appendix F.2 (Eq. (63) for MAR and Eq. (64) for MNAR) uses the factorization p(c_{1:T}|z_{1:T}) in the generative model, and Eq. (5)/(13) in the main text use a KL divergence against p(c_{1:T}) without the conditioning on x^o_t or x_{t-1}. The normalizing-flow prior estimators in Sections 3.2 and 3.4 estimate p(\\hat c_t|x^o_t) (or p(\\hat c_t|x_{t-1})), which are then plugged into the KL terms. This mixing of p(c|x), p(c|z), and p(c) means the optimized objective does not correspond to the generative process for which identifiability is claimed, and it is unclear which distribution is being identified.","section":"Appendix F.2, Eqs. (63)-(64)"}],"minor_comments":[{"comment":"The symbol p(\\hat c_t|x^o_t) is used both as a prior and as a variational posterior; Eqs. (11)-(12) and (19)-(20) should clarify whether the normalizing flow estimates the prior or the approximation q.","section":"Sections 3.2 and 3.4"},{"comment":"Table 3 and Table 12 report MCC for z and c on simulated data, but there is no comparison to a trivial baseline (e.g., predicting c_t from x^o_t without any missingness) and no confidence intervals; the claim of 'high estimation accuracy' is not statistically supported.","section":"Tables 3 and 12"},{"comment":"The notation in Eq. (13) writes E_{q(z_{1:T},c_{1:T}|x_{1:T})} but the second and third terms use q(z|x^o) and q(c|x_{1:T-1}); the joint q is not consistently defined.","section":"Eq. (13)"},{"comment":"The abstract says 'latent variables are identifiable' without qualification; the theorems give sufficient conditions for component-wise identifiability up to an invertible transformation, which should be stated explicitly in the abstract.","section":"Abstract and Section 4"},{"comment":"There are numerous typos and awkward phrasings (e.g., 'one of the most challenge problems', 'the causal relationship between observed and missing variables are unknown', 'we can with the RHS of Equation (47)'), which should be corrected before any resubmission.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The referee assessment aligns with the reader's take: the c_t identification gap is fundamental. The paper would need to model the mask as an observed variable and redo the proof and experiments with a mask-based likelihood; that is beyond a minor revision. The empirical study is extensive but does not compensate for the theoretical gap. The manuscript may be resubmittable if the authors address the mask-modeling issue and clarify the relation between the theory and the optimized objective."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the only genuinely new theoretical piece—the missing-cause variable c_t—is not actually identified by the proof. Second, the experimental study is extensive and suggests the mechanism-specific priors help, but that does not rescue the paper's central claim.\n\nWhat's new: the z_t identification result is borrowed from TDRL (Yao et al. 2022) with the same assumptions and the same derivative-matching argument. The new element is the latent missing-cause c_t, with different conditioning sets for MAR and MNAR, plus normalizing-flow prior estimators. That is a legitimate extension, and the empirical work is unusually thorough: ETT, Exchange, Weather, MIMIC, several baselines, supervised and unsupervised settings, ablation, sensitivity, mixed missing mechanisms, and simulation MCC for both z_t and c_t. The authors deserve credit for that.\n\nThe soft spot is load-bearing. In the generative models (Eqs. 3–4) and the ELBOs (5 and 13), the observed missingness mask never appears. c_t only connects to the unobserved x^m_t. In the proof of Theorem 1, the c_t argument starts with \"Similarly, we have p(h_c(\\hat c_t)) = p(c_t)\" — an assertion, not a derivation from any matched observed marginal. For z_t the proof at least begins from p(\\hat x_t)=p(x_t); for c_t there is no analogue, because the only variable it is supposed to generate is missing. An arbitrary smooth invertible reparameterization of c_t leaves the observed-data likelihood and the training objective unchanged, so component-wise identifiability of c_t cannot hold as stated. This is not a matter of strong assumptions; the proof simply omits the link between c_t and the observations. The paper's limitation section (Appendix G) discusses invertible mixing but never flags this gap. So the abstract's claim that \"latent variables are identifiable\" is unsupported for c_t.\n\nMinor: the identifiability definition in Section 4 is just existence of an invertible map, which is trivial; the intended component-wise statement is what the proof targets. Also the ELBO derivation in Appendix F.2 is sloppy with p(c|z) appearing without explanation.\n\nWho this is for: someone working on missing-data imputation might still find the mechanism-specific prior idea useful, and the experiments give a decent benchmark comparison. But the theoretical guarantee is the selling point, and it doesn't hold. I'd send this to peer review—a good reviewer could push the authors to either include the mask as an observed variable and redo the proof, or reframe the paper as an empirical method without identification claims. As is, reject.","headline":"The paper's new missing-cause identifiability claim is asserted rather than proven — c_t is never connected to observed data — but the empirical study is extensive and the method may still be useful.","tokens_in":44257,"tokens_out":3167,"would_cite":false,"duration_ms":30089,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that time series imputation under MAR and MNAR missingness can recover both the temporal latent states and the latent missing-cause variables, and that these recoveries are component-wise identifiable.","keywords":["time series imputation","missing at random","missing not at random","identifiability","nonlinear independent component analysis","variational inference","normalizing flow","imputation m-graph"],"falsifier":"Simulate data with known ground-truth $c_t$ that generates the mask, train DMM with the mask withheld, and measure the correlation between estimated and true $c_t$; if $c_t$ is not recovered while $z_t$ is, the identifiability claim is false. A sharper version constructs two different ground-truth data-generation processes with the same observed marginal but different $c_t$, and asks the model to distinguish them.","tokens_in":43151,"feed_emoji":"📉","tokens_out":9587,"duration_ms":85151,"temperature":0.7,"pith_summary":"The paper argues that imputation models fail when they ignore which missing-data mechanism generated the gaps. It proposes DMM, a variational framework with separate architectures for missing-at-random (MAR) and missing-not-at-random (MNAR) data, in which temporal latent states $z_t$ and missing-cause variables $c_t$ are estimated jointly. The central theoretical claim is that, under smooth strictly positive conditionally factorized densities and a linear-independence condition, $z_t$ and $c_t$ are component-wise identifiable under both MAR and MNAR. If true, imputation can be tailored to the actual mechanism and the missingness itself becomes interpretable. Experiments on semisynthetic and benchmark time series show that mechanism-matched DMM models reduce imputation error relative to single-mechanism baselines.","feed_headline":"Missing data causes become identifiable in time series imputation","feed_subtitle":"A variational framework separates MAR from MNAR and recovers the latent states and missing-cause variables behind the gaps.","key_machinery":"The central object is the imputation m-graph, a causal graph with observed variables $x^o_t$, missing variables $x^m_t$, latent temporal states $z_t$, and latent missing-cause variables $c_t$. The argument runs on a Jacobian-sparsity mechanism: matching the observed marginal forces an invertible map $h$ between estimated and true latents, conditional independence makes mixed second cross-derivatives of the log-density vanish, and the linear-independence assumptions A2/A3 imply that each row of the Jacobian has exactly one non-zero entry, giving component-wise identifiability. A normalizing-flow prior estimator supplies the log-probabilities and change-of-variable Jacobians needed to compute the KL terms for both $z_t$ and $c_t$.","core_discovery":"The paper establishes identifiability theorems for the time series imputation setting: if observations follow $x_t = g(z_t)$ with an invertible nonlinear mixing $g$, the temporal latent process $z_{t,i}=f_i(z_{t-\\tau}, ...)$, and latent missing causes $c_t$ that drive $x^m_t$, then the learned latent states and missing causes are recoverable up to a component-wise invertible transformation. The proof starts from matched marginal $p(\\hat{x}_t)=p(x_t)$, derives $p(h(\\hat{z}_t))=p(z_t)$ for the invertible map $h = g^{-1} \\circ \\hat{g}$, uses conditional independence of latent components to force cross-derivatives of the log-density to zero, and applies the linear-independence conditions to conclude that the Jacobian of $h$ has a single non-zero entry per row. The same structure, conditioned on $x^o_t$ for MAR and on $x_{t-1}$ for MNAR, yields component-wise identifiability of $c_t$.","pith_inferences":["The model-selection comparison could be turned into an explicit missing-mechanism classifier: train DMM-MAR and DMM-MNAR on labeled synthetic data, then use relative ELBO or imputation error on a new series to announce the mechanism.","The same identification strategy plausibly transfers to other mask-driven generative models, such as image inpainting or tabular missing-value recovery, whenever the conditional-independence and linear-independence conditions hold.","In clinical time series, an identifiable missing-cause variable could become a decision-support feature, signaling patient disengagement before the next scheduled visit."],"forward_implications":["A practitioner can run the mechanism-matched DMM, read off $z_t$ and $c_t$, and impute by sampling from $p(x^m_t \\mid z_t, c_t, x^o_t)$ rather than using a one-size-fits-all model.","Model selection between DMM-MAR and DMM-MNAR serves as a missing-mechanism test: the variant with better validation performance indicates the likely mechanism, and the experiments show mismatching the mechanism degrades results.","MCAR data is declared not identifiable without auxiliary variables, so the framework predicts that latent-cause recovery cannot explain imputation performance on MCAR-dominated data.","The recovered missing-cause variables provide an interpretable reason for why values are absent, not only a numerical filling of the gaps."],"supporting_citations":[{"why":"Defines the MAR/MNAR/MCAR taxonomy that motivates separate models for different missingness.","marker":"[Rubin, 1976]"},{"why":"Supplies the m-graph formalism the paper extends into imputation m-graphs.","marker":"[Mohan et al., 2013]"},{"why":"Provides the smooth-positive-conditional-independence and linear-independence assumptions (A1/A2/A3) and the Jacobian proof template for temporal latent identifiability.","marker":"[Yao et al., 2022]"},{"why":"Contributes the temporally causal latent process model and the change-of-variable prior estimation used for latent states.","marker":"[Yao et al., 2021]"},{"why":"Grounds the VAE/nonlinear-ICA identifiability strategy that links ELBO optimization to identifiable latent representations.","marker":"[Khemakhem et al., 2020a]"},{"why":"Supplies the non-identifiability result for MCAR without auxiliary variables, which the paper uses to justify focusing on MAR and MNAR.","marker":"[Locatello et al., 2019]"}],"fun_headline_variants":["Missing-cause variables recoverable in time series imputation","Identifiability proven for latent states and missing causes","MAR and MNAR distinguished for time series imputation","Causal identifiability for MAR and MNAR imputation","Recovering missing-cause variables in time series imputation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The identifiability of the missing causes rests on the assumption that $c_t$ can be recovered from the observed time series alone, even though the model never includes the pattern of which values are absent that $c_t$ is supposed to generate.","fun_headline_variants_meta":{"raw":{"variants":["Missing-cause variables recoverable in time series imputation","Identifiability proven for latent states and missing causes","MAR and MNAR distinguished for time series imputation","Causal identifiability for MAR and MNAR imputation","Recovering missing-cause variables in time series imputation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000638,"raw_usage":{"total_tokens":2960,"prompt_tokens":985,"completion_tokens":1975,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":1896}},"tokens_in":601,"tokens_out":1975,"duration_ms":12994,"temperature":1.0,"reasoning_tokens":1896,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:23:19.127527+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate data with known ground-truth $c_t$ that generates the mask, train DMM with the mask withheld, and measure the correlation between estimated and true $c_t$; if $c_t$ is not recovered while $z_t$ is, the identifiability claim is false. A sharper version constructs two different ground-truth data-generation processes with the same observed marginal but different $c_t$, and asks the model to distinguish them.","supporting_citations":[{"cited_title":"Inference and missing data","cited_arxiv_id":null,"evidence_quote":"Defines the MAR/MNAR/MCAR taxonomy that motivates separate models for different missingness."},{"cited_title":"Graphical models for inference with missing data","cited_arxiv_id":null,"evidence_quote":"Supplies the m-graph formalism the paper extends into imputation m-graphs."},{"cited_title":"Temporally disentangled representation learn- ing.Advances in Neural Information Processing Systems, 35:26492–26503,","cited_arxiv_id":null,"evidence_quote":"Provides the smooth-positive-conditional-independence and linear-independence assumptions (A1/A2/A3) and the Jacobian proof template for temporal latent identifiability."},{"cited_title":"Challenging common assumptions in the unsupervised learning of disentangled representations","cited_arxiv_id":null,"evidence_quote":"Supplies the non-identifiability result for MCAR without auxiliary variables, which the paper uses to justify focusing on MAR and MNAR."}],"review_version":1}