Pith. sign in

REVIEW 2 major objections 6 minor 65 references

Censor Dependent Variational Inference

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2502.09591 v2 pith:WBQJR7Y6 submitted 2025-02-13 cs.LG stat.ML

Chuanhui Liu , Xiao Wang This is my paper · ORCID
classification cs.LGstat.ML MSC 62N0162F1568T07
keywords variationalinferencesurvivalanalysiscensoringlatentvariablemodelsgapposteriorcollapseautoencodercensor-dependent
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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 $L(\theta)$.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

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.

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 (2)
  1. [Section 5.2 and Appendix C.2] 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.
  2. [Section 5.3 and Tables 4-5, 8-10] 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.
minor comments (6)
  1. [Section 3.1.1 and Lemma 3.1] 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.
  2. [Remark 3.2] 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.
  3. [Equation (15)] 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.
  4. [Theorem 4.3.1 proof] The proof chain contains a strict inequality 'max(...) > min(...)' that may fail under equality; the monotonicity statement remains correct with non-strict inequalities throughout.
  5. [Theorem 3.2.1] 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.
  6. [Appendix C.2 and Table 4] 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'.

Circularity Check

1 steps flagged · score 6.0 of 10

Simulated 'true posterior' is predefined to depend on δ, so the Table 2 inference-gap reduction is built into the target; the proof chain itself is not circular.

  1. self definitional [Section 5.2, Table 2; Appendix C.2]
    "we use Gibbs sampling, where the true posterior is known and predefined. Both P(Z|X,Y,I=1) and P(Z|X,Y,I=0) are set to normal distributions... For δ=0,1, P(Z|X,Y,δ) is normal distributed with mean µz = (2δ−1)(3/exp(x+y),3/exp(x+y))."

    Table 2 reports 'the average KL divergence between the encoder and true posterior' and concludes CD-CV AE 'significantly reduces' it. But this 'true posterior' was not computed from the declared generative model P(U|X,Z) with prior on Z; its mean was manually defined to flip sign with δ. Since CDVI's encoder conditions on δ (Definition 3.2) while vanilla VI's q(z|x,y) does not, the KL comparison measures how well each encoder matches a target that was constructed to require exactly the censor dependence the paper claims to discover. The reduced inference gap is therefore a built-in property of the definition of the target, not independent empirical confirmation that the posterior is δ-dependent.

full rationale

The theoretical derivation chain is self-contained: Lemma 3.1, Proposition 3.1, Theorem 3.2.1, and Theorem 3.2.2 follow from the likelihood in (3), the variational lower bounds in (5)-(6), and standard posterior calculations. No load-bearing self-citation was found; the one self-citation (Liu & Wang 2025) is descriptive in Proposition 4.2 and does not support the central claim. However, the empirical validation of the central inference-gap claim is circular in the specific sense required by the rubric: the 'true posterior' used to compute E-KL and C-KL in Table 2 is predefined in Appendix C.2 as a normal distribution whose mean is (2δ−1)(3/exp(x+y), 3/exp(x+y)), so the target already encodes δ-dependence. Moreover, this conditional is not the posterior implied by the stated generative model P(U|X,Z) ~ N(z1 + x·z2, σ²) with a normal prior, so the alternating sampler is not a valid Gibbs sampler for that model and Table 2 does not measure the inference gap defined in Equation (9). The real-data benchmarks provide independent evidence about time-to-event modeling, and the theoretical results remain unaffected, but the specific demonstration that CDVI reduces the inference gap is partially circular because its success is guaranteed by the construction of the comparison target.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central theoretical claims rely on standard likelihood assumptions, including independent censoring, location-scale family, and regularity conditions. The most fragile entry is the simulation's predefined posterior, which is an ad hoc assumption that the empirical KL comparisons rest on.

free parameters (1)
  • Simulation true-posterior mean mu_z = (2delta-1)(3/exp(x+y), 3/exp(x+y)) for delta in {0,1}
    Hand-specified in Appendix C.2 as the true posterior for KL comparisons, but not derived from the declared generative model. The simulation's validity depends on this arbitrary choice.
assumptions (6)
  • domain assumption Independent censoring: U is independent of C given X, and Y = min(U,C), I = 1(U <= C).
    Section 2.1, Eq. (1). Standard in survival analysis; used throughout the likelihood factorization.
  • domain assumption U|X,Z follows a location-scale family with location mu_theta(x,z) and scale sigma.
    Assumed before Proposition 3.1; needed for the location degradation result.
  • standard math Fubini's theorem applies to interchange integration over z and u.
    Invoked in the proof of Lemma 3.1 to derive equality conditions for the survival bound.
  • domain assumption In Theorem 3.2.1, U|X and C|X have the same support, C is independent of Z given X, and censoring is independent.
    Assumed in Appendix B.2 proof to cancel censoring factors and show q* is independent of the censoring parameters eta.
  • ad hoc to paper The predefined normal posterior in simulations is the true conditional distribution P(Z|X,Y,delta).
    Appendix C.2 sets this distribution directly; it is not derived from the generative model, so the simulation ground truth is an assumption without derivation.
  • standard math Finite moments alpha_i and beta_i for importance-weighted estimators.
    Assumed in Lemma 1 for Taylor expansions; standard regularity for asymptotic results.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Censor Dependent Variational Inference." pith.science (2026). https://pith.science/paper/WBQJR7Y6

@misc{pith2026250209591,
  author       = {Pith},
  title        = {Pith review of: Censor Dependent Variational Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WBQJR7Y6}},
  note         = {Machine review of arXiv:2502.09591}
}
read the original abstract

This paper provides a comprehensive analysis of variational inference in latent variable models for survival analysis, emphasizing the distinctive challenges associated with applying variational methods to survival data. We identify a critical weakness in the existing methodology, demonstrating how a poorly designed variational distribution may hinder the objective of survival analysis tasks - modeling time-to-event distributions. We prove that the optimal variational distribution, which perfectly bounds the log-likelihood, may depend on the censoring mechanism. To address this issue, we propose censor-dependent variational inference (CDVI), tailored for latent variable models in survival analysis. More practically, we introduce CD-CVAE, a V-structure Variational Autoencoder (VAE) designed for the scalable implementation of CDVI. Further discussion extends some existing theories and training techniques to survival analysis. Extensive experiments validate our analysis and demonstrate significant improvements in the estimation of individual survival distributions.

Figures

Figures reproduced from arXiv: 2502.09591 by the authors.

Figure 1
Figure 1. Directed acyclic graphs of LVSM. The shaded [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Comparison on simulated datasets SD4 (see [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Generative graph of CD-CVAE. standard normal distribution, we have ∂ELBO-C ∂σ = Eq[ X i:δi=1 ( y˜ 2 i σ − 1 σ ) + X i:δi=0 h(˜yi) y˜i σ ], where y˜ = (y − µζ (x, z))/σ is the standardized y and h() is standard normal hazard function. The proof of Prop.4.2 is given in Appendix B.4. 4.3. Augmented CDVI and the Implementations Next, we introduce two variants of our proposed model, namely IS and DVI, incorporating estab… view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: Implementations of Vanilla VI and CDVI. First, we propose the Censor-dependent Conditional VAE (CD-CVAE) that estimates parameters θ, ϕ as weights of neural networks. As illustrated in Fig.3, our proposed CDVI implementation uniquely incorporates both y and the event i…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 57 canonical work pages

  1. [1]

    Nonparametric inference for a family of counting processes

    Aalen, O. Nonparametric inference for a family of counting processes. The Annals of Statistics, pp.\ 701--726, 1978

    work page 1978

  2. [2]

    Angelova, J. A. On moments of sample mean and variance. Int. J. Pure Appl. Math, 79 0 (1): 0 67--85, 2012

    work page 2012

  3. [3]

    A time-dependent discrimination index for survival data

    Antolini, L., Boracchi, P., and Biganzoli, E. A time-dependent discrimination index for survival data. Statistics in medicine, 24 0 (24): 0 3927--3944, 2005

    work page 2005

  4. [4]

    A., Parras, J., and Zazo, S

    Apell \'a niz, P. A., Parras, J., and Zazo, S. Leveraging the variational bayes autoencoder for survival analysis. Scientific Reports, 14 0 (1): 0 24567, Oct 2024. ISSN 2045-2322. doi:10.1038/s41598-024-76047-z

    work page doi:10.1038/s41598-024-76047-z 2024

  5. [5]

    Mills' ratio: Monotonicity patterns and functional inequalities

    Baricz, \'A . Mills' ratio: Monotonicity patterns and functional inequalities. Journal of Mathematical Analysis and Applications, 340 0 (2): 0 1362--1370, 2008

    work page 2008

  6. [6]

    R., Vilnis, L., Vinyals, O., Dai, A

    Bowman, S. R., Vilnis, L., Vinyals, O., Dai, A. M., Józefowicz, R., and Bengio, S. Generating sentences from a continuous space. In CoNLL, pp.\ 10--21. ACL, 2016. ISBN 978-1-945626-19-7

    work page 2016

  7. [7]

    Brier, G. W. Verification of forecasts expressed in terms of probability. Monthly weather review, 78 0 (1): 0 1--3, 1950

    work page 1950

  8. [8]

    Brown, L. D. Fundamentals of statistical exponential families: with applications in statistical decision theory. Lecture Notes-Monograph Series, pp.\ i--279, 1986. ISSN 07492170. URL http://www.jstor.org/stable/4355554

    work page arXiv 1986

Show all 65 references
  1. [9]

    Importance weighted autoencoders

    Burda, Y., Grosse, R., and Salakhutdinov, R. Importance weighted autoencoders. arXiv preprint arXiv:1509.00519, 2015

    2015 arXiv

  2. [10]

    Survival cluster analysis

    Chapfuwa, P., Li, C., Mehta, N., Carin, L., and Henao, R. Survival cluster analysis. In Proceedings of the ACM Conference on Health, Inference, and Learning, pp.\ 60--68, 2020

    2020

  3. [11]

    Cox, D. R. Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34 0 (2): 0 187--202, 1972

    1972

  4. [12]

    Inference suboptimality in variational autoencoders

    Cremer, C., Li, X., and Duvenaud, D. Inference suboptimality in variational autoencoders. In International Conference on Machine Learning, pp.\ 1078--1086. PMLR, 2018

    2018

  5. [13]

    Deep contrastive survival analysis with dual-view clustering

    Cui, C., Tang, Y., and Zhang, W. Deep contrastive survival analysis with dual-view clustering. Electronics, 13 0 (24), 2024. ISSN 2079-9292. doi:10.3390/electronics13244866

    2024 doi

  6. [14]

    B., Tran, D., Ranganath, R., Paisley, J., and Blei, D

    Dieng, A. B., Tran, D., Ranganath, R., Paisley, J., and Blei, D. M. The -divergence for approximate inference. In Neural Information Processing Systems, 2017

    2017

  7. [15]

    and Sheldon, D

    Domke, J. and Sheldon, D. R. Importance weighting and variational inference. In Advances in Neural Information Processing Systems, volume 31, 2018

    2018

  8. [16]

    and Simon, R

    Faraggi, D. and Simon, R. A neural network model for survival data. Statistics in medicine, 14 0 (1): 0 73--82, 1995

    1995

  9. [17]

    F., Rana, P., Cruz, A., Calderon, V

    Franco, E. F., Rana, P., Cruz, A., Calderon, V. V., Azevedo, V., Ramos, R. T., and Ghosh, P. Performance comparison of deep learning autoencoders for cancer subtype detection using multi-omics data. Cancers, 13 0 (9): 0 2013, 2021

    2013

  10. [18]

    Frees, E. W. Regression modeling with actuarial and financial applications. Cambridge University Press, 2009

    2009

  11. [19]

    Cyclical annealing schedule: A simple approach to mitigating KL vanishing

    Fu, H., Li, C., Liu, X., Gao, J., Celikyilmaz, A., and Carin, L. Cyclical annealing schedule: A simple approach to mitigating KL vanishing. In Proceedings of the 2019 Conference of the North A merican Chapter of the Association for Computational Linguistics: Human Language Tec...

    2019

  12. [20]

    Rnn-surv: A deep recurrent model for survival analysis

    Giunchiglia, E., Nemchenko, A., and van der Schaar, M. Rnn-surv: A deep recurrent model for survival analysis. In Artificial Neural Networks and Machine Learning--ICANN 2018: 27th International Conference on Artificial Neural Networks, Rhodes, Greece, October 4-7, 2018, Procee...

    2018

  13. [21]

    Assessment and comparison of prognostic classification schemes for survival data

    Graf, E., Schmoor, C., Sauerbrei, W., and Schumacher, M. Assessment and comparison of prognostic classification schemes for survival data. Statistics in medicine, 18 0 (17-18): 0 2529--2545, 1999

    1999

  14. [22]

    Gumbel, E. J. Statistics of Extremes. Columbia University Press, 1958

    1958

  15. [23]

    Effective ways to build and evaluate individual survival distributions

    Haider, H., Hoehn, B., Davis, S., and Greiner, R. Effective ways to build and evaluate individual survival distributions. Journal of Machine Learning Research, 21 0 (85): 0 1--63, 2020

    2020

  16. [24]

    E., Califf, R

    Harrell, F. E., Califf, R. M., Pryor, D. B., Lee, K. L., and Rosati, R. A. Evaluating the yield of medical tests. Jama, 247 0 (18): 0 2543--2546, 1982

    1982

  17. [25]

    Harrell, F. E. et al. Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis, volume 608. Springer, 2001

    2001

  18. [26]

    beta- VAE : Learning basic visual concepts with a constrained variational framework

    Higgins, I., Matthey, L., Pal, A., Burgess, C., Glorot, X., Botvinick, M., Mohamed, S., and Lerchner, A. beta- VAE : Learning basic visual concepts with a constrained variational framework. In International Conference on Learning Representations, 2017

    2017

  19. [27]

    Transformer-based deep survival analysis

    Hu, S., Fridgeirsson, E., van Wingen, G., and Welling, M. Transformer-based deep survival analysis. In Survival Prediction-Algorithms, Challenges and Applications, pp.\ 132--148. PMLR, 2021

    2021

  20. [28]

    B., Blackstone, E

    Ishwaran, H., Kogalur, U. B., Blackstone, E. H., and Lauer, M. S. Random survival forests. The Annals of Applied Statistics, 2: 0 841--860, 2008. doi:10.1214/08-AOAS169

    2008 doi

  21. [29]

    Autosurv: interpretable deep learning framework for cancer survival analysis incorporating clinical and multi-omics data

    Jiang, L., Xu, C., Bai, Y., Liu, A., Gong, Y., Wang, Y.-P., and Deng, H.-W. Autosurv: interpretable deep learning framework for cancer survival analysis incorporating clinical and multi-omics data. NPJ precision oncology, 8 0 (1): 0 4, 2024

    2024

  22. [30]

    I., Ghahramani, Z., Jaakkola, T

    Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., and Saul, L. K. An introduction to variational methods for graphical models. Machine learning, 37: 0 183--233, 1999

    1999

  23. [31]

    Capturing label characteristics in \ vae \ s

    Joy, T., Schmon, S., Torr, P., N, S., and Rainforth, T. Capturing label characteristics in \ vae \ s. In International Conference on Learning Representations, 2021

    2021

  24. [32]

    Kalbfleisch, J. D. and Prentice, R. L. The statistical analysis of failure time data. John Wiley & Sons, 2002

    2002

  25. [33]

    L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., and Kluger, Y

    Katzman, J. L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., and Kluger, Y. Deepsurv: personalized treatment recommender system using a cox proportional hazards deep neural network. BMC medical research methodology, 18: 0 1--12, 2018

    2018

  26. [34]

    Kingma, D. P. and Welling, M. Auto-Encoding Variational Bayes . In 2nd International Conference on Learning Representations, 2014

    2014

  27. [35]

    P., Mohamed, S., Jimenez Rezende, D., and Welling, M

    Kingma, D. P., Mohamed, S., Jimenez Rezende, D., and Welling, M. Semi-supervised learning with deep generative models. Advances in neural information processing systems, 27, 2014

    2014

  28. [36]

    P., Salimans, T., Jozefowicz, R., Chen, X., Sutskever, I., and Welling, M

    Kingma, D. P., Salimans, T., Jozefowicz, R., Chen, X., Sutskever, I., and Welling, M. Improved variational inference with inverse autoregressive flow. Advances in neural information processing systems, 29, 2016

    2016

  29. [37]

    Time-to-event prediction with neural networks and cox regression

    Kvamme, H., Borgan, ., and Scheel, I. Time-to-event prediction with neural networks and cox regression. Journal of machine learning research, 20 0 (129): 0 1--30, 2019

    2019

  30. [38]

    Lagakos, S. W. General right censoring and its impact on the analysis of survival data. Biometrics, pp.\ 139--156, 1979

    1979

  31. [39]

    Lawless, J. F. Statistical Models and Methods for Lifetime Data. Wiley, 2nd edition, 2003. ISBN 9780471372158

    2003

  32. [40]

    Deephit: A deep learning approach to survival analysis with competing risks

    Lee, C., Zame, W., Yoon, J., and Van Der Schaar, M. Deephit: A deep learning approach to survival analysis with competing risks. In Proceedings of the AAAI conference on artificial intelligence, volume 32, 2018

    2018

  33. [41]

    and Turner, R

    Li, Y. and Turner, R. E. R \'e nyi divergence variational inference. Advances in neural information processing systems, 29, 2016

    2016

  34. [42]

    and Wang, X

    Liu, C. and Wang, X. Doubly robust conditional VAE via decoder calibration: An implicit KL annealing approach. Transactions on Machine Learning Research, 2025. ISSN 2835-8856

    2025

  35. [43]

    Understanding posterior collapse in generative latent variable models

    Lucas, J., Tucker, G., Grosse, R., and Norouzi, M. Understanding posterior collapse in generative latent variable models. Advances in Neural Information Processing Systems, 32, 2019

    2019

  36. [44]

    C., Weikert, T., Sauter, A., Gotta, V., M \"u ller, T., Vasella, F., Neidert, M

    Manduchi, L., Marcinkevi c s, R., Massi, M. C., Weikert, T., Sauter, A., Gotta, V., M \"u ller, T., Vasella, F., Neidert, M. C., Pfister, M., Stieltjes, B., and Vogt, J. E. A deep variational approach to clustering survival data. In International Conference on Learning Represe...

    2022

  37. [45]

    Miller, R. G. Least squares regression with censored data. Biometrika, 63 0 (3): 0 449--464, 1976

    1976

  38. [46]

    Analytic inequalities, 1970

    Mitrinovic, D. Analytic inequalities, 1970

    1970

  39. [47]

    Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks

    Nagpal, C., Li, X., and Dubrawski, A. Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks. IEEE Journal of Biomedical and Health Informatics, 25 0 (8): 0 3163--3175, 2021 a

    2021

  40. [48]

    Deep cox mixtures for survival regression

    Nagpal, C., Yadlowsky, S., Rostamzadeh, N., and Heller, K. Deep cox mixtures for survival regression. In Machine Learning for Healthcare Conference, pp.\ 674--708. PMLR, 2021 b

    2021

  41. [49]

    auton-survival: an open-source package for regression, counterfactual estimation, evaluation and phenotyping with censored time-to-event data

    Nagpal, C., Potosnak, W., and Dubrawski, A. auton-survival: an open-source package for regression, counterfactual estimation, evaluation and phenotyping with censored time-to-event data. arXiv preprint arXiv:2204.07276, 2022

    2022 arXiv

  42. [50]

    Nelson, W. B. Applied life data analysis. John Wiley & Sons, 2005

    2005

  43. [51]

    Debiasing evidence approximations: On importance-weighted autoencoders and jackknife variational inference

    Nowozin, S. Debiasing evidence approximations: On importance-weighted autoencoders and jackknife variational inference. In International conference on learning representations, 2018

    2018

  44. [52]

    scikit-survival: A library for time-to-event analysis built on top of scikit-learn

    P \"o lsterl, S. scikit-survival: A library for time-to-event analysis built on top of scikit-learn. Journal of Machine Learning Research, 21 0 (212): 0 1--6, 2020

    2020

  45. [53]

    Black box variational inference

    Ranganath, R., Gerrish, S., and Blei, D. Black box variational inference. In Artificial intelligence and statistics, pp.\ 814--822. PMLR, 2014

    2014

  46. [54]

    Deep survival analysis

    Ranganath, R., Perotte, A., Elhadad, N., and Blei, D. Deep survival analysis. In Machine Learning for Healthcare Conference, pp.\ 101--114. PMLR, 2016

    2016

  47. [55]

    J., Mohamed, S., and Wierstra, D

    Rezende, D. J., Mohamed, S., and Wierstra, D. Stochastic backpropagation and approximate inference in deep generative models. In International conference on machine learning, pp.\ 1278--1286. PMLR, 2014

    2014

  48. [56]

    Simple and effective vae training with calibrated decoders

    Rybkin, O., Daniilidis, K., and Levine, S. Simple and effective vae training with calibrated decoders. In International Conference on Machine Learning, pp.\ 9179--9189. PMLR, 2021

    2021

  49. [57]

    Learning structured output representation using deep conditional generative models

    Sohn, K., Lee, H., and Yan, X. Learning structured output representation using deep conditional generative models. In Advances in Neural Information Processing Systems, volume 28, 2015

    2015

  50. [58]

    A collapsed variational bayesian inference algorithm for latent dirichlet allocation

    Teh, Y., Newman, D., and Welling, M. A collapsed variational bayesian inference algorithm for latent dirichlet allocation. Advances in neural information processing systems, 19, 2006

    2006

  51. [59]

    J., D'Agostino, R

    Uno, H., Cai, T., Pencina, M. J., D'Agostino, R. B., and Wei, L.-J. On the c-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in medicine, 30 0 (10): 0 1105--1117, 2011

    2011

  52. [60]

    F-divergence variational inference

    Wan, N., Li, D., and Hovakimyan, N. F-divergence variational inference. Advances in neural information processing systems, 33: 0 17370--17379, 2020

    2020

  53. [61]

    Wang, Y., Blei, D., and Cunningham, J. P. Posterior collapse and latent variable non-identifiability. In Advances in Neural Information Processing Systems, 2021

    2021

  54. [62]

    Deep learning for survival analysis: a review

    Wiegrebe, S., Kopper, P., Sonabend, R., Bischl, B., and Bender, A. Deep learning for survival analysis: a review. Artificial Intelligence Review, 57 0 (3): 0 65, 2024

    2024

  55. [63]

    Variational learning of individual survival distributions

    Xiu, Z., Tao, C., and Henao, R. Variational learning of individual survival distributions. In Proceedings of the ACM Conference on Health, Inference, and Learning, pp.\ 10--18, 2020

    2020

  56. [64]

    Sample mean and sample variance: Their covariance and their (in) dependence

    Zhang, L. Sample mean and sample variance: Their covariance and their (in) dependence. The American Statistician, 61 0 (2): 0 159--160, 2007

    2007

  57. [65]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.