Pith. sign in

REVIEW 4 major objections 5 minor 42 references

A Robust Local Fr\'echet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data

T0 review · 4 major / 5 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 By swapping balanced for unbalanced optimal transport in local Fréchet regression, the paper claims more accurate interpolation of single-cell distributions over time and recovery of differentiation trajectories.

desk verdict The method is a plausible new combination, but the main benchmark claim is not supported because the pretraining and hyperparameter tuning both leak held-out time point information into the model. read the letter →

arxiv 2506.11969 v1 pith:DO6FTSG3 submitted 2025-06-13 stat.AP

Binghao Yan , Hongzhe Li This is my paper · ORCID
classification stat.AP
keywords single-cellRNAsequencingFréchetregressionunbalancedoptimaltransportWassersteinbarycenterfixed-pointalgorithmneuralcelltrajectoryinferencedistributionalinterpolation
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

The paper's claim is that cellular gene-expression distributions measured at a few time points can be interpolated at any intermediate time by a local Fréchet regression whose metric is the unbalanced optimal-transport Wasserstein distance, and that this estimate is more accurate than standard balanced transport or trajectory-flow baselines on real single-cell data. The authors support this with a neural fixed-point algorithm that alternates between fitting unbalanced transport maps from the current estimated distribution to each observed time point and moving the estimate along their weighted average. Theorem 1 shows the objective never increases under this update, so the iteration descends to a local minimum. On three scRNA-seq differentiation datasets, the interpolated distributions achieve lower held-out error than MioFlow and baselines under MMD, EMD, and Wasserstein-2 metrics, and the composed transport maps recover differentiation branches whose early marker genes match known biology.

What carries the argument

The load-bearing object is the average conditional push-forward map $\overline{T}(\mu)$, built from the optimal conditional plans $\gamma^*_{i,x}$ of each unbalanced transport problem $W_{2,\mathrm{ub}}^2(\mu,\nu_i)$: it sends a point $x$ to the weighted mean $\sum_i \alpha_i \int y\,d\gamma^*_{i,x}(y)$ and then pushes $\mu$ forward along that displacement. The fixed-point iteration $\mu_{n+1}=\overline{T}(\mu_n)$ is the algorithm, and Theorem 1's inequality $V(\mu)\ge V(\overline{T}(\mu))$ is what licenses it. To make the update computable in high dimension, the authors reparameterize the barycenter as the push-forward of a latent Gaussian by a generator $G_\xi$, and each unbalanced transport problem by a neural stochastic map $T_{\theta_i}$ and potential $v_{\omega_i}$ solving the semi-dual form, with a VAE-normalizing-flow pretraining step to avoid mode collapse.

What would settle it

Run the iterative algorithm on a symmetric two-mode Gaussian mixture with unbalanced tolerance set to 1, recording generated samples after each pass; if the target error keeps falling while the generated distribution keeps alternating between the two modes instead of stabilizing, the practical convergence needed for trustworthy interpolation is refuted.

Watch

Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that the unbalanced Wasserstein barycenter defined by $V(\mu)=\sum_{i=1}^{N}\alpha_i(t)W_{2,\mathrm{ub}}^2(\mu,\nu_i)$ is a fixed point of the average transport map $\overline{T}(\mu)=\#\left(\sum_{i=1}^{N}\alpha_i T^*_{\mu\to\nu_i}\right)$, where $T^*_{\mu\to\nu_i}(x)=\int y\,d\gamma^*_{i,x}(y)$ is the mean of the optimal unbalanced conditional plan. Theorem 1 establishes $V(\mu)\ge V(\overline{T}(\mu))$, so the iteration $\mu_{n+1}=\overline{T}(\mu_n)$ monotonically decreases the local Fréchet objective, with equality characterizing the barycenter. The paper parameterizes $\mu$ by a generator network and each conditional plan by a stochastic neural map solving the semi-dual unbalanced optimal transport problem, then reports leave-one-out benchmarks on three single-cell datasets in which the unbalanced version matches or beats balanced OT and MioFlow, with the largest gains at noisy later time points.

Load-bearing premise

The load-bearing premise is that the iterative algorithm, which the paper only proves makes the target error never increase, actually settles on a good solution in practice; if the iterations stall in a bad pattern or jump around, the interpolated cell distributions and trajectories are not trustworthy.

Editorial extensions

If this is right

  • Given samples from the trained generator, cell populations can be produced at any target time, so the temporal resolution of a time-course experiment is no longer limited to the profiled snapshots.
  • Composing the learned unbalanced transport maps between interpolated distributions assigns each starting cell a trajectory, and DTW clustering of those trajectories separates differentiation branches such as mesodermal versus neuroectodermal fates.
  • Reconstructing gene expression from the PC-space trajectories and fitting linear mixed models identifies early genes whose expression differs by branch, giving testable candidates for regulators of lineage choice.
  • Because $\tau\to\infty$ recovers classical OT, the method contains balanced transport as a limit case and provides a single tolerance parameter that controls how aggressively outliers are discounted.

Reading between the lines

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

  • Editorial inference: the mass creation and destruction permitted by unbalanced OT could be read as net cell proliferation or death between time points, giving a quantitative link between transport divergence and biology that the paper does not itself draw.
  • Editorial inference: the observed mode-collapse difficulty suggests replacing VAE-normalizing-flow pretraining with a diffusion-based pretraining step, a swap that could be tested directly on the three datasets.
  • Editorial inference: held-out interpolation error could be used as a data-driven criterion for selecting bandwidth $h$ and unbalanced tolerance $\tau$, turning the reported sensitivity grids into automatic tuning.
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 / 5 minor

Summary. The paper proposes a robust local Fréchet regression for probability distributions indexed by time, using an unbalanced optimal transport-based Wasserstein distance as the metric. The estimator is defined as a weighted UOT barycenter, and the authors develop a neural fixed-point algorithm (extending Korotin et al., 2022) with a VAE-NF pretraining step to mitigate mode collapse. The method is evaluated on three scRNA-seq datasets by holding out one time point, interpolating its cell distribution from the remaining time points, and comparing against MioFlow and two baselines using MMD, EMD, and Wasserstein-2 metrics. The paper also reconstructs cell trajectories from estimated transport maps and identifies trajectory-associated marker genes.

Significance. If the empirical claims are valid, the paper contributes a useful framework for distributional regression over time in high-dimensional single-cell data, with the attractive properties of robustness to outliers via unbalanced OT and linear scaling in the number of observed distributions. The theoretical result (Theorem 1) gives a monotone-decrease guarantee for the fixed-point iteration, and the application section is extensive, including three real datasets and downstream biological validation via known marker genes. However, the central empirical claim of superior interpolation is currently weakened by evaluation-design issues: hyperparameters are selected using the same held-out time points later reported in the benchmark, and the leave-one-out pretraining protocol is not specified in a way that excludes the held-out time point. These issues must be resolved before the significance can be assessed.

major comments (4)
  1. [Section 6.1 and Section 6.5, Table 2] The hyperparameters h and τ are selected via sensitivity analyses performed on the same held-out time points that are later used in the Table 1 benchmark. Section 6.1 states that h=0.5 and τ=5 for the Reprogramming dataset were chosen based on Section 6.5, but Table 2(a)-(b) evaluate h at t=10 and t=16.5, both of which are held-out time points in Table 1. Similarly, Table 2(c) evaluates τ on the Embryoid dataset at t=7.5 and t=13.5, which are also held-out points in Table 1. This makes the benchmark an in-sample comparison for hyperparameter selection, so the reported margins (e.g., MMD 0.111 vs 0.114 at t=13.5) cannot be interpreted as independent evidence of predictive skill. Please use a nested or fully separate validation procedure for hyperparameter selection and report benchmark results with hyperparameters fixed before any test-time point is examined.
  2. [Algorithm 2 and Section 6.2] The leave-one-out benchmark has a potential information leak through the VAE-NF pretraining. Algorithm 2, Step 1 defines P_data = (1/N) * sum_n \hat P_n, pooling the empirical distributions of all N time points. The benchmark protocol in Section 6.2 says one time point is held out and the distribution is predicted from the remaining time points, but it does not state that the pretraining pooling is recomputed per fold with the held-out time point excluded. As written, the generator G_ξ can already encode the held-out distribution before the fixed-point updates begin, which would inflate the reported interpolation accuracy. Please clarify the exact per-fold protocol, and if the current implementation pools all time points, rerun the benchmark with pretraining performed only on the training time points.
  3. [Section 3, Theorem 1 and Remark] The theoretical support for the method is limited to monotone decrease of the objective V, and the authors explicitly state that weak convergence of the iterates is difficult to establish. This means the fixed-point iteration is not guaranteed to converge to a minimizer of (5), and if the iterates stall or oscillate, the interpolated distributions and all downstream trajectory and gene analyses are not trustworthy. Since the paper's conclusions depend on the generator approximating the true barycenter, please add per-fold numerical convergence diagnostics (e.g., evolution of V, fixed-point residual averaged over samples, or stability across random seeds) for the real-data benchmarks, or provide a convergence guarantee under stronger assumptions.
  4. [Table 1] The claimed advantage of the unbalanced formulation over the balanced OT version is not uniformly supported by the reported numbers. For the Embryoid dataset at t=13.5, OT has better EMD and W2 (5.076 and 5.319) than UOT (5.121 and 5.424), and at t=19.5 OT is better on EMD and W2 as well (5.390/5.629 vs 5.433/5.717). Only at t=7.5 is UOT clearly better on all three metrics. The abstract and Section 6.2 state that UOT 'consistently outperforms' or leads to 'better single cell interpolations' overall; this overstates the evidence. Please either temper the claim or provide a statistical comparison (e.g., confidence intervals or paired tests across repetitions) that justifies a global conclusion.
minor comments (5)
  1. [Table 1] All metrics are 'averaged over 100 repetitions,' but no standard errors, standard deviations, or confidence intervals are reported. Given that several differences between UOT and OT are small (e.g., MMD 0.086 vs 0.087), reporting uncertainty would help the reader judge whether the differences are meaningful.
  2. [Section 6.1] There is an inconsistency in the choice of τ: the benchmark section states τ=1 for the Statefate dataset, but the paragraph on estimating transport plans says 'In all applications, we set the unbalanced tolerance parameter τ=5.' Please clarify which value was actually used for transport-map estimation in the Statefate analysis.
  3. [Equation (4) and surrounding text] The definition of the scaled convex conjugate is confusingly worded: the text says 'we scale the convex conjugate and define ψ*_τ(s) as follows: ψ*(s)=...' but the displayed formula appears to define ψ*_τ directly. Please rewrite the notation to distinguish ψ, ψ*, and ψ*_τ.
  4. [Various] There are several typographical errors that should be corrected: 'trjectory' (Section 6.3), 'scRAN-seq' (Section 6 heading), 'Pretained' (Algorithm 2 output), 'plant to further investigate' (Section 7), and 'we uses fully connected neural networks' (Section 6.1).
  5. [Algorithm 1] The loss L_T in line 7 of Algorithm 1 uses the notation ν_{ω_n} for what is elsewhere called the potential network v_ω; please use a consistent symbol for the potential to avoid confusion with the data measures ν_i.

Circularity Check

2 steps flagged · score 6.0 of 10

The reported interpolation gains are partly circular: h and τ are selected using the same held-out time points that Table 1 then 'predicts', and the VAE-NF pretraining pools all N time points, so the leave-one-out target distribution can enter the model before the fixed-point iterations begin.

  1. fitted input called prediction [Section 6.1 'Implementation details', Section 6.5 'Sensitivity Analysis', Table 1]
    "Guided by the sensitivity analysis in Section 6.5, in our benchmark experiments on temporal datasets, we set: (1) the bandwidth h=3 for the Embryoid dataset, h=2 for the Statefate dataset, and h=0.5 for the Reprogramming dataset; (2) the unbalanced tolerance τ=5 for the Embryoid and Reprogramming datasets, and τ=1 for the Statefate dataset. ... We conduct a sensitivity analysis to guide the choice of these two parameters. Table 2 reports the discrepancies between the predicted and ground truth distributions under different bandwidth choices h for two time points for the Reprogramming dataset."

    The hold-out evaluation in Table 1 reports interpolation error at t=7.5, 13.5, 19.5 (Embryoid), t=4 (Statefate), and t=10, 13.5, 16.5 (Reprogramming). The sensitivity analysis in Section 6.5 selects h and τ by measuring prediction error at the same type of held-out time points (e.g., t=7.5 and 13.5 for τ in the Embryoid dataset; t=10 and 16.5 for h in the Reprogramming dataset). Thus the numbers in Table 1 are post-selection estimates at the very time points used to pick the smoothing bandwidth and imbalance tolerance. The 'prediction' is therefore not an independent out-of-sample evaluation: the weights α_i(t) in objective (5) are tuned to minimize error at the target time, and the same target time is then reported as predicted.

  2. other [Algorithm 2, Step 1; Section 4.3; Section 6.2]
    "To address the mode collapse issue, we propose to pretrain the generator Gξ to approximate the empirical distribution of the entire dataset before estimating the barycenter. ... Algorithm 2: Step 1: Pooling. Form P_data = 1/N Σ_{n=1}^N \hat P_n; ... Section 6.2: Specifically, we hold out cells from one time point and predict the distribution of that time point using cells from the remaining time points."

    The leave-one-out protocol is described as predicting a held-out time point using only the remaining time points. But the VAE-NF pretraining used to initialize the generator is defined on P_data, the pooled empirical distribution of all N time points, with no statement that the held-out time point is excluded when pretraining within each fold. Since Gξ is initialized to capture the modes of the entire dataset, the held-out time point's cells can be encoded in the generator before the fixed-point updates begin. The 'prediction' for that time point then partly reduces to reproducing a distribution that was already seen in the generator's pretraining input, rather than being an interpolation from the remaining time points alone.

full rationale

The theoretical core of the paper is not circular. V(µ) is defined as a kernel-weighted sum of unbalanced Wasserstein distances, the average map T̄ is built from the optimal unbalanced couplings, and Theorem 1's monotone decrease V(µ) ≥ V(T̄(µ)) follows from the standard quadratic-identity argument in the supplement: the inequality is a genuine contraction bound, not an assumption equivalent to the conclusion. There are no load-bearing self-citations: the cited fixed-point, semi-dual, and neural-OT results are external. The paper's own Remark honestly concedes that weak convergence of the iterates is not established, which is a convergence-risk limitation but not a circular step. The circularity concern is confined to the empirical evaluation. Section 6.1 fixes h and τ using the Section 6.5 sensitivity analysis, which evaluates error at the same held-out time points later reported in Table 1; and Algorithm 2's pretraining pools all N time points, so a leave-one-out target distribution can enter the generator initialization. Both channels transfer target-time information into the reported 'predictions.' Because the paper's headline claim is empirical ('we show that the proposed methods lead to better single cell interpolations'), this leakage makes the benchmark partially circular. Removing the leakage would require choosing h/τ on a separate validation fold and pooling only the training folds in Algorithm 2; the method itself is not tautological. Score 6 reflects partial circularity in the central empirical claim, not in the mathematical derivation.

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

The central claim rests on a large number of user-chosen hyperparameters, especially h and τ, which are tuned on the evaluation time points, and on several prior theoretical results that are cited but not derived. No new physical entities are introduced. The main ad hoc element is the assumption that the neural fixed-point algorithm converges to the barycenter despite the absence of a convergence proof.

free parameters (6)
  • bandwidth h = h=3 (Embryoid), h=2 (Statefate), h=0.5 (Reprogramming)
    Chosen per dataset based on sensitivity analysis in Section 6.5, where the same held-out time points as the benchmark are used; this is a free parameter fitted to the evaluation data.
  • unbalanced tolerance τ = τ=5 (Embryoid, Reprogramming), τ=1 (Statefate)
    Selected via sensitivity analysis on the benchmark time points; controls the degree of mass imbalance tolerance and directly affects the transport distance.
  • PC dimension = 20 (benchmarks), 50 (COVID supplement)
    Choice of dimensionality for cell state representation; not justified beyond following prior work and is not varied in sensitivity analysis.
  • neural network hyperparameters = widths 196/256, 4 layers, lr 1e-4/3e-4, K_G=50, K_T=10, K_v=50/500, batch 64/128, epochs 25-35
    Many architecture and optimization choices are given as fixed values; no sensitivity analysis is reported for these, and they likely affect results.
  • weight threshold for Reprogramming = 0.01
    Time points with kernel weights below 0.01 are dropped in the Reprogramming dataset (Section 6.1); a heuristic choice that affects the estimator.
  • number of trajectory clusters (DTW) = 2 (Embryoid, Statefate), 3 (Reprogramming)
    Chosen via inspection of DTW dissimilarities; downstream gene analyses depend on this choice.
assumptions (6)
  • standard math Existence and integrability of optimal couplings and conditional plans for unbalanced optimal transport with KL divergence.
    Used throughout Section 2 and the proof of Theorem 1; standard results from Chizat et al. (2018) and Villani (2008).
  • standard math Semi-dual formulation of unbalanced OT (Eq. 4) with the scaled convex conjugate ψ*_τ(s)=τ(e^{s/τ}-1) for KL divergence.
    Invoked in Section 2.1 and in the neural parameterization (Eq. 9); cited from Choi et al. (2024).
  • domain assumption Theorem 2 of Gazdieva et al. (2024): the optimal conditional plan of the UOT problem is contained in the optimal saddle points of the semi-dual, justifying the stochastic map parameterization Tθ.
    Used in Section 4.1 to justify neural approximation of the transport map; this is a prior result the paper relies on without reproducing.
  • domain assumption The empirical distribution of cells in a low-dimensional PC space at each time point is an adequate representation of the biological cell-state distribution.
    This underlies the entire analysis; no validation is provided that the PCA projection preserves the transport geometry or biology.
  • ad hoc to paper The fixed-point iteration µ_{n+1}=T̄(µ_n) converges to a meaningful minimizer in practice.
    Theorem 1 only shows monotone decrease of V; the paper explicitly states that weak convergence is difficult to establish (Section 3 Remark), yet the algorithm's output is treated as the barycenter.
  • domain assumption The local linear kernel weights from Petersen and Müller (2019) with chosen bandwidth h correctly specify the conditional mean distribution.
    The entire local Fréchet regression model rests on this choice; h is tuned on test data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Robust Local Fr\'echet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data." pith.science (2026). https://pith.science/paper/DO6FTSG3

@misc{pith2026250611969,
  author       = {Pith},
  title        = {Pith review of: A Robust Local Fr\'echet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DO6FTSG3}},
  note         = {Machine review of arXiv:2506.11969}
}
read the original abstract

Single-cell RNA sequencing (scRNA-seq) technologies have enabled the profiling of gene expression for a collection of cells across time during a dynamic biological process. Given that each time point provides only a static snapshot, modeling and understanding the underlying cellular dynamics remains a central yet challenging task in modern genomics. To associate biological time with single cell distributions, we develop a robust local Fr\'echet regression for interpolating the high-dimensional cellular distribution at any given time point using data observed over a finite time points. To allow for robustness in cell distributions, we propose to apply the unbalanced optimal transport-based Wasserstein distance in our local Fr\'echet regression analysis. We develop a computationally efficient algorithm to generate the cell distribution for a given time point using generative neural networks. The resulting single cell generated models and the corresponding transport plans can be use to interpolate the single cells at any unobserved time point and to track the cell trajectory during the cell differentiation process. We demonstrate the methods using three single cell differentiation data sets, including differentiation of human embryonic stem cells into embryoids, mouse hematopoietic and progenitor cell differentiation, and reprogramming of mouse embryonic fibroblasts. We show that the proposed methods lead to better single cell interpolations, reveal different cell differential trajectories, and identify early genes that regulate these cell trajectories.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 38 canonical work pages

  1. [1]

    , Buscaglia , Georgia G

    barticle [author] Aiken , Jayne J. , Buscaglia , Georgia G. , Bates , Emily A E. A. Moore , Jeffrey K J. K. ( 2017 ). The -tubulin gene TUBA1A in brain development: a key ingredient in the neuronal isotype blend . Journal of developmental biology 5 8 . barticle

    work page 2017

  2. [2]

    barticle [author] \'A lvarez-Esteban , Pedro C P. C. , Del Barrio , E E. , Cuesta-Albertos , JA J. Matr \'a n , C C. ( 2016 ). A fixed-point approach to barycenters in Wasserstein space . Journal of Mathematical Analysis and Applications 441 744--762 . barticle

    work page 2016

  3. [3]

    , Xu , Lei L

    binproceedings [author] Amos , Brandon B. , Xu , Lei L. Kolter , J Zico J. Z. ( 2017 ). Input convex neural networks . In International conference on machine learning 146--155 . PMLR . binproceedings

    work page 2017

  4. [4]

    Bottou , L \'e on L

    barticle [author] Arjovsky , Martin M. Bottou , L \'e on L. ( 2017 ). Towards principled methods for training generative adversarial networks . arXiv preprint arXiv:1701.04862 . barticle

    arXiv 2017

  5. [5]

    , Chintala , Soumith S

    binproceedings [author] Arjovsky , Martin M. , Chintala , Soumith S. Bottou , L \'e on L. ( 2017 ). Wasserstein generative adversarial networks . In International conference on machine learning 214--223 . PMLR . binproceedings

    work page 2017

  6. [6]

    ( 1997 )

    barticle [author] Borregaard , Niels N. ( 1997 ). Neutrophil granules: Biochemistry and functional significance . Immunological Reviews 155 79--92 . barticle

    work page 1997

  7. [7]

    , Papaxanthos , Laetitia L

    binproceedings [author] Bunne , Charlotte C. , Papaxanthos , Laetitia L. , Krause , Andreas A. Cuturi , Marco M. ( 2022 ). Proximal optimal transport modeling of population dynamics . In International Conference on Artificial Intelligence and Statistics 6511--6528 . PMLR . binproceedings

    work page 2022

  8. [8]

    , Stark , Stefan G S

    barticle [author] Bunne , Charlotte C. , Stark , Stefan G S. G. , Gut , Gabriele G. , Del Castillo , Jacobo Sarabia J. S. , Levesque , Mitch M. , Lehmann , Kjong-Van K.-V. , Pelkmans , Lucas L. , Krause , Andreas A. R \"a tsch , Gunnar G. ( 2023 ). Learning single-cell perturbation responses using neural optimal transport . Nature methods 20 1759--1768 . barticle

    work page 2023

Show all 42 references
  1. [9]

    , Puschmann , Till B T

    barticle [author] Chen , Meng M. , Puschmann , Till B T. B. , Marasek , Pavel P. , Inagaki , Masaki M. , Pekna , Marcela M. , Wilhelmsson , Ulrika U. Pekny , Milos M. ( 2018 ). Increased neuronal differentiation of neural progenitor cells derived from phosphovimentin-deficient...

    2018

  2. [10]

    , Yang , Sujuan S

    barticle [author] Chen , Yang Y. , Yang , Sujuan S. , Lovisa , Sara S. , Ambrose , Catherine G C. G. , McAndrews , Kathleen M K. M. , Sugimoto , Hikaru H. Kalluri , Raghu R. ( 2021 ). Type-I collagen produced by distinct fibroblast lineages reveals specific function during emb...

    2021

  3. [11]

    , Peyr\' e , Gabriel G

    barticle [author] Chizat , Quentin Q. , Peyr\' e , Gabriel G. , Schmitzer , Bernhard B. Vialard , Fran c ois\-Xavier F.-X. ( 2018 ). Unbalanced Optimal Transport: Dynamic and Kantorovich Formulations . Journal of Functional Analysis 274 3090--3123 . 10.1016/j.jfa.2018.02.007 barticle

    2018 doi

  4. [12]

    , Choi , Jaewoong J

    barticle [author] Choi , Jaemoo J. , Choi , Jaewoong J. Kang , Myungjoo M. ( 2024 ). Generative modeling through the semi-dual formulation of unbalanced optimal transport . Advances in Neural Information Processing Systems 36 . barticle

    2024

  5. [13]

    barticle [author] Corcoran , Jonathan P J. P. Ferretti , Patrizia P. ( 1997 ). Keratin 8 and 18 expression in mesenchymal progenitor cells of regenerating limbs is associated with cell proliferation and differentiation . Developmental dynamics: an official publication of the A...

    1997

  6. [14]

    Ferretti , Elisabetta E

    barticle [author] Farkas , Karin K. Ferretti , Elisabetta E. ( 2023 ). Derivation of Human Extraembryonic Mesoderm-like Cells from Primitive Endoderm . International Journal of Molecular Sciences 24 11366 . barticle

    2023

  7. [15]

    , Choi , Jaemoo J

    barticle [author] Gazdieva , Milena M. , Choi , Jaemoo J. , Kolesov , Alexander A. , Choi , Jaewoong J. , Mokrov , Petr P. Korotin , Alexander A. ( 2024 ). Robust barycenter estimation using semi-unbalanced neural optimal transport . arXiv preprint arXiv:2410.03974 . barticle

    2024 arXiv

  8. [16]

    , Bettermann , Kira K

    barticle [author] Golob-Schwarzl , Nicole N. , Bettermann , Kira K. , Mehta , Anita Kuldeep A. K. , Kessler , Sonja M S. M. , Unterluggauer , Julia J. , Krassnig , Stefanie S. , Kojima , Kensuke K. , Chen , Xintong X. , Hoshida , Yujin Y. , Bardeesy , Nabeel M N. M. et al. ( 2...

    2019

  9. [17]

    , Magruder , Daniel Sumner D

    barticle [author] Huguet , Guillaume G. , Magruder , Daniel Sumner D. S. , Tong , Alexander A. , Fasina , Oluwadamilola O. , Kuchroo , Manik M. , Wolf , Guy G. Krishnaswamy , Smita S. ( 2022 ). Manifold interpolating optimal-transport flows for trajectory inference . Advances ...

    2022

  10. [18]

    barticle [author] Jankowski , Michael P M. P. , Cornuet , Pamela K P. K. , McIlwrath , Sabrina S. , Koerber , H Richard H. R. Albers , Kathryn M K. M. ( 2006 ). SRY-box containing gene 11 (Sox11) transcription factor is required for neuron survival and neurite growth . Neurosc...

    2006

  11. [19]

    barticle [author] Kantorovich , Leonid V. L. V. ( 1942 ). On the translocation of masses . Doklady Akademii Nauk SSSR 37 199–201 . barticle

    1942

  12. [20]

    , Abernethy , Jacob J

    barticle [author] Kodali , Naveen N. , Abernethy , Jacob J. , Hays , James J. Kira , Zsolt Z. ( 2017 ). On convergence and stability of gans . arXiv preprint arXiv:1705.07215 . barticle

    2017 arXiv

  13. [21]

    , Egiazarian , Vage V

    barticle [author] Korotin , Alexander A. , Egiazarian , Vage V. , Li , Lingxiao L. Burnaev , Evgeny E. ( 2022 ). Wasserstein iterative networks for barycenter estimation . Advances in Neural Information Processing Systems 35 15672--15686 . barticle

    2022

  14. [22]

    , Bouwmeester , Tewis T

    barticle [author] Leyns , Luc L. , Bouwmeester , Tewis T. , Kim , Sung-Hyun S.-H. , Piccolo , Stefano S. De Robertis , Eddy M E. M. ( 1997 ). Frzb-1 is a secreted antagonist of Wnt signaling expressed in the Spemann organizer . Cell 88 747--756 . barticle

    1997

  15. [23]

    barticle [author] Melms , Johannes C J. C. , Biermann , Jana J. , Huang , Huachao H. , Wang , Yiping Y. , Nair , Ajay A. , Tagore , Somnath S. , Katsyv , Igor I. , Rendeiro , Andr \'e F A. F. , Amin , Amit Dipak A. D. , Schapiro , Denis D. et al. ( 2021 ). A molecular single-c...

    2021

  16. [24]

    barticle [author] Moon , Kevin R K. R. , Van Dijk , David D. , Wang , Zheng Z. , Gigante , Scott S. , Burkhardt , Daniel B D. B. , Chen , William S W. S. , Yim , Kristina K. , Elzen , Antonia van den A. v. d. , Hirn , Matthew J M. J. , Coifman , Ronald R R. R. et al. ( 2019 )....

    2019

  17. [25]

    , Cseke , Botond B

    barticle [author] Nowozin , Sebastian S. , Cseke , Botond B. Tomioka , Ryota R. ( 2016 ). f-gan: Training generative neural samplers using variational divergence minimization . Advances in neural information processing systems 29 . barticle

    2016

  18. [26]

    , Arkin , Yael Y

    barticle [author] Paul , Florian F. , Arkin , Yael Y. , Giladi , Amit A. , Jaitin , David A. D. A. , Kenigsberg , Elad E. , Keren-Shaul , Hanah H. , Winter , David D. , Lara-Astiaso , Daniel D. , Gury , Michal M. , Weiner , Assaf A. , David , Eilon E. , Cohen , Noam N. , Lauri...

    2015

  19. [27]

    M \"u ller , Hans-Georg H.-G

    barticle [author] Petersen , Alexander A. M \"u ller , Hans-Georg H.-G. ( 2019 ). Fr \'e chet regression for random objects with Euclidean predictors . The Annals of Statistics 47 691--719 . barticle

    2019

  20. [28]

    Mohamed , Shakir S

    binproceedings [author] Rezende , Danilo D. Mohamed , Shakir S. ( 2015 ). Variational inference with normalizing flows . In International conference on machine learning 1530--1538 . PMLR . binproceedings

    2015

  21. [29]

    Chiba , Seibi S

    barticle [author] Sakoe , Hiroaki H. Chiba , Seibi S. ( 2003 ). Dynamic programming algorithm optimization for spoken word recognition . IEEE transactions on acoustics, speech, and signal processing 26 43--49 . barticle

    2003

  22. [30]

    , Shu , Jian J

    barticle [author] Schiebinger , Geoffrey G. , Shu , Jian J. , Tabaka , Marcin M. , Cleary , Brian B. , Subramanian , Vidya V. , Solomon , Aryeh A. , Gould , Joshua J. , Liu , Siyan S. , Lin , Stacie S. , Berube , Peter P. et al. ( 2019 ). Optimal-transport analysis of single-c...

    2019

  23. [31]

    barticle [author] Shahin , Weam S W. S. , Ebed , Shima O S. O. , Tyler , Scott R S. R. , Miljkovic , Branko B. , Choi , Soon H S. H. , Zhang , Yulong Y. , Zhou , Weihong W. , Evans , Idil A I. A. , Yeaman , Charles C. Engelhardt , John F J. F. ( 2023 ). Redox-dependent Igfbp2 ...

    2023

  24. [32]

    , B \"o iers , Charlotta C

    barticle [author] Stavish , Dylan D. , B \"o iers , Charlotta C. , Price , Christopher C. , Frith , Thomas JR T. J. , Halliwell , Jason J. , Salda \ n a-Guerrero , Ingrid I. , Wray , Jason J. , Brown , John J. , Carr , Jonathon J. , James , Chela C. et al. ( 2020 ). Generation...

    2020

  25. [33]

    , Ichikawa-Tomikawa , Naoki N

    barticle [author] Sugimoto , Kotaro K. , Ichikawa-Tomikawa , Naoki N. , Satohisa , Seiro S. , Akashi , Yushi Y. , Kanai , Risa R. , Saito , Tsuyoshi T. , Sawada , Norimasa N. Chiba , Hideki H. ( 2013 ). The tight-junction protein claudin-6 induces epithelial differentiation fr...

    2013

  26. [34]

    Tran , Truyen T

    binproceedings [author] Thanh-Tung , Hoang H. Tran , Truyen T. ( 2020 ). Catastrophic forgetting and mode collapse in GANs . In 2020 international joint conference on neural networks (ijcnn) 1--10 . IEEE . binproceedings

    2020

  27. [35]

    , Huang , Jessie J

    binproceedings [author] Tong , Alexander A. , Huang , Jessie J. , Wolf , Guy G. , Van Dijk , David D. Krishnaswamy , Smita S. ( 2020 ). Trajectorynet: A dynamic optimal transport network for modeling cellular dynamics . In International conference on machine learning 9526--953...

    2020

  28. [36]

    bbook [author] Villani , C \'e dric C. et al. ( 2008 ). Optimal transport: old and new 338 . Springer . bbook

    2008

  29. [37]

    , Rodriguez-Fraticelli , Alejo A

    barticle [author] Weinreb , Caleb C. , Rodriguez-Fraticelli , Alejo A. , Camargo , Fernando D F. D. Klein , Allon M A. M. ( 2020 ). Lineage tracing on transcriptional landscapes links state to fate during differentiation . Science 367 eaaw3381 . barticle

    2020

  30. [38]

    barticle [author] Wilken , Madison B M. B. , Fonar , Gennadiy G. , Qiu , Rong R. , Bennett , Laura L. , Tober , Joanna J. , Nations , Catriana C. , Pavani , Giulia G. , Tsao , Victor V. , Garifallou , James J. , Petit , Chayanne C. et al. ( 2024 ). Tropomyosin 1 deficiency fac...

    2024

  31. [39]

    , Kreis , Karsten K

    barticle [author] Xiao , Zhisheng Z. , Kreis , Karsten K. Vahdat , Arash A. ( 2021 ). Tackling the generative learning trilemma with denoising diffusion gans . arXiv preprint arXiv:2112.07804 . barticle

    2021 arXiv

  32. [40]

    , Zhang , Qiaoning Q

    barticle [author] Zhang , Xiaomei X. , Zhang , Qiaoning Q. , Sun , Xiujun X. Shi , Xiangjun X. ( 2008 ). PLAC8 regulates terminal differentiation and function of neutrophils . Blood 112 4099--4107 . barticle

    2008

  33. [41]

    , Huang , Cindy T C

    barticle [author] Zhang , Xiaoqing X. , Huang , Cindy T C. T. , Chen , Jing J. , Pankratz , Matthew T M. T. , Xi , Jiajie J. , Li , Jin J. , Yang , Ying Y. , LaVaute , Timothy M T. M. , Li , Xue-Jun X.-J. , Ayala , Melvin M. et al. ( 2010 ). Pax6 is a human neuroectoderm cell ...

    2010

  34. [42]

    barticle [author] Zoeller , Jason J J. J. , Pimtong , Wittaya W. , Corby , Helen H. , Goldoni , Silvia S. , Iozzo , Alex E A. E. , Owens , Rick T R. T. , Ho , Shiu-Ying S.-Y. Iozzo , Renato V R. V. ( 2009 ). A central role for decorin during vertebrate convergent extension . J...

    2009

Pith tools

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