Pith. sign in

REVIEW 4 major objections 5 minor 300 references

Smoothed bootstrap lets CRT use external data without losing validity.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 16:46 UTC pith:TRWLAFBY

load-bearing objection CRT* is a clever synthesis with a real theory contribution, but its type-I error guarantee silently assumes identical error densities across cohorts — an assumption that fails in the motivating genomics example. the 4 major comments →

arxiv 2607.17859 v1 pith:TRWLAFBY submitted 2026-07-20 stat.ME

CRT*: Conditional Randomization Testing with Heterogeneous External and Unlabeled Data

Yingjie Zhang , Ziqi Chen , Chenlei Leng This is my paper
classification stat.ME MSC 62G1062H1562J07
keywords conditional independence testingconditional randomization testresidual bootstraptransfer learningdata fusiontype I error controllocal asymptotic powerhigh-dimensional inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to show that conditional independence testing—deciding whether X and Y are independent after adjusting for covariates Z—can make productive use of two types of auxiliary data: unlabeled samples that help estimate the distribution of X given Z, and an external labeled cohort that can amplify signal. Its proposed procedure, CRT*, combines a smoothed residual bootstrap with transfer learning to estimate conditional distributions under cross-cohort heterogeneity, then fuses internal and external test statistics with a data-driven weight. The central claim is that this yields asymptotic type-I error control at α + o(1) even when the external data only approximately satisfy the null, while delivering strictly higher local power than a CRT restricted to internal data. A sympathetic reader would care because the result offers a principled route to valid and more powerful model-X-style testing whenever internal samples are scarce but public auxiliary data are plentiful.

Core claim

On its own terms, the paper establishes that CRT* controls type-I error in the conditional randomization test framework when the conditional distribution of X given Z is unknown and estimated from heterogeneous sources. Theorem 1 bounds the null p-value by α plus three terms: the external conditional mutual information, and the expected total variation distances between the estimated and true conditional distributions for the internal and external cohorts. The paper proves that the smoothed residual bootstrap estimator converges to the true conditional law in expected total variation even when p grows with n, provided the underlying model is sparse and linear and the informative unlabeled se

What carries the argument

The central mechanism is the smooth residual bootstrap (SRB) with transfer learning. Residuals are computed from sparse linear fits of X on Z for the internal, external, and selected 'informative' unlabeled cohorts; those residuals are centered, resampled with replacement, and perturbed by Gaussian noise whose bandwidth tends to zero. The smoothing is what makes the resampled distribution continuous, so its total variation distance to the truth can vanish—an unsmoothed bootstrap remains discrete and is always at TV distance one from a continuous law. Informative sets are chosen by ℓ1 closeness of coefficient vectors between unlabeled and target cohorts, guarding against heterogeneity. For po

Load-bearing premise

The load-bearing premise is that in every cohort X equals a sparse linear function of Z plus independent sub-Gaussian noise, because the residual bootstrap can only approximate the conditional distribution of X|Z if that additive linear structure is the truth.

What would settle it

Simulate X|Z from a nonlinear additive or heteroscedastic model (e.g., X = sin(Zβ) + ε or X = (Zβ)·ε) while keeping every other assumption; if CRT*'s empirical rejection rate under the null drifts above α as n grows, the total-variation convergence claim does not hold for non-linear conditional laws.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Public unlabeled cohorts can be used to estimate X|Z without requiring them to match the target population exactly, as long as the transfer-learning informative set condition holds.
  • An external labeled cohort can be included even when it has a different conditional dependence strength; type-I error remains controlled if its conditional mutual information is o(1/|I_E|).
  • Power gains from the external cohort are monotone in external sample size and external signal strength, and the inverse-residual weight converges to the optimal fusion weight.
  • The validity guarantee extends to high-dimensional conditioning sets, provided sparsity and total unlabeled sample size satisfy the stated rates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A modular reading of the theory suggests any conditional estimator whose expected total variation error vanishes could replace the linear-SRB estimator, extending CRT* to nonparametric or deep-learned conditional models—provided a comparable informative-set structure is available.
  • The linear additive assumption is the point most likely to limit real use; a natural extension would replace the linear fit by an additive or heteroscedastic model and check whether the TV bound still holds.
  • One untested downstream use is variable selection via model-X knockoffs: the same fused conditional sampler could generate knockoff copies from pooled heterogeneous cohorts, but the informative-set and weighting conditions would need to be re-derived.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes CRT*, a conditional randomization test that integrates internal labeled data, external labeled data, and auxiliary unlabeled data. The method estimates conditional distributions of X|Z via a smooth residual bootstrap with transfer learning, and fuses internal and external distilled test statistics through an adaptively estimated convex weight. The main theoretical claims are: (i) asymptotic type-I error control under the null, even when the external data only approximately satisfy conditional independence; (ii) convergence in expected total variation of the SRB-based conditional distribution estimator; and (iii) strict local asymptotic power improvement over CRT without external data, achieved by an optimal inverse-variance-type weight. The methodology is demonstrated in simulations and in an RNA-seq breast cancer analysis testing conditional dependence between BRCA1 and BRCA1P1.

Significance. If the results hold, the paper would make a valuable contribution: it is the first framework to jointly exploit external and unlabeled data for CRT-based conditional independence testing while explicitly modeling cross-cohort heterogeneity. The theoretical program is ambitious, covering type-I error, TV convergence of a smoothed residual bootstrap, and local power under high-dimensional sparse models. The paper also ships a concrete algorithm, a data-driven weighting scheme, and a real-data application, which increases its practical relevance. However, the advertised robustness to distributional heterogeneity is currently supported only under a common error-density assumption, and there is an apparent internal inconsistency in the displayed convergence rate. These issues are load-bearing for the central validity claim and need to be resolved before the contribution can be fully assessed.

major comments (4)
  1. [§2.2, displayed rate before Eq. (12)] The type-I error guarantee of Theorem 1 (11) requires E[d_TV(ρ_|I_I|, bρ_|I_I|)] -> 0 and its external analogue. The SRB scheme pools residuals from internal and unlabeled cohorts before resampling. If the error densities differ across cohorts—even with the same mean and variance—the resampling distribution converges to a mixture, not to the internal density; for any a_n -> 0 the TV distance is bounded below by a positive constant. Assumption A2's 'common density' is exactly what avoids this, but it is not part of the stated model in §2.1 and is not checked in §4. The reference to Section S.8 for non-identically distributed noise does not repair Theorem 1 as stated, because the algorithm in Step 3 contains no cohort-specific weighting or correction. This gap is load-bearing because the abstract and title advertise heterogeneous data, not merely coefficient heterogeneity. Please either pr
  2. [§2.2, displayed rate for E[d_TV | D_A]] The rate is stated as O_P(a_n√|I_I| + (√|I_I|/a_n)( e s log p/(|I_I^c|+N_A) + e s log p/(e_n ∧ eη_h) ) ), with eη_h = (h√(log p/e_n)) ∧ h^2. Under the stated condition h = o(|I_I|^{-1}), eη_h = o(|I_I|^{-2}) because h^2 dominates; the denominator e_n ∧ eη_h is then o(|I_I|^{-2}), so the second variance-type term diverges rather than vanishes. The claim that this rate vanishes when h = o(|I_I|^{-1}) and N_A ≫ |I_I|^2 e s log p is therefore not supported by the displayed formula. This is not a presentation nit: the TV convergence in Theorem S.2 is the basis for the o(1) in Theorem 1. Please correct the formula (e.g., replacing the denominator with an appropriate max/plus form) and re-verify the rate, or state the exact condition under which the displayed expression tends to zero.
  3. [§2.3, Theorem 2 conditions (17)–(21)] The local-power theorem is stated under a long list of conditions, several of which are not primitive and are not verified for the Lasso-based nuisance estimators used in the simulations and application. In particular, (19) requires the product of the squared estimation errors of bg and bµ to be o_P(|I_I|^{-1}), and (20)–(21) involve conditional moments E_{H1n}(ϵ_i | Y_i, Z_i) that are not defined in the main text. Without sufficient primitive conditions (e.g., sparsity, smoothness, rates) under which (18)–(21) hold for the implemented estimators, the claim that CRT* 'achieves strictly higher power than standard CRT without external data' is not fully established. Please state explicit sufficient conditions or empirically verify these conditions in the simulation settings.
  4. [§3, §4 (in-sample training)] The theoretical results (Theorems 1–3) are proved for the sample-splitting version of CRT* (Algorithm S.2). However, the simulations and, more importantly, the real-data analysis use 'in-sample training' (Algorithm S.8), in which all labeled data are used both for distribution estimation and for computing the test statistic. No theorem in the main text covers this variant; Theorem 1 conditions on holdout subsets, and the residual-bootstrap distribution is estimated on the complementary subsets. The manuscript should either add a rigorous justification for in-sample training or clearly state that the theoretical guarantees apply only to the hold-out version and that the in-sample results are empirical.
minor comments (5)
  1. [§2.1, Eq. (3) and Assumption A2] The main text describes the noise terms as 'sub-Gaussian' and then, in Assumption A2, requires a 'common density'. Please clarify that TV convergence needs this stronger condition and explain how the SRB would behave if the common-density assumption is violated.
  2. [§1.3, Table 1] The table is compact but confusing: the columns for 'Type-I error' list nE=0, while the 'Power' columns list nE=0 and nE=200. Consider splitting the table or adding explicit row/column labels to avoid ambiguity.
  3. [§4.2] Typographical issue: '0 .015' and '0 .045' should be formatted as '0.015' and '0.045'.
  4. [§2.2, Theorem 1] The display following Eq. (10) uses 'r 1/2 |I_E| · I(...)' which appears to be a typesetting error for sqrt((1/2)|I_E| I(...)); please fix the notation.
  5. [§3, §4] The paper does not state whether code and data preprocessing scripts are publicly available. For a methods paper with real-data analyses, this information is useful for reproducibility.

Circularity Check

0 steps flagged

No significant circularity: the derivation is self-contained under explicit model assumptions.

full rationale

The paper's central claims are derived under explicit modeling assumptions rather than being equivalent to fitted quantities. Theorem 1 is a standard CRT-type total-variation bound; the subsequent TV consistency and local power results are stated as theorems with stated conditions (A1, A2, sparse linear models, local alternatives), not as consequences of the procedure's own fitted outputs. The adaptive weight bw in Theorem 3 is shown to be a consistent estimator of the analytically derived optimal weight, and the power formula is derived from local alternative models rather than from observed power values. Self-citations, notably to Zhao et al. (2026), appear in literature-review and motivation passages, but the load-bearing transfer-learning estimator is the external oracle Trans-Lasso of Li et al. (2022), and no central equation or theorem reduces to a self-citation. The concern about heterogeneity of residual densities is a real restrictiveness of Assumption A2, but it is an assumption limitation, not circular reasoning. No fitted parameters are renamed as predictions, and no theorem's conclusion is identical to its input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on strong distributional assumptions (sparse linearity, Gaussian design, weak external dependence, noise regularity). No new latent variables, forces, or physical entities are introduced; the informative sets A and AE are data subsets, not invented entities.

free parameters (4)
  • SRB smoothing bandwidth a_n (and a_nE) = a_n ≍ (s̃ log p/(|I_c| + N_A) + s̃ log p/e_n ∧ h²)^{1/4}; a_nE analog
    User-chosen smoothing parameter used to balance bias and variance; no concrete data-driven selection rule is given in the main text, only an asymptotic rate.
  • Data-splitting fractions w1, w2 = in (0,1), chosen by user; simulations often use equal halves
    The internal and external hold-out sizes are |I_I| = floor(w1 n) and |I_E| = floor(w2 n_E); power depends on w1 and w2, and no optimal choice is provided.
  • Informative-set thresholds h and hE = unknown; must satisfy h = o(|I_I|^{-1}) for type-I control; data-driven estimation deferred to Supplement S.9
    Used to define A and AE in Eqs. (4)–(5). If set too large, dissimilar unlabeled cohorts enter the transfer-learning pool and the TV convergence rate no longer vanishes.
  • Adaptive fusion weight bw = inverse-residual estimator: (S_int/√ζ) / (S_ext/(|I_E|/|I_I|) + S_int/√ζ)
    Data-dependent estimate of the asymptotically optimal weight w_opt in Eq. (22); consistency is proven in Theorem 3, so it is not a hand-fitted constant.
axioms (5)
  • domain assumption Sparse linear additive models X = Zβ + ε, X^E = Z^Eβ^E + ε^E, X^(k) = Z^(k)w^(k) + ε^(k), with Z independent of noise; all noise sub-Gaussian.
    Eqs. (1)–(3), Section 2.1. Load-bearing: SRB resamples from residuals of these linear fits; if the true conditional law is non-linear or non-additive, TV convergence and type-I control can fail.
  • domain assumption Gaussian design: Z, Z^E, Z^(k) are i.i.d. N(0, Σ) with eigenvalues of Σ bounded away from 0 and ∞.
    Assumption A1, Section 2.2. Used for the Trans-Lasso estimation bounds and the TV convergence rate; real RNA-seq covariates may violate Gaussianity.
  • domain assumption External data approximately satisfy conditional independence: I(X^E; Y^E | Z^E) = o(1/|I_E|).
    Used after Theorem 1 to obtain asymptotic type-I error control. If external dependence is not weak, the extra term in the bound does not vanish.
  • domain assumption Noise densities satisfy regularity conditions stated in Supplementary S.4.
    Imposed for convergence of the SRB estimator in expected total variation; the exact conditions are not in the main text.
  • domain assumption Oracle Trans-Lasso estimation bounds from Li et al. (2022) hold in this framework.
    Used in Step 2 and Theorem S.2 to control coefficient estimation error; the paper imports these bounds without proof.

pith-pipeline@v1.3.0-alltime-deepseek · 16730 in / 17307 out tokens · 165721 ms · 2026-08-01T16:46:12.604332+00:00 · methodology

0 comments
read the original abstract

The conditional randomization test (CRT) provides a principled approach to conditional independence (CI) testing, guaranteeing exact type-I error control when the true conditional distribution is known. In practice, however, this distribution must be estimated, and estimation errors can inflate type-I errors, while high dimensionality and limited sample sizes can reduce power. Although external and unlabeled data offer the potential to improve CI testing, naive integration that ignores distributional heterogeneity can compromise type-I error control and fail to enhance power. We propose \textbf{CRT*}, a novel framework that robustly integrates external and unlabeled datasets to enhance CI testing in heterogeneous scenarios. CRT* employs smooth residual-bootstrap (SRB) with transfer learning for conditional distribution estimation, combined with adaptive data fusion via an optimal convex combination of test statistics. We theoretically establish that the SRB-based estimator converges to the true conditional distribution in expected total variation distance. Furthermore, even in high-dimensional regimes, CRT* maintains valid type-I error control and achieves strictly higher power than standard CRT without external data. Simulations and RNA-seq breast cancer data analyses demonstrate that CRT* substantially improves power while maintaining type-I error control in heterogeneous settings.

Figures

Figures reproduced from arXiv: 2607.17859 by Chenlei Leng, Yingjie Zhang, Ziqi Chen.

Figure 1
Figure 1. Figure 1: The CRT* Workflow: Leveraging unlabeled data for robust distribution estimation via SRB with transfer learning, while utilizing external data for adaptive power enhancement through optimal weighting. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the CRT* procedure with a given test statistic [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Type-I error (left) and power (right) for CRT* under hold-out and in-sample training in [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 19 linked inside Pith

  1. [1]

    2019 IEEE EMBS International Conference on Biomedical & Health Informatics (BHI) , pages=

    Centroid of Age Neighborhoods: A Generalized Approach to Estimate Biological Age , author=. 2019 IEEE EMBS International Conference on Biomedical & Health Informatics (BHI) , pages=. 2019 , organization=

    2019

  2. [2]

    arXiv preprint arXiv:1409.0473 , year=

    Neural machine translation by jointly learning to align and translate , author=. arXiv preprint arXiv:1409.0473 , year=

    Pith/arXiv arXiv

  3. [3]

    Journal of the American College of Cardiology , volume=

    Cardiorespiratory fitness and mortality in healthy men and women , author=. Journal of the American College of Cardiology , volume=. 2018 , publisher=

    2018

  4. [4]

    Proceedings of the IEEE International Conference on Computer Vision , pages=

    Unified deep supervised domain adaptation and generalization , author=. Proceedings of the IEEE International Conference on Computer Vision , pages=

  5. [5]

    2013 , publisher=

    ACSM's guidelines for exercise testing and prescription , author=. 2013 , publisher=

    2013

  6. [6]

    2012 , publisher=

    Machine learning: A probabilistic perspective , author=. 2012 , publisher=

    2012

  7. [7]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    3D convolutional neural networks for human action recognition , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2012 , publisher=

    2012

  8. [8]

    Advances in Neural Information Processing Systems , pages=

    Imagenet classification with deep convolutional neural networks , author=. Advances in Neural Information Processing Systems , pages=

  9. [9]

    Nature Reviews Genetics , volume=

    DNA methylation-based biomarkers and the epigenetic clock theory of ageing , author=. Nature Reviews Genetics , volume=. 2018 , publisher=

    2018

  10. [10]

    Aging (Albany NY) , volume=

    Quantitative characterization of biological age and frailty based on locomotor activity records , author=. Aging (Albany NY) , volume=. 2018 , publisher=

    2018

  11. [11]

    Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages=

    Face aging with identity-preserved conditional generative adversarial networks , author=. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages=

  12. [12]

    Nature , volume=

    Deep learning , author=. Nature , volume=. 2015 , publisher=

    2015

  13. [13]

    Fine-Grained Age Estimation in the wild with Attention

    Zhang, Ke and Liu, Na and Yuan, Xingfang and Guo, Xinyao and Gao, Ce and Zhao, Zhenbing , journal=. Fine-Grained Age Estimation in the wild with Attention

  14. [14]

    Deep learning for health informatics , author=. IEEE. 2016 , publisher=

    2016

  15. [15]

    Briefings in

    Deep learning for healthcare: review, opportunities and challenges , author=. Briefings in. 2017 , publisher=

    2017

  16. [16]

    Centroid of Age Neighborhoods: A New Approach to Estimate Biological Age , author=. IEEE. 2019 , publisher=

    2019

  17. [17]

    Scientific

    Deep Learning using Convolutional LSTM estimates Biological Age from Physical Activity , author=. Scientific. 2019 , publisher=

    2019

  18. [18]

    Advances in

    Generative adversarial nets , author=. Advances in

  19. [19]

    IEEE/ACM Transactions on Computational Biology and Bioinformatics , year=

    Predicting DNA methylation states with hybrid information based deep-learning model , author=. IEEE/ACM Transactions on Computational Biology and Bioinformatics , year=

  20. [20]

    Scientific

    PEDLA: predicting enhancers with a deep learning-based algorithmic framework , author=. Scientific. 2016 , publisher=

    2016

  21. [21]

    NeuroImage , volume=

    Predicting brain age with deep learning from raw imaging data results in a reliable and heritable biomarker , author=. NeuroImage , volume=. 2017 , publisher=

    2017

  22. [22]

    Journal of Biomedical Informatics , volume=

    Predicting age by mining electronic medical records with deep learning characterizes differences between chronological and physiological age , author=. Journal of Biomedical Informatics , volume=. 2017 , publisher=

    2017

  23. [23]

    Part 1: A new approach to calculating biological age , author=

    Improving the precision of biological age determinations. Part 1: A new approach to calculating biological age , author=. Experimental Gerontology , volume=. 1989 , publisher=

    1989

  24. [24]

    Biogerontology , volume=

    On the use of regression analysis for the estimation of human biological age , author=. Biogerontology , volume=. 2000 , publisher=

    2000

  25. [25]

    BioRxiv , pages=

    Phenotypic Age: A novel signature of mortality and morbidity risk , author=. BioRxiv , pages=. 2018 , publisher=

    2018

  26. [26]

    American Journal of Epidemiology , volume=

    Eleven telomere, epigenetic clock, and biomarker-composite quantifications of biological aging: do they measure the same thing? , author=. American Journal of Epidemiology , volume=. 2017 , publisher=

    2017

  27. [27]

    Population Specific Biomarkers of Human Aging: A Big Data Study Using

    Mamoshina, Polina and Kochetov, Kirill and Putin, Evgeny and Cortese, Franco and Aliper, Alexander and Lee, Won-Suk and Ahn, Sung-Min and Uhn, Lee and Skjodt, Neil and Kovalchuk, Olga and others , journal=. Population Specific Biomarkers of Human Aging: A Big Data Study Using. 2018 , publisher=

    2018

  28. [28]

    Bobrov, Eugene and Georgievskaya, Anastasia and Kiselev, Konstantin and Sevastopolsky, Artem and Zhavoronkov, Alex and Gurov, Sergey and Rudakov, Konstantin and Tobar, Maria del Pilar Bonilla and Jaspers, S. Photo. Aging (Albany NY) , volume=. 2018 , publisher=

    2018

  29. [29]

    Ageing Research Reviews , year=

    Artificial intelligence for aging and longevity research: Recent advances and perspectives , author=. Ageing Research Reviews , year=

  30. [30]

    The Journal of Machine Learning Research , volume=

    Dropout: A simple way to prevent neural networks from overfitting , author=. The Journal of Machine Learning Research , volume=. 2014 , publisher=

    2014

  31. [31]

    2016 , journal=

    Incorporating Nesterov Momentum into Adam , author=. 2016 , journal=

    2016

  32. [32]

    2018 , url =

    , title =. 2018 , url =

    2018

  33. [33]

    Informativeness of indices of blood pressure, obesity and serum lipids in relation to ischaemic heart disease mortality:

    M. Informativeness of indices of blood pressure, obesity and serum lipids in relation to ischaemic heart disease mortality:. European Journal of Epidemiology , volume=. 2011 , publisher=

    2011

  34. [34]

    arXiv preprint arXiv:1412.6980 , year=

    Adam: A method for stochastic optimization , author=. arXiv preprint arXiv:1412.6980 , year=

    Pith/arXiv arXiv

  35. [35]

    Journal of the American Statistical Association , volume=

    Nonparametric estimation from incomplete observations , author=. Journal of the American Statistical Association , volume=. 1958 , publisher=

    1958

  36. [36]

    , author=

    The descriptive epidemiology of selected physical activities and body weight among adults trying to lose weight: the Behavioral Risk Factor Surveillance System survey, 1989. , author=. International Journal of Obesity and Related Metabolic Disorders: Journal of the International Association for the Study of Obesity , volume=

    1989

  37. [37]

    , author=

    The demography of physical activity. , author=. Physical Activity, Fitness, and Health: International Proceedings and Consensus Statement , pages=. 1994 , publisher=

    1994

  38. [38]

    Medicine and Science in Sports and Exercise , volume=

    National estimates of physical activity among older adults , author=. Medicine and Science in Sports and Exercise , volume=

  39. [39]

    The Journals of Gerontology Series A: Biological Sciences and Medical Sciences , volume=

    Physical activity in aging: changes in patterns and their relationship to health and function , author=. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences , volume=. 2001 , publisher=

    2001

  40. [40]

    Worldwide trends in insufficient physical activity from 2001 to 2016: a pooled analysis of 358 population-based surveys with 1

    Guthold, Regina and Stevens, Gretchen A and Riley, Leanne M and Bull, Fiona C , journal=. Worldwide trends in insufficient physical activity from 2001 to 2016: a pooled analysis of 358 population-based surveys with 1. 2018 , publisher=

    2001

  41. [41]

    Proceedings of the

    Understanding the difficulty of training deep feedforward neural networks , author=. Proceedings of the

  42. [42]

    American Journal of Epidemiology , volume=

    Time-to-event analysis of longitudinal follow-up of a survey: choice of the time-scale , author=. American Journal of Epidemiology , volume=. 1997 , publisher=

    1997

  43. [43]

    1984 , publisher=

    Analysis of survival data , author=. 1984 , publisher=

    1984

  44. [44]

    Expert opinion on biological therapy , volume=

    Human models of aging and longevity , author=. Expert opinion on biological therapy , volume=. 2008 , publisher=

    2008

  45. [45]

    Proceedings of the National Academy of Sciences , volume=

    Quantification of biological aging in young adults , author=. Proceedings of the National Academy of Sciences , volume=. 2015 , publisher=

    2015

  46. [46]

    Journals of Gerontology Series A: Biomedical Sciences and Medical Sciences , volume=

    Heterogeneity of human aging and its assessment , author=. Journals of Gerontology Series A: Biomedical Sciences and Medical Sciences , volume=. 2016 , publisher=

    2016

  47. [47]

    Modeling the rate of senescence:

    Levine, Morgan E , journal=. Modeling the rate of senescence:. 2012 , publisher=

    2012

  48. [48]

    Mechanisms of Ageing and Development , volume=

    Assessment of biological age by principal component analysis , author=. Mechanisms of Ageing and Development , volume=. 1988 , publisher=

    1988

  49. [49]

    Medical Informatics , volume=

    Evaluation of biological age and physical age by multiple regression analysis , author=. Medical Informatics , volume=. 1982 , publisher=

    1982

  50. [50]

    A novel strategy for forensic age prediction by

    Xu, Cheng and Qu, Hongzhu and Wang, Guangyu and Xie, Bingbing and Shi, Yi and Yang, Yaran and Zhao, Zhao and Hu, Lan and Fang, Xiangdong and Yan, Jiangwei and others , journal=. A novel strategy for forensic age prediction by. 2015 , publisher=

    2015

  51. [51]

    IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages=

    Human age estimation using bio-inspired features , author=. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages=. 2009 , organization=

    2009

  52. [52]

    IEEE Transactions on Multimedia , volume=

    Human age estimation with regression on discriminative aging manifold , author=. IEEE Transactions on Multimedia , volume=. 2008 , publisher=

    2008

  53. [53]

    2013 , publisher=

    Horvath, Steve , journal=. 2013 , publisher=

    2013

  54. [54]

    Molecular Psychiatry , year=

    Brain age predicts mortality , author=. Molecular Psychiatry , year=

  55. [55]

    Aging Cell , volume=

    Biomarker signatures of aging , author=. Aging Cell , volume=. 2017 , publisher=

    2017

  56. [56]

    2017 , publisher=

    Piccirilli, Marco and Doretto, Gianfranco and Adjeroh, Donald , journal=. 2017 , publisher=

    2017

  57. [57]

    Computer Science Letters , volume=

    Automatic age estimation by hand photos , author=. Computer Science Letters , volume=

  58. [58]

    Comparison of performance-based measures among native

    Aoyagi, Kiyoshi and Ross, Philip D and Nevitt, Michael C and Davis, James W and Wasnich, Richard D and Hayashi, Takuo and Takemoto, Tai-ichiro , journal=. Comparison of performance-based measures among native. 2001 , publisher=

    2001

  59. [59]

    Nutrition and handgrip strength of older adults in rural

    Chilima, Dorothy M and Ismail, Suraiya J , journal=. Nutrition and handgrip strength of older adults in rural. 2001 , publisher=

    2001

  60. [60]

    Prediction equations for handgrip strength in healthy

    Vaz, M and Hunsberger, S and Diffey, B , journal=. Prediction equations for handgrip strength in healthy. 2002 , publisher=

    2002

  61. [61]

    A study on hand grip strength in female labourers of

    Koley, Shyamal and Kaur, Navdeep and Sandhu, JS , journal=. A study on hand grip strength in female labourers of

  62. [62]

    International Conference on Artificial Neural Networks , pages=

    Sch. International Conference on Artificial Neural Networks , pages=. 1997 , organization=

    1997

  63. [63]

    Jolliffe, Ian , year=

  64. [64]

    Handgrip strength and mortality in older

    Al Snih, Soham and Markides, Kyriakos S and Ray, Laura and Ostir, Glenn V and Goodwin, James S , journal=. Handgrip strength and mortality in older. 2002 , publisher=

    2002

  65. [65]

    American Journal of Respiratory and Critical Care Medicine , volume=

    Acquired weakness, handgrip strength, and mortality in critically ill patients , author=. American Journal of Respiratory and Critical Care Medicine , volume=. 2008 , publisher=

    2008

  66. [66]

    Handgrip strength and mortality in the oldest old population:

    Ling, Carolina HY and Taekema, Diana and de Craen, Anton JM and Gussekloo, Jacobijn and Westendorp, Rudi GJ and Maier, Andrea B , journal=. Handgrip strength and mortality in the oldest old population:. 2010 , publisher=

    2010

  67. [67]

    PLoS ONE , volume=

    Epigenetic predictor of age , author=. PLoS ONE , volume=. 2011 , publisher=

    2011

  68. [68]

    2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06) , volume=

    Modeling age progression in young faces , author=. 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06) , volume=. 2006 , organization=

    2006

  69. [69]

    Physiological Basis of Aging and Geriatrics , pages=

    Cellular senescence and cell death , author=. Physiological Basis of Aging and Geriatrics , pages=

  70. [70]

    European Journal of Cancer , volume=

    The biology of replicative senescence , author=. European Journal of Cancer , volume=. 1997 , publisher=

    1997

  71. [71]

    Normal oxidative damage to mitochondrial and nuclear

    Richter, Christoph and Park, Jeen-Woo and Ames, Bruce N , journal=. Normal oxidative damage to mitochondrial and nuclear. 1988 , publisher=

    1988

  72. [72]

    Antioxidants and Redox Signaling , volume=

    The free radical theory of aging , author=. Antioxidants and Redox Signaling , volume=. 2003 , publisher=

    2003

  73. [73]

    Clinical Interventions in Aging , volume=

    The aging process and potential interventions to extend life expectancy , author=. Clinical Interventions in Aging , volume=. 2007 , publisher=

    2007

  74. [74]

    Biomarker profiling by nuclear magnetic resonance spectroscopy for the prediction of all-cause mortality:

    Fischer, Krista and Kettunen, Johannes and W. Biomarker profiling by nuclear magnetic resonance spectroscopy for the prediction of all-cause mortality:. PLoS Med , volume=. 2014 , publisher=

    2014

  75. [75]

    Age estimation:

    Ritz-Timme, S and Cattaneo, C and Collins, MJ and Waite, ER and Sch. Age estimation:. International Journal of Legal Medicine , volume=. 2000 , publisher=

    2000

  76. [76]

    Measuring human functional age:

    Anstey, Kaarin J and Lord, Stephen R and Smith, Glen A , journal=. Measuring human functional age:. 1996 , publisher=

    1996

  77. [77]

    Bone and Mineral , volume=

    Development of bone mass and bone density of the spine and femoral neck—a prospective study of 65 children and adolescents , author=. Bone and Mineral , volume=. 1993 , publisher=

    1993

  78. [78]

    A new body shape index predicts mortality hazard independently of

    Krakauer, Nir Y and Krakauer, Jesse C , journal=. A new body shape index predicts mortality hazard independently of. 2012 , publisher=

    2012

  79. [79]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    Automatic age estimation based on facial aging patterns , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2007 , publisher=

    2007

  80. [80]

    J Forensic Odontostomatol , volume=

    A review of the most commonly used dental age estimation techniques , author=. J Forensic Odontostomatol , volume=

Showing first 80 references.