Pith. sign in

REVIEW 4 major objections 6 minor 37 references

Trajectory Inference of Human Aging from Cross-Sectional DNA Methylation Data

T0 review · 4 major / 6 minor · reviewed 2026-07-11 · grok-4.5

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

Pith's one-line read Lifelong epigenetic aging trajectories can be reconstructed from static DNA methylation snapshots by coupling an age-ordered latent map with unbalanced optimal transport.

desk verdict Solid transfer of unbalanced OT trajectory inference to pan-tissue DNAm aging; the late-life growth surge is real in the numbers but under-determined as pure biology. read the letter →

arxiv 2607.06583 v1 pith:X64XI3SC submitted 2026-07-04 q-bio.QM cs.LG

Chandan Gupta , Syed Haider , Pietro Liò This is my paper · ORCID
classification q-bio.QMcs.LG
keywords DNAmethylationepigeneticagingtrajectoryinferenceunbalancedoptimaltransportvariationalautoencoderstochasticdriftcross-sectionaldataCpGarchetypes
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

Conventional epigenetic clocks collapse high-dimensional DNA methylation profiles into a single age score and cannot show how the entire profile evolves. This paper reframes lifelong human aging as a trajectory-inference problem that starts from ordinary cross-sectional samples binned by chronological age. An age-regularized variational autoencoder first embeds the profiles onto a low-dimensional manifold that is forced to progress smoothly with age, while a generative decoder keeps a bridge back to the original CpG sites. Continuous motion on that manifold is then recovered by solving a regularized unbalanced optimal-transport problem whose growth field is free to create or remove mass, thereby accommodating survivorship bias and cellular attrition. On an 80-year pan-tissue collection the model interpolates held-out age distributions, exhibits a sharp late-life surge in the growth field that matches the known expansion of epigenetic variance, and, when decoded, recovers four classic kinetic archetypes of individual CpG sites. The result supplies a generative, continuous description of molecular aging that static clocks cannot provide.

What carries the argument

The age-regularized VAE (ELBO plus auxiliary chronological-age regression loss that organizes the latent space) together with the DeepRUOT solver of the regularized unbalanced optimal-transport problem (joint learning of velocity, score and growth fields under a Fokker–Planck constraint that permits mass creation or destruction).

What would settle it

Independent longitudinal DNA-methylation time series from the same individuals whose decoded continuous trajectories, late-life growth surge and site-specific kinetic archetypes systematically disagree with the model’s interpolations would falsify the central claim.

Watch

Extended reading notes

Core claim

A two-stage pipeline—an age-regularized variational autoencoder that produces a chronologically ordered latent manifold, followed by DeepRUOT resolution of regularized unbalanced optimal transport—recovers continuous lifelong trajectories of human DNA methylation from discrete cross-sectional age bins, accommodates non-conservative density shifts, exhibits a late-life growth-field surge that captures stochastic epigenetic drift, and decodes into empirically verified site-specific aging archetypes.

Load-bearing premise

Four coarse chronological age bins drawn from heterogeneous pan-tissue cross-sectional samples can be treated as sequential snapshots of a single continuous aging process whose density changes are fully captured by the learned growth field.

Editorial extensions

If this is right

  • Entire high-dimensional methylation profiles can be simulated continuously across the human lifespan from static data alone.
  • Late-life variance expansion appears as a localized surge in the growth field without requiring hand-crafted biological priors.
  • Decoding latent paths recovers and verifies four distinct CpG archetypes: linear hypermethylation, linear hypomethylation, late-onset drift and age-invariant maintenance sites.
  • Population-level phenomena such as survivorship bias and cellular attrition are absorbed by the unbalanced mass term rather than distorting the drift field.
  • Any continuous latent trajectory can be mapped back to interpretable, site-resolved biomarker curves.

Reading between the lines

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

  • The same pipeline could be re-trained on disease cohorts to quantify how pathological states (for example cancer) rewire the normal aging velocity and growth fields.
  • Finer age binning or multi-omics inputs would test whether the four-bin discretization currently smooths over rapid life-stage transitions such as puberty or menopause.
  • The magnitude of the late-life growth surge could be treated as a population-level biomarker of systemic maintenance failure and compared across independent aging cohorts.
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

4 major / 6 minor

Summary. The manuscript frames lifelong human epigenetic aging as trajectory inference from cross-sectional DNA methylation snapshots. It proposes a two-stage pipeline: (i) an age-regularized VAE that embeds high-dimensional CpG profiles into a chronologically ordered latent manifold with a generative decoder, and (ii) Regularized Unbalanced Optimal Transport (RUOT) solved by DeepRUOT to learn coupled velocity, score, and growth fields that accommodate non-conservative density shifts. On the Altumage pan-tissue cohort (0–80 years, four age bins), leave-one-timepoint-out evaluation reports stable W1 distances and a sharp late-life rise in Total Mass Variation; decoded mean latent paths are used to define and overlay four kinetic CpG archetypes (linear hyper/hypomethylation, late-onset drift, age-invariant sites).

Significance. If the technical claims hold, the work offers a generative alternative to scalar epigenetic clocks by reconstructing continuous joint methylome dynamics and site-level curves from widely available cross-sectional data. The explicit use of unbalanced OT (growth field) to handle survivorship and attrition is a well-motivated methodological step beyond mass-conserving Schrödinger-bridge / OT models used in single-cell trajectory inference. Strengths include leave-one-timepoint-out distribution metrics (Table 1), visualization of velocity and growth fields (Fig. 2), and direct decoding of latent paths back to CpG space with empirical overlays against raw cross-sectional clouds (Supp. Figs. 4–6). These elements make the contribution potentially useful for aging systems biology, provided the biological reading of the growth field and the pan-tissue / coarse-bin assumptions are more tightly controlled.

major comments (4)
  1. [§4.1, Table 1, Fig. 2(d), Eq. (5)] Table 1 and Fig. 2(d): The central claim that the late-life surge in g_θg (and the four-fold TMV jump at T=3: 0.754/0.620 → 2.321) captures stochastic epigenetic drift / survivorship bias is under-determined. Cohort sizes are unbalanced (Supp. Table 2: 3362/2041/3967/3069), and L_Recons (Eq. 5) uses localized cardinality matching plus particle weights w_θg, so residual density or tissue-composition mismatch in the 61–80 bin can be absorbed into g without reflecting true biological mass change. No ablation with g≡0 (balanced OT), equal-mass re-binning, or tissue-stratified cohorts is reported. Without these controls, the biological interpretation of the growth field—and thus the main justification for RUOT over mass-conserving OT—remains speculative.
  2. [§3.2, §4.1] §3.2: Discretization into only four 20-year bins (t0–t3) is load-bearing for the continuous lifelong trajectory claim. Leave-one-timepoint-out then interpolates across multi-decade gaps; rapid life-stage transitions (puberty, menopause, etc.) are necessarily smoothed. The Discussion notes this limitation but does not quantify sensitivity (e.g., 5–10 year bins, or continuous age conditioning). Given that DeepRUOT is trained on these four snapshots, coarser binning can itself induce apparent late-life expansion when variance and sample composition change. A sensitivity analysis on bin width/number is needed to support the continuous-dynamics narrative.
  3. [§2.1, §3.1] §2.1 and §3.1: The age-regularized VAE is asserted to isolate a universal aging signal from pan-tissue heterogeneity (whole blood, brain, saliva, solid tissues). Age regression on the latent bottleneck (L_age, γ=0.3) encourages chronological order but does not guarantee removal of tissue-driven axes that co-vary with age in the Altumage collection. No tissue-held-out or tissue-stratified transport experiments are shown, nor is latent tissue predictability reported. Residual tissue structure could bias both the velocity field and the late-life growth surge, weakening the claim of a systemic aging manifold.
  4. [§4.2, Fig. 3] §4.2: The four archetypes are defined post-hoc by kinetic summaries of decoded curves (max positive/negative shift, max absolute second difference, min temporal variance). Overlays against raw clouds (Supp. Figs. 4–6) show that mean paths track the empirical center of mass, which supports interpolation fidelity, but does not independently verify that the selected CpGs match established biological classes (e.g., bivalent promoters, Alu/LINE-1, housekeeping loci) beyond literature citations. Calling this “empirical verification of distinct biological aging archetypes” overstates the evidence; either annotate the top sites with genomic context / known clock membership or rephrase as kinetic clustering of reconstructed trajectories.
minor comments (6)
  1. [§4.1] Results §4.1: typo “We then visualised the the generated trajectories”.
  2. [§2.1] Notation inconsistency: “V AE” / “VAE”, “β-V AE”, and occasional spacing around math operators; standardize throughout.
  3. [§2.2, Eq. (4)] Eq. (4): the energy loss is dense; a short prose walk-through of each term (especially the weight tracker w_θg and the Fisher-regularization pieces) would help non-OT readers.
  4. [Fig. 2] Fig. 2(c–d): streamlines and growth heatmaps lack a clear colorbar scale and units for growth rate; add them for reproducibility.
  5. [§3.3] Hyperparameters (β, γ, d=16, top-2000 CpGs, λ_mass/λ_OT/λ_energy, σ, bin edges) are free; a brief sensitivity or selection rationale in Methods or Supp. would strengthen reproducibility claims.
  6. [Abstract, §1] Abstract and Introduction assert accommodation of “survivorship bias and cellular attrition without requiring rigid biological priors”; this is a modeling capacity claim, not a demonstrated identification of those processes—tone down or flag as interpretation.

Circularity Check

2 steps flagged · score 3.0 of 10

Mild circularity: chronological latent flow and late-life growth surge largely follow by construction from age-regularized VAE loss and unbalanced mass-matching; biological labels (drift, archetypes) are post-hoc.

  1. self definitional [Section 2.1 Eq. (1); Results 4.1 / Fig. 2(c)]
    "To explicitly enforce chronological organization within this geometry, we append an auxiliary age-regression network fψ(z) directly to the latent bottleneck. ... LV AE=L recon +βL KL +γL age ... the continuous velocity field visualized in Figure 2(c) reveals a globally stable, unidirectional flow from youthful baseline states (purple) toward late-life states (yellow)."

    The latent coordinates are explicitly penalized by the age-MSE term so that z is monotonically ordered by chronological age by construction. DeepRUOT then learns a velocity field between these already age-ordered bins; the reported 'continuous chronological progression' therefore reduces largely to the definition of the age-regularized embedding rather than an independent dynamical discovery.

  2. fitted input called prediction [Section 4.1 Table 1 / Fig. 2(d); Eqs. (3)–(5)]
    "while W1 remains stable, the TMV reveals a distinct shift ... minimal during early-to-mid-life transitions (0.754 for T=1; 0.620 for T=2). However, predicting the oldest age bin requires a substantial, nearly four-fold increase in TMV (2.321 for T=3). ... the model exhibits a prominent, localized surge in the growth term. ... We hypothesize that this mathematical shift mirrors the biological onset of stochastic epigenetic drift."

    gθg and the dynamic weights wθg are optimized end-to-end by LRecons=λm LMass + λd LOT (plus energy) to match the empirical cardinalities and normalized distributions of the age-binned snapshots. The late-life TMV jump and growth surge are therefore exactly the fitted residual needed to accommodate the higher spatial variance of the t3 cohort; the claim that the surge 'mathematically captures ... stochastic epigenetic drift' renames this fit residual as a biological prediction.

full rationale

The paper applies an external DeepRUOT solver (Zhang et al. 2025, no author overlap) after an age-supervised VAE; it does not claim parameter-free first-principles derivation of aging laws. The age-MSE term forces chronological ordering of the latent manifold by design, so the subsequent unidirectional velocity streamlines are largely definitional. The growth field and TMV are optimized via the reconstruction loss to match empirical age-bin densities and cardinalities, so the late-life surge is the residual required to accommodate the observed higher variance of the oldest cohort; labeling it 'stochastic epigenetic drift' or 'survivorship' is interpretive, not an independent prediction. Archetype categories are defined post-decoding by simple kinetic statistics (max shift, max curvature, min variance) and then overlaid on raw data, which must track centers of mass by the OT reconstruction objective. Leave-one-out W1/TMV and decoder fidelity supply limited external checks, and no self-citation uniqueness theorems or ansatz smuggling appear. Thus only mild fitted-observation-as-discovery circularity; the generative pipeline itself remains non-circular. Score 3 is proportionate.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The central claim rests on treating cross-sectional age bins as temporal snapshots, on the RUOT growth term being a sufficient model of non-conservative aging, and on a large set of architectural and loss-weight free parameters chosen by the authors. No new physical entities are postulated; the growth field and archetypes are either inherited from DeepRUOT or defined post-hoc from decoded curves.

free parameters (6)
  • VAE β (KL weight)
    Set to 0.1; controls latent smoothness and directly shapes the manifold on which transport is solved.
  • VAE γ (age-regression weight)
    Set to 0.3; forces chronological ordering of the latent space that is a prerequisite for the subsequent OT stage.
  • latent dimension d
    Fixed at 16; determines the geometry of the aging manifold.
  • number of CpG features
    Top 2000 selected by ANOVA F-statistic on the training set; selection itself is age-supervised and can bias toward clock-like sites.
  • DeepRUOT λ_mass, λ_OT, λ_energy, α, σ
    Multiple loss weights and diffusion scale (σ=0.1) set by hand across three training phases; they control the balance between mass change, transport fidelity and energy.
  • age-bin boundaries
    Four fixed bins 0–20/21–40/41–60/61–80 chosen by the authors; coarser or finer partitions would alter the learned fields.
assumptions (4)
  • domain assumption Cross-sectional chronological age bins constitute sequential temporal snapshots of a continuous aging process
    Stated in Introduction and §2; required for any trajectory-inference framing of static data.
  • domain assumption RUOT / Wasserstein–Fisher–Rao growth term adequately captures non-conservative population effects (survivorship, attrition) without additional biological priors
    Core modeling choice of §2.2; inherited from DeepRUOT but applied without independent validation that the growth field isolates those biological mechanisms.
  • ad hoc to paper Age-regularized latent manifold isolates a universal aging signal from tissue heterogeneity
    Enforced by the auxiliary age-regression head (§2.1); pan-tissue design deliberately averages tissue-specific kinetics.
  • standard math Standard VAE ELBO + MSE age loss yields a topologically suitable manifold for OT
    Uses Kingma & Welling VAE and β-VAE regularization; standard but the joint weighting is paper-specific.
invented entities (1)
  • Four kinetic aging archetypes (linear accumulators, linear decay, exponential/late-onset drift, age-invariant maintenance) independent evidence
    purpose: Categorize decoded continuous CpG trajectories into biologically interpretable classes
    Defined post-hoc by simple kinetic statistics (max shift, max curvature, min variance) on the decoded curves; not new molecular entities but new operational categories derived from the model.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Trajectory Inference of Human Aging from Cross-Sectional DNA Methylation Data." pith.science (2026). https://pith.science/paper/X64XI3SC

@misc{pith2026260706583,
  author       = {Pith},
  title        = {Pith review of: Trajectory Inference of Human Aging from Cross-Sectional DNA Methylation Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X64XI3SC}},
  note         = {Machine review of arXiv:2607.06583}
}
read the original abstract

DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging. While conventional epigenetic clocks accurately predict chronological age from high-dimensional CpG profiles, they treat aging as a static regression task, meaning they can only output a single score rather than simulating how an entire profile continuously changes over time. To reconstruct these continuous dynamics, we frame lifelong human epigenetic aging as a trajectory inference problem across discrete age snapshots derived from widely available cross-sectional data. We introduce a two-stage computational pipeline: first, an age-regularized Variational Autoencoder (VAE) maps high-dimensional CpG profiles onto a chronologically ordered latent manifold while preserving a generative decoder bridge back to the original methylation space. Second, we model the continuous movement across this latent space via Regularized Unbalanced Optimal Transport (RUOT) that unifies deterministic drift, random diffusion, and non-conservative mass changes. By resolving this RUOT formulation using the DeepRUOT framework, our model fluidly accommodates population-level density shifts like survivorship bias and cellular attrition without requiring rigid biological priors. Evaluated on a large-scale, 80-year pan-tissue dataset, our model demonstrates robust distribution interpolation and uncovers a prominent late-life surge in the learned growth field that mathematically captures the variance expansion driven by stochastic epigenetic drift. Finally, by decoding continuous latent paths back to individual CpG sites, we reconstruct and empirically verify distinct biological aging archetypes, offering a rigorous, generative paradigm for simulating human molecular aging.

Figures

Figures reproduced from arXiv: 2607.06583 by the authors.

Figure 1
Figure 1. Methodological framework for inferring continuous biological aging trajectories. (1) Cross [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Trajectory inference of human epigenetic aging in latent space. (a) Ground truth PCA pro [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Biological archetypes of DNA methylation aging. Continuous trajectories were generated [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Empirical verification of Age-Invariant Maintenance Sites. The inferred mean continuous [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Empirical verification of Linear Accumulators. The continuous trajectory correctly tracks [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Empirical verification of Exponential & Late-Onset Drift sites. The model successfully [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

37 extracted references · 3 linked inside Pith

  1. [1]

    Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming.Cell, 176(4):928–943, 2019

    Geoffrey Schiebinger, Jian Shu, Marcin Tabaka, Brian Cleary, Vidya Subramanian, Aryeh Solomon, Joshua Gould, Siyan Liu, Stacie Lin, Peter Berube, et al. Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming.Cell, 176(4):928–943, 2019

    2019

  2. [2]

    Learning single- cell perturbation responses using neural optimal transport.Nature methods, 20(11):1759–1768, 2023

    Charlotte Bunne, Stefan G Stark, Gabriele Gut, Jacobo Sarabia Del Castillo, Mitch Levesque, Kjong-Van Lehmann, Lucas Pelkmans, Andreas Krause, and Gunnar Rätsch. Learning single- cell perturbation responses using neural optimal transport.Nature methods, 20(11):1759–1768, 2023

    2023

  3. [3]

    Towards a mathematical theory of trajectory inference.arXiv preprint arXiv:2102.09204, 2021

    Hugo Lavenant, Stephen Zhang, Young-Heon Kim, and Geoffrey Schiebinger. Towards a mathematical theory of trajectory inference.arXiv preprint arXiv:2102.09204, 2021. 8

    arXiv 2021

  4. [4]

    Optimal transport for single-cell and spatial omics.Nature Reviews Methods Primers, 4(1):58, 2024

    Charlotte Bunne, Geoffrey Schiebinger, Andreas Krause, Aviv Regev, and Marco Cuturi. Optimal transport for single-cell and spatial omics.Nature Reviews Methods Primers, 4(1):58, 2024

    2024

  5. [5]

    Dna methylation and healthy human aging.Aging cell, 14(6):924–932, 2015

    Meaghan J Jones, Sarah J Goodman, and Michael S Kobor. Dna methylation and healthy human aging.Aging cell, 14(6):924–932, 2015

    2015

  6. [6]

    Dna methylation clocks in aging: categories, causes, and consequences.Molecular cell, 71(6):882–895, 2018

    Adam E Field, Neil A Robertson, Tina Wang, Aaron Havas, Trey Ideker, and Peter D Adams. Dna methylation clocks in aging: categories, causes, and consequences.Molecular cell, 71(6):882–895, 2018

    2018

  7. [7]

    Dna methylation age of human tissues and cell types.Genome biology, 14(10):3156, 2013

    Steve Horvath. Dna methylation age of human tissues and cell types.Genome biology, 14(10):3156, 2013

    2013

  8. [8]

    Genome-wide methylation profiles reveal quantitative views of human aging rates.Molecular cell, 49(2):359–367, 2013

    Gregory Hannum, Justin Guinney, Ling Zhao, LI Zhang, Guy Hughes, SriniVas Sadda, Brandy Klotzle, Marina Bibikova, Jian-Bing Fan, Yuan Gao, et al. Genome-wide methylation profiles reveal quantitative views of human aging rates.Molecular cell, 49(2):359–367, 2013

    2013

Show all 37 references
  1. [9]

    An epigenetic biomarker of aging for lifespan and healthspan.Aging (albany NY), 10(4):573, 2018

    Morgan E Levine, Ake T Lu, Austin Quach, Brian H Chen, Themistocles L Assimes, Stefania Bandinelli, Lifang Hou, Andrea A Baccarelli, James D Stewart, Yun Li, et al. An epigenetic biomarker of aging for lifespan and healthspan.Aging (albany NY), 10(4):573, 2018

    2018

  2. [10]

    Dna methylation grimage strongly predicts lifespan and healthspan.Aging (albany NY), 11(2):303, 2019

    Ake T Lu, Austin Quach, James G Wilson, Alex P Reiner, Abraham Aviv, Kenneth Raj, Lifang Hou, Andrea A Baccarelli, Yun Li, James D Stewart, et al. Dna methylation grimage strongly predicts lifespan and healthspan.Aging (albany NY), 11(2):303, 2019

    2019

  3. [11]

    Human epigenetic ageing is logarithmic with time across the entire lifespan.Epigenetics, 14(9):912–926, 2019

    Sagi Snir, Colin Farrell, and Matteo Pellegrini. Human epigenetic ageing is logarithmic with time across the entire lifespan.Epigenetics, 14(9):912–926, 2019

    2019

  4. [12]

    Fractional calculus in epigenet- ics: Modelling dna methylation dynamics using mittag–leffler function.Fractal and Fractional, 9(9):616, 2025

    Hosein Nasrolahpour, Matteo Pellegrini, and Tomas Skovranek. Fractional calculus in epigenet- ics: Modelling dna methylation dynamics using mittag–leffler function.Fractal and Fractional, 9(9):616, 2025

    2025

  5. [13]

    E. J. Allen and B. B. U. P. Perera. Biological aging modeled with stochastic differential equations.Communications in Applied Analysis, 22(2):271–293, 2018

    2018

  6. [14]

    A mathematical model which examines age-related stochastic fluctuations in dna maintenance methylation.Experimental Gerontology, 156:111623, 2021

    Loukas Zagkos, Jason Roberts, and Mark Mc Auley. A mathematical model which examines age-related stochastic fluctuations in dna maintenance methylation.Experimental Gerontology, 156:111623, 2021

    2021

  7. [15]

    Dna methylation age of blood predicts all-cause mortality in later life.Genome biology, 16(1):25, 2015

    Riccardo E Marioni, Sonia Shah, Allan F McRae, Brian H Chen, Elena Colicino, Sarah E Harris, Jude Gibson, Anjali K Henders, Paul Redmond, Simon R Cox, et al. Dna methylation age of blood predicts all-cause mortality in later life.Genome biology, 16(1):25, 2015

    2015

  8. [16]

    Accounting for cellular heterogeneity is critical in epigenome-wide association studies.Genome biology, 15(2):R31, 2014

    Andrew E Jaffe and Rafael A Irizarry. Accounting for cellular heterogeneity is critical in epigenome-wide association studies.Genome biology, 15(2):R31, 2014

    2014

  9. [17]

    A computational fluid mechanics solution to the monge-kantorovich mass transfer problem.Numerische Mathematik, 84(3):375–393, 2000

    Jean-David Benamou and Yann Brenier. A computational fluid mechanics solution to the monge-kantorovich mass transfer problem.Numerische Mathematik, 84(3):375–393, 2000

    2000

  10. [18]

    A survey of the schr\" odinger problem and some of its connections with optimal transport.arXiv preprint arXiv:1308.0215, 2013

    Christian Léonard. A survey of the schr\" odinger problem and some of its connections with optimal transport.arXiv preprint arXiv:1308.0215, 2013

    2013 arXiv

  11. [19]

    The most likely evolution of diffusing and vanishing particles: Schrodinger bridges with unbalanced marginals.SIAM Journal on Control and Optimization, 60(4):2016–2039, 2022

    Yongxin Chen, Tryphon T Georgiou, and Michele Pavon. The most likely evolution of diffusing and vanishing particles: Schrodinger bridges with unbalanced marginals.SIAM Journal on Control and Optimization, 60(4):2016–2039, 2022

    2016

  12. [20]

    An interpolat- ing distance between optimal transport and fisher–rao metrics.F oundations of Computational Mathematics, 18(1):1–44, 2018

    Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard. An interpolat- ing distance between optimal transport and fisher–rao metrics.F oundations of Computational Mathematics, 18(1):1–44, 2018

    2018

  13. [21]

    Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport

    Zhenyi Zhang, Tiejun Li, and Peijie Zhou. Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport. InInternational Conference on Learning Representations, volume 2025, pages 19888–19919, 2025. 9

    2025

  14. [22]

    Auto-encoding variational bayes

    Diederik P Kingma and Max Welling. Auto-encoding variational bayes. InInternational Conference on Learning Representations (ICLR), 2014

    2014

  15. [23]

    β-vae: Learning basic visual con- cepts with a constrained variational framework

    Irina Higgins, Loïc Matthey, Arka Pal, Christopher P Burgess, Xavier Glorot, Matthew Botvinick, Shakir Mohamed, and Alexander Lerchner. β-vae: Learning basic visual con- cepts with a constrained variational framework. InInternational Conference on Learning Representations (ICLR), 2017

    2017

  16. [24]

    A pan-tissue dna- methylation epigenetic clock based on deep learning.npj Aging, 8(1):4, 2022

    Lucas Paulo de Lima Camillo, Louis R Lapierre, and Ritambhara Singh. A pan-tissue dna- methylation epigenetic clock based on deep learning.npj Aging, 8(1):4, 2022

    2022

  17. [25]

    USAF school of Aviation Medicine, 1985

    Evelyn Fix.Discriminatory analysis: nonparametric discrimination, consistency properties, volume 1. USAF school of Aviation Medicine, 1985

    1985

  18. [26]

    Dropout: a simple way to prevent neural networks from overfitting.The journal of machine learning research, 15(1):1929–1958, 2014

    Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting.The journal of machine learning research, 15(1):1929–1958, 2014

    1929

  19. [27]

    Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

    Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

    2014 arXiv

  20. [28]

    Epige- netic differences arise during the lifetime of monozygotic twins.Proceedings of the National Academy of Sciences, 102(30):10604–10609, 2005

    Mario F Fraga, Esteban Ballestar, Maria F Paz, Santiago Ropero, Fernando Setien, Maria L Ballestar, Damia Heine-Suñer, Juan C Cigudosa, Miguel Urioste, Javier Benitez, et al. Epige- netic differences arise during the lifetime of monozygotic twins.Proceedings of the National Ac...

    2005

  21. [29]

    The rate of epigenetic drift scales with maximum lifespan across mammals.Nature Communications, 14(1):7731, 2023

    Emily M Bertucci-Richter and Benjamin B Parrott. The rate of epigenetic drift scales with maximum lifespan across mammals.Nature Communications, 14(1):7731, 2023

    2023

  22. [30]

    Making sense of the ageing methylome.Nature Reviews Genetics, 23(10):585–605, 2022

    Kirsten Seale, Steve Horvath, Andrew Teschendorff, Nir Eynon, and Sarah V oisin. Making sense of the ageing methylome.Nature Reviews Genetics, 23(10):585–605, 2022

    2022

  23. [31]

    Age-related accrual of methylomic variability is linked to fundamental ageing mechanisms

    Roderick C Slieker, Maarten van Iterson, René Luijk, Marian Beekman, Daria V Zhernakova, Matthijs H Moed, Hailiang Mei, Michiel Van Galen, Patrick Deelen, Marc Jan Bonder, et al. Age-related accrual of methylomic variability is linked to fundamental ageing mechanisms. Genome b...

    2016

  24. [32]

    Hallmarks of aging: An expanding universe.Cell, 186(2):243–278, 2023

    Carlos López-Otín, Maria A Blasco, Linda Partridge, Manuel Serrano, and Guido Kroemer. Hallmarks of aging: An expanding universe.Cell, 186(2):243–278, 2023

    2023

  25. [33]

    Human aging- associated dna hypermethylation occurs preferentially at bivalent chromatin domains.Genome research, 20(4):434, 2010

    Vardhman K Rakyan, Thomas A Down, Siarhei Maslau, Toby Andrew, Tsun-Po Yang, Huriya Beyan, Pamela Whittaker, Owen T McCann, Sarah Finer, Ana M Valdes, et al. Human aging- associated dna hypermethylation occurs preferentially at bivalent chromatin domains.Genome research, 20(4)...

    2010

  26. [34]

    Decline in genomic dna methy- lation through aging in a cohort of elderly subjects.Mechanisms of ageing and development, 130(4):234–239, 2009

    Valentina Bollati, Joel Schwartz, Robert Wright, Augusto Litonjua, Letizia Tarantini, Helen Suh, David Sparrow, Pantel V okonas, and Andrea Baccarelli. Decline in genomic dna methy- lation through aging in a cohort of elderly subjects.Mechanisms of ageing and development, 130(...

    2009

  27. [35]

    Senescent cells harbour features of the cancer epigenome.Nature cell biology, 15(12):1495– 1506, 2013

    Hazel A Cruickshanks, Tony McBryan, David M Nelson, Nathan D VanderKraats, Parisha P Shah, John Van Tuyn, Taranjit Singh Rai, Claire Brock, Greg Donahue, Donncha S Dunican, et al. Senescent cells harbour features of the cancer epigenome.Nature cell biology, 15(12):1495– 1506, 2013

    2013

  28. [36]

    Charting a dynamic dna methylation landscape of the human genome.Nature, 500(7463):477– 481, 2013

    Michael J Ziller, Hongcang Gu, Fabian Müller, Julie Donaghey, Linus T-Y Tsai, Oliver Kohlbacher, Philip L De Jager, Evan D Rosen, David A Bennett, Bradley E Bernstein, et al. Charting a dynamic dna methylation landscape of the human genome.Nature, 500(7463):477– 481, 2013

    2013

  29. [37]

    Aging and epigenetic drift: a vicious cycle.The Journal of clinical investigation, 124(1):24–29, 2014

    Jean-Pierre Issa et al. Aging and epigenetic drift: a vicious cycle.The Journal of clinical investigation, 124(1):24–29, 2014. 10 A Supplementary Material This supplementary document provides data distributions, and empirical validation figures for epige- netic archetypes supp...

    2014

Pith tools

Reviewed July 11, 2026 · model on record in the stance chip above.