{"id":"7ea6687b-3cec-4cfb-86c5-d1dc13da349e","arxiv_id":"2502.09591","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"The optimal variational posterior in latent variable survival models depends on the censoring indicator, and the proposed CD-CVAE uses separate encoders for events and censored observations to reduce inference bias.","lead":"This paper argues that variational inference for survival models should condition the approximate posterior on whether an observation is censored, not just on the observed time and covariates. It introduces censor-dependent variational inference (CDVI) and a VAE implementation, and reports improved C-index and Brier scores on several clinical benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The simulated 'true posterior' in Appendix C.2 is not the posterior of the declared generative model, so Table 2 does not demonstrate that CDVI reduces the inference gap.","rationale":"The reader's weakest_assumption identifies precisely the most load-bearing empirical flaw: the simulated 'true posterior' is not derived from the generative model, so the headline claim of reduced inference gaps is not actually demonstrated. The theoretical argument itself appears internally consistent: Proposition 3.1 correctly shows that a single q(z|x,y) cannot be simultaneously tight for both event and censored contributions at overlapping points unless the decoder is degenerate, and Theorem 3.2.1 correctly identifies the optimal q as the censor-conditioned posterior. Thus the core conceptual contribution is not threatened. The concern is that the paper's own validation of this contribution is broken. The simulation in Appendix C.2 defines the Gibbs step P(Z|X,Y,I) arbitrarily, and the two conditional steps are incompatible with the declared generative model; the KL numbers in Table 2 therefore compare encoders to a hand-specified normal target, not to the model's posterior. This is a serious internal inconsistency in the empirical section, and it should be fixed before acceptance. I also note that the real-data experiments do not include a same-architecture vanilla CVAE baseline, which further weakens the practical claim, but the simulation mismatch is the more fundamental issue because it invalidates the direct measurement of the inference gap. The reader's CONDITIONAL verdict is appropriate: the theory can stand, but the paper needs a corrected simulation or a redesigned experiment before the empirical claims are taken at face value.","tokens_in":29079,"tokens_out":9131,"duration_ms":98630,"concrete_test":"Recompute Table 2 using the true posterior implied by the declared generative model. For each simulated (x_i, y_i, δ_i), with the prior used in the released code (e.g., p(z)=N(0,I)) and known σ, compute unnormalized posterior weights w(z)=p(z)·N(y_i; z1+x_i·z2, σ²)^δ_i · (1−Φ((y_i−z1−x_i·z2)/σ))^{1−δ_i} on a fine grid or via importance sampling; normalize to obtain the exact posterior. Then compute the average KL divergence from the trained CD-CVAE and CV-AE encoders to this posterior for event and censored subsets. If CD-CVAE and its IS/DVI variants still dominate CV-AE on these recomputed E-KL/C-KL, the empirical claim survives; otherwise the inference-gap experiment must be redesigned around the model's actual posterior.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.2 and Appendix C.2: the simulation is described as Gibbs sampling with a known true posterior, but the step P(Z|X,Y,I) is manually set to N((2δ−1)(3/exp(x+y), 3/exp(x+y)), I). For the declared generative model P(U|X,Z)=N(z1+x·z2, σ²) with a prior on Z, the actual posterior is proportional to p(z)·f_U(y|x,z) for δ=1 and to p(z)·S_U(y|x,z) for δ=0. These two conditional specifications are not compatible, so the alternating sampler is not a valid Gibbs sampler for the declared model, and the 'true posterior' used in Table 2 and Figure 2 is an arbitrary target rather than the model's posterior. Consequently E-KL/C-KL in Table 2 do not measure the inference gap defined in Section 2.4. This removes the primary empirical support for the claim that CDVI reduces the inference gap. The theoretical results (Proposition 3.1 and Theorem 3.2.1) are not affected, but the empirical bridge between the theory and the proposed method is missing a valid check.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies variational inference for latent variable survival models (LVSMs) under right censoring. It argues that the standard choice q(z|x,y) used in vanilla VI cannot simultaneously provide tight bounds for both the event density and the survival function, except in degenerate cases (Proposition 3.1). It proposes censor-dependent variational inference (CDVI) with q(z|x,y,delta), derives the corresponding ELBO-C, and introduces CD-CVAE with importance-sampling and delta-method variants. Theoretical appendices prove monotonicity of the inference gap, an SNIS-type KL representation, consistency of the estimators, and asymptotic bias reduction for the delta variant. Experiments include a simulation study measuring KL to a predefined 'true posterior', plus benchmark survival datasets comparing C-index, time-dependent C-index, and Brier score.","tokens_in":29281,"tokens_out":6049,"duration_ms":64520,"significance":"The central theoretical claim—that the optimal variational distribution for the censored survival likelihood is the posterior p(z|x,y,delta), and that a single shared q(z|x,y) achieves a zero inference gap only under degenerate decoders—is coherent and practically relevant for survival analysis. The extensions of importance-weighted bounds and self-normalized importance sampling to the event/censoring mixture setting are nontrivial, and the code is released. However, the main empirical demonstration is compromised because the simulated 'true posterior' is not the posterior of the declared generative model, so Table 2 does not currently test the paper's inference-gap claims. With a corrected simulation, this could be a solid contribution; as written, the empirical bridge between the theory and the proposed method is missing a valid check.","major_comments":[{"comment":"The simulation defines P(Z|X,Y,delta) manually as a normal distribution with mean (2delta-1)(3/exp(x+y), 3/exp(x+y)) and identity covariance, but this is not the posterior of the declared generative model P(U|X,Z) ~ N(z1 + x*z2, sigma^2) with a prior on Z. For delta=1, the actual posterior is proportional to p(z|x) * N(y | z1 + x*z2, sigma^2), and for delta=0 it is proportional to p(z|x) * (1 - Phi((y - (z1+x*z2))/sigma)); neither matches the manually specified normal distribution. Consequently, the alternating sampler in Appendix C.2 is not a valid Gibbs sampler for the declared model, and the E-KL/C-KL values in Table 2 and Figure 2 measure divergence to an arbitrary target rather than the inference gap B(theta,phi) defined in Eq. (9). This removes the primary empirical support for the claim that CDVI reduces the inference gap. Please replace this with a valid check: either compute the actual posterior of the declared generative model by numerical integration or MCMC, or define a generative model whose exact posterior has the intended normal form.","section":"Section 5.2 and Appendix C.2"},{"comment":"The paper reports the highest test metric over five repeated runs (Appendix C.4) and claims 'significant improvements', but Tables 8-10 show that on most benchmark datasets the differences between CD-CVAE and strong baselines are within one standard deviation. For example, on SUPPORT the C-index of CD-CVAE is 0.679 +/- 0.003 versus 0.677 +/- 0.005 for RSF, and on PBC the Brier score is 0.127 +/- 0.004 versus 0.123 +/- 0.005 for RSF. Selecting the best of five runs inflates apparent performance and is not a standard basis for claiming significance. Please report mean +/- standard deviation for the actual evaluation protocol and, if 'significant improvements' is claimed, provide paired statistical tests with appropriate multiple-comparison correction.","section":"Section 5.3 and Tables 4-5, 8-10"}],"minor_comments":[{"comment":"In the definition f_theta(u,z|x) := f_theta(u|x,z) p_theta(x|z), the factor should be p_theta(z|x), not p_theta(x|z); this same typo appears in the surrounding discussion.","section":"Section 3.1.1 and Lemma 3.1"},{"comment":"The claim that the marginal q*(z|x,y) equals q*_i(z|x,y) if and only if P(delta=2-i | Y=y)=1 is not strictly true: equality also holds whenever p(z|x,y,delta=1) and p(z|x,y,delta=0) coincide. The remark should be qualified with the non-degenerate condition.","section":"Remark 3.2"},{"comment":"The definitions P1(m) proportional to z_{1:m} J1(m) and P2(k) proportional to z_{1:k} J2(k) are dimensionally inconsistent; as used in the proof of Theorem 4.3.2, P1(m) and P2(k) should be proportional to J1(m) and J2(k) respectively.","section":"Equation (15)"},{"comment":"The proof chain contains a strict inequality 'max(...) > min(...)' that may fail under equality; the monotonicity statement remains correct with non-strict inequalities throughout.","section":"Theorem 4.3.1 proof"},{"comment":"The theorem should state explicitly that the variational family is unrestricted over all distributions on Z; as written, 'optimal' is essentially the definition of the posterior, and the novelty lies in the consequences for vanilla VI rather than in the theorem itself.","section":"Theorem 3.2.1"},{"comment":"The phrase 'true posterior is known and predefined' is confusing: a predefined conditional distribution is not the posterior of the declared generative model unless the model is specifically constructed to have that posterior. Also, the header 'MTBC' in Table 4 should be 'METABRIC'.","section":"Appendix C.2 and Table 4"}],"recommendation":"major_revision","confidential_remarks":"The theoretical core is defensible, but the simulation flaw is load-bearing because it invalidates the paper's main empirical demonstration of reduced inference gaps. I do not see evidence of misconduct; this looks like a design oversight in the simulation. The fix is within scope: replace the arbitrary 'true posterior' with the actual posterior of the declared generative model, or redefine the generative model so that the intended posterior holds exactly. If the authors cannot produce a valid simulation check, the inference-gap claims should be substantially downgraded and the paper should rely only on benchmark performance, with appropriate statistical reporting. I would also encourage the authors to temper the 'first comprehensive study' and 'significant improvements' wording."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core theoretical claim here is genuinely new and, as far as I can tell, correct: in a latent variable survival model the posterior of the latent depends on whether the label is an event or a censoring time, so a variational family that conditions only on (x, y) is trying to fit two different conditionals with one distribution. Proposition 3.1 and Theorem 3.2.2 give a coherent characterization of the resulting degradation (lazy posterior, posterior collapse, decoder independent of z), and the censor-dependent ELBO is the natural fix. The extensions of IWAE, SNIS, and the delta method to censored likelihoods are competently done; I did not find a gap in the main proofs, only a few typos like p_theta(x|z) where p_theta(z|x) was meant. The paper earns credit for identifying a real blind spot in the LVSM literature.\n\nThe soft spots are mostly in the experiments, and one of them is serious. Appendix C.2 defines the 'true posterior' P(Z|X,Y,delta) as a hand-specified normal with mean (2δ−1)(3/exp(x+y), 3/exp(x+y)) and identity covariance. That distribution is not the posterior of the declared generative model P(U|X,Z)=N(z1+x·z2, σ²) with a normal prior. So Table 2's E-KL/C-KL values are distances to an arbitrary target, not the inference gap defined in Section 2.4. The stress-test note is right: the primary empirical support for the claim that CDVI reduces the inference gap does not hold as written. The theory is unaffected, but the bridge from theory to practice is missing a valid check.\n\nOther issues are less severe but still worth fixing. The real-data benchmarks never include a same-architecture vanilla CVAE baseline, so the improvements reported on WHAS etc. could partly come from architecture or tuning rather than conditioning on delta. The main tables report the best test metric across five seeds, not mean±std; the appendix gives means and std, which are more honest, and some of the advantages shrink or vanish there. The conclusion also overclaims: calling this the 'first comprehensive study' and 'a pioneering paradigm' is more than the evidence supports.\n\nBottom line: this is a paper worth serious refereeing. The theoretical contribution is solid, novel, and likely to be cited. The simulation needs to be redesigned so the true posterior is derived from the generative model, or the claims about reduced inference gaps need to be downgraded to 'consistent with the theory on a synthetic target'. With that fixed, and with a same-architecture vanilla baseline added, I would be comfortable with acceptance.","headline":"The censor-dependent VI idea is right and worth publishing, but the simulation does not validate it because the 'true posterior' is imposed rather than derived, so the empirical section needs rework before acceptance.","tokens_in":29851,"tokens_out":1394,"would_cite":true,"duration_ms":16401,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62N01","62F15","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Variational inference for survival models must condition on the censoring indicator; a shared posterior that ignores it provably collapses the latent representation unless the decoder is degenerate.","keywords":["variational inference","survival analysis","censoring","latent variable models","inference gap","posterior collapse","variational autoencoder","censor-dependent variational inference"],"falsifier":"Recompute the inference-gap comparison using the posterior actually implied by the paper's generative model—decoder $P(U|X,Z)$ normal with mean $z_1 + x z_2$ and variance $\\sigma^2$, and a normal prior on $Z$—by conditioning that joint model on $(X,Y,\\delta)$; if CD-CVAE's learned $q$ is not closer to this model-implied posterior than the vanilla CVAE's $q$ across censoring rates, the paper's empirical claim fails. Alternatively, exhibit a single non-degenerate location-scale LVSM with overlapping event and censoring spaces where vanilla VI attains zero inference gap, which would contradict Proposition 3.1.","tokens_in":28819,"feed_emoji":"⏳","tokens_out":10626,"duration_ms":225906,"temperature":0.7,"pith_summary":"This paper claims that latent-variable survival models have been using the wrong target for variational inference. The optimal variational distribution that exactly bounds the survival log-likelihood is the posterior of the latent variable given covariates, observed event time, and the censoring indicator—so the approximating family should change when the censoring status changes. The authors prove that a single shared posterior $q(z|x,y)$, the choice made by existing VAE-based survival models, can achieve a zero inference gap only if the decoder's hazard and location are both independent of the latent variable, which makes the latent representation useless and can trigger full posterior collapse. They introduce censor-dependent variational inference (CDVI) with $q(z|x,y,\\delta)=q_{\\phi_1}(z|x,y)^\\delta q_{\\phi_2}(z|x,y)^{1-\\delta}$, implemented as a V-structure conditional VAE, and extend importance-sampling and delta-method bounds to this setting with monotonicity, self-normalized importance-sampling, and consistency guarantees. If the claim holds, survival models can be trained with the same decoders but censor-aware encoders, yielding tighter likelihood bounds and better individual survival distributions.","feed_headline":"Censor-blind variational inference breaks latent survival models","feed_subtitle":"Vanilla VI ignores the latent under censoring; censor-aware encoders tighten the bound and lift benchmark scores.","key_machinery":"The censor-dependent variational distribution $q_{\\phi_1,\\phi_2}(z|x,y,\\delta) := q_{\\phi_1}(z|x,y)^\\delta q_{\\phi_2}(z|x,y)^{1-\\delta}$, a pair of encoders switched by the event indicator $\\delta$. It is the object that carries the argument: it is exactly the posterior for the joint likelihood (2), it breaks the constraint $\\phi_1=\\phi_2$ that forces the vanilla optimum to ignore the latent variable, and it defines the ELBO-C objective (13) used for training. The supporting machinery is the inference-gap identity $B(\\theta,\\phi)=L(\\theta)-\\mathrm{ELBO}(\\theta,\\phi)$ and the degradation analysis (Lemma 3.1, Proposition 3.1, Remark 3.1) that locates the failure of vanilla VI in the overlap of event and censoring spaces.","core_discovery":"The central claim is that the variational distribution which optimally bounds the censored log-likelihood is the conditional posterior $p(z|x,y,\\delta)$, and that every practical failure mode of vanilla VI traces to marginalizing $\\delta$ out. Theorem 3.2.1 proves that the pointwise optimal $q_{\\phi^*}(z|x,y,\\delta)$ equals the posterior density of $P(Z|X,Y,\\delta)$ and, when event and censoring sample spaces coincide, is independent of the censoring-time parameters. Proposition 3.1 shows that if one shared $q(z|x,u)$ is required to make both the density bound (5) and the survival bound (6) tight, then under a location-scale decoder the hazard function and the location parameter must both be independent of $z$, so the optimal posterior is just the prior: the encoder is lazy and, under a V-structure latent, posterior collapse is unavoidable. The paper's proposed fix is the censor-dependent family of Definition 3.2, whose two components $q_{\\phi_1}$ and $q_{\\phi_2}$ are linked by $q_{\\phi_1}(z|x,y) \\propto_z h_\\theta(y|x,z) q_{\\phi_2}(z|x,y)$ at optimality (Theorem 3.2.2), and which admits a strictly tighter ELBO on a strictly larger set of decoders than vanilla VI. The augmented variants transfer importance-weighted and delta-method corrections to the censor-dependent ELBO, giving a monotone sequence of bounds converging to $L(\\theta)$.","pith_inferences":["The same conditioning principle should carry over to other missing-data patterns in survival analysis—competing risks, interval censoring, and left truncation—where the variational family would condition on the full observation mask rather than on covariates and one scalar time.","A practical diagnostic follows from the theory: in any trained survival VAE, compare the encoders evaluated on event versus censored patients; if they coincide at convergence, the model has landed at the vanilla optimum and the decoder is likely ignoring the latent variable.","The paper's simulation protocol hand-specifies the posterior target for $Z$; re-running the comparison against the posterior actually implied by the stated generative model would separate the benefit of censor-dependent structure from the benefit of a favorable simulation target, a check the paper does not perform."],"forward_implications":["Existing latent-variable survival models that use a censoring-blind encoder carry a provably positive inference gap on any dataset where event and censoring regions overlap, which includes standard benchmark data.","CDVI can be dropped into current VAE-based survival models without changing the decoder, so the theoretical fix translates to a modest implementation change.","The importance-sampling and delta-method variants give practitioners a tunable trade-off: more samples per observation strictly shrink the inference gap (Theorem 4.3.1) and the estimators are consistent as sample counts grow.","Under a V-structure latent where $z$ is independent of covariates, CDVI is posterior-collapse-free while vanilla VI provably collapses, so representations of individual-level latent factors survive censoring.","On the paper's benchmark experiments, CD-CVAE reports the highest concordance index on FLCHAIN, NWTCO, and WHAS and the lowest Brier score on FLCHAIN and METABRIC among the compared models."],"supporting_citations":[{"why":"Defines the inference gap $B(\\theta,\\phi)=L(\\theta)-\\mathrm{ELBO}(\\theta,\\phi)$ and the notion of inference suboptimality that the paper's optimality analysis builds on.","marker":"Cremer et al. (2018)"},{"why":"Source of the latent non-identifiability and posterior-collapse concepts that Proposition 3.1 extends to censored survival settings.","marker":"Wang et al. (2021)"},{"why":"Provides the importance-weighted bound whose monotonicity Theorem 4.3.1 generalizes to the censor-dependent ELBO with $m$ and $k$ samples.","marker":"Burda et al. (2015)"},{"why":"Supplies the self-normalized importance-sampling KL identity that Theorem 4.3.2 corrects and adapts to censored data.","marker":"Domke & Sheldon (2018)"},{"why":"Basis of the delta-method variant DVI and the asymptotic bias reduction proved in Theorem A.4.","marker":"Nowozin (2018)"},{"why":"The 'lazy posterior' variational strategy this paper criticizes; also a benchmark baseline in the experiments.","marker":"Nagpal et al. (2021a)"},{"why":"VAE-based survival model whose x-only encoder ignores the observed time; it is a target of the critique and a benchmark baseline.","marker":"Apellániz et al. (2024)"},{"why":"Provides the reparameterization trick used to implement amortized CDVI in the CD-CVAE encoder.","marker":"Kingma & Welling (2014)"}],"fun_headline_variants":["Optimal variational distribution depends on censoring","CDVI: Censor-dependent inference for survival models","Censor-aware encoders fix latent survival VI","Survival VI needs censor-dependent posterior","Censoring breaks naive VI; use CDVI instead"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The empirical case for reduced inference gaps assumes that the hand-set normal distribution used as the Gibbs-sampling target for $Z$ in the simulations is the true posterior, even though the paper's own generative model for $U$ implies a different posterior.","fun_headline_variants_meta":{"raw":{"variants":["Optimal variational distribution depends on censoring","CDVI: Censor-dependent inference for survival models","Censor-aware encoders fix latent survival VI","Survival VI needs censor-dependent posterior","Censoring breaks naive VI; use CDVI instead"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001464,"raw_usage":{"total_tokens":5919,"prompt_tokens":1003,"completion_tokens":4916,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":4844}},"tokens_in":619,"tokens_out":4916,"duration_ms":29412,"temperature":1.0,"reasoning_tokens":4844,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T20:56:32.687379+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the inference-gap comparison using the posterior actually implied by the paper's generative model—decoder $P(U|X,Z)$ normal with mean $z_1 + x z_2$ and variance $\\sigma^2$, and a normal prior on $Z$—by conditioning that joint model on $(X,Y,\\delta)$; if CD-CVAE's learned $q$ is not closer to this model-implied posterior than the vanilla CVAE's $q$ across censoring rates, the paper's empirical claim fails. Alternatively, exhibit a single non-degenerate location-scale LVSM with overlapping event and censoring spaces where vanilla VI attains zero inference gap, which would contradict Proposition 3.1.","supporting_citations":[{"cited_title":"Inference suboptimality in variational autoencoders","cited_arxiv_id":null,"evidence_quote":"Defines the inference gap $B(\\theta,\\phi)=L(\\theta)-\\mathrm{ELBO}(\\theta,\\phi)$ and the notion of inference suboptimality that the paper's optimality analysis builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the latent non-identifiability and posterior-collapse concepts that Proposition 3.1 extends to censored survival settings."},{"cited_title":"and Sheldon, D","cited_arxiv_id":null,"evidence_quote":"Supplies the self-normalized importance-sampling KL identity that Theorem 4.3.2 corrects and adapts to censored data."},{"cited_title":"Debiasing evidence approximations: On importance-weighted autoencoders and jackknife variational inference","cited_arxiv_id":null,"evidence_quote":"Basis of the delta-method variant DVI and the asymptotic bias reduction proved in Theorem A.4."}],"review_version":1}