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REVIEW 3 major objections 6 minor 27 references

Modeling Time-course Gene Expression Data through Bayesian Partition Functional Principal Component Analysis

T0 review · 3 major / 6 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read A Bayesian mixture of multivariate FPCAs jointly recovers both gene groups and their shared temporal dynamics, outperforming two-step baselines.

desk verdict Solid joint Bayesian mixture-of-MFPCA with clear simulation gains over two-step baselines; variational approximation is the ordinary soft spot, not a deal-breaker. read the letter →

arxiv 2607.11558 v1 pith:IOIZIIRO submitted 2026-07-13 stat.ME stat.AP

Marion Kerioui , Daniel Temko , Shahin Tavakoli , Hélène Ruffieux This is my paper
classification stat.MEstat.AP MSC 62H2562M1062P10
keywords functionalprincipalcomponentanalysismixturemodellongitudinalgeneexpressionvariationalinferencehigh-dimensionalbiomarkerspartitionlearning
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

High-dimensional longitudinal biomarkers, such as gene expression measured repeatedly over time, contain coordinated patterns that standard methods cannot extract at once: they either ignore shared dynamics across genes or require a known partition of genes. The paper introduces Partition Functional Principal Component Analysis (PFPCA), a Bayesian hierarchical model that places a mixture of multivariate functional principal-component models over the variables. A scalable annealed mean-field variational algorithm jointly estimates group assignments, individual scores, mean and eigenfunctions, and the effective numbers of groups and components. Simulations on sparse, unequal-sized groups show that joint inference recovers the true partition far more often than first running univariate FPCA and then clustering the scores. On H3N2 influenza gene-expression trajectories the method isolates an “Influenza A” pathway group whose leading scores cleanly separate symptomatic from asymptomatic subjects, demonstrating that the latent temporal structure is biologically interpretable.

What carries the argument

PFPCA: a Dirichlet mixture over groups, each group carrying its own multivariate Karhunen–Loève expansion whose scores are shared across all variables assigned to that group; inference is performed by an annealed mean-field variational algorithm that updates all parameters jointly.

What would settle it

On synthetic data generated from known unequal-sized groups and sparse observation grids, if the recovered partition matches the true labels in fewer than 5 % of replicates (comparable to or worse than the two-step baseline) while the same data are recovered accurately by an oracle that knows the groups, the claimed gain from joint inference would be refuted.

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Extended reading notes

Core claim

Joint Bayesian inference of a mixture of multivariate FPCAs recovers both the latent partition of variables and the within-group functional structure more accurately than any two-step pipeline of univariate FPCA followed by clustering; in the hardest simulated regime the true partition is retrieved in 27 % of replicates versus 1 % for the two-step baseline.

Load-bearing premise

The mean-field factorization that treats mean functions, eigenfunctions and individual scores as independent a posteriori remains accurate enough for reliable group assignments even when true posterior dependence is strong.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes Partition Functional Principal Component Analysis (PFPCA), a Bayesian hierarchical model that jointly clusters high-dimensional longitudinal variables into groups sharing latent temporal dynamics and performs multivariate FPCA within each group. Inference uses a mean-field variational algorithm with simulated annealing (AMFVB), with post-hoc orthonormalization of scores and eigenfunctions, and data-driven selection of the number of groups Q and components L via overfitted mixtures and cumulative variance thresholds. Simulations (N=200, p=100, unequal groups, sparse grids) report that joint PFPCA recovers the true partition in 27% of replicates versus 1% for a two-step baseline of univariate FPCA plus K-medoids, with ARI 0.94 versus 0.85, and estimation accuracy close to an Oracle MFPCA that knows the partition. A small-scale HMC comparison (p=6) shows close agreement with AMFVB. Applied to H3N2 influenza gene-expression data (N=17, 1000 high-CV genes), PFPCA recovers an Influenza-A-enriched module whose leading scores separate symptomatic from asymptomatic individuals.

Significance. If the comparative claims hold, PFPCA fills a genuine methodological gap: existing clustering of time-dependent variables is largely single-subject, while global MFPCA assumes all variables share one latent process. Joint recovery of partition and within-group functional structure, with a scalable variational algorithm and a public R package (partFPCA), is a concrete contribution for high-dimensional longitudinal omics and related biomarker settings. Strengths include a systematic simulation design (group size, sparsity/density), an Oracle-MFPCA benchmark, a small HMC check of the variational approximation, and a biologically coherent case study. The work is primarily computational/methodological rather than theoretical; its value rests on empirical recovery gains and practical usability rather than asymptotic guarantees.

major comments (3)
  1. Section 4.3.3 and Figure 3: the headline exact-recovery rates (27% PFPCA vs 1% two-step) are driven largely by a size-2 group that is inherently hard to identify (correct assignment in only 34% of replicates; frequent absorption into larger groups). Exact partition recovery is therefore a harsh and somewhat design-dependent metric. The ARI comparison (0.94 vs 0.85) and the near-Oracle accuracy on the three larger groups are more informative of the central claim. Please restructure the primary reporting around ARI and group-size-stratified recovery, and add at least one balanced-group scenario (e.g., four groups of comparable size) so that the 27%-vs-1% figure is not the sole headline for the hardest regime.
  2. Sections 3.1–3.2 and 4.2, Eq. (6): the mean-field factorization treats mean functions, eigenfunctions and individual scores as a posteriori independent, and annealing uses fixed defaults (T=2, 100 iterations). The only MCMC check is for p=6 with known Q and L. The main comparative claims (partition recovery and score/function accuracy at p=100) therefore rest on an unvalidated high-dimensional variational approximation. Because the two-step baseline also uses variational UFPCA, the relative ranking may still be fair, but absolute statements about recovered partitions and curve credible intervals need clearer qualification. Please add diagnostics (e.g., multiple random starts, sensitivity of ARI/ELBO to annealing length, or a moderate-p HMC/variational comparison) and an explicit limitations paragraph on possible miscalibration of assignment probabilities and intervals when group membersh
  3. Section 5.4: with N=17 (9 symptomatic, 8 asymptomatic), the claim that first-component scores “may serve as a low-dimensional proxy for this response, potentially useful for prediction purposes” is under-supported. Separation is shown visually (Figure 6) and via a baseline-only sensitivity analysis, but there is no formal association test, cross-validated discrimination metric, or uncertainty quantification that accounts for partition uncertainty. Please either provide a simple quantitative assessment (e.g., leave-one-out score separation or a permutation test) or substantially tone down the predictive language to descriptive association only.
minor comments (6)
  1. Section 2.2 / Eq. (4): α_q is first set to 1/Q, then Section 3.3 recommends α = Q^{-1}; these coincide numerically but the wording should be unified and the default stated once.
  2. Section 4.1: the mean function formula μ^{(j)}(t) = (−1)^j × sin{2π + (j mod 5)×t} is slightly ambiguous in typesetting (argument of sin); please clarify the intended expression.
  3. Figure 2–6 captions: several panels are dense; adding panel labels consistently in the text callouts (e.g., “Figure 6(a)–(d)”) and ensuring colorblind-safe palettes would help.
  4. Section 3.3: the 95% cumulative variance rule for selecting L is conventional but arbitrary; a brief sensitivity check (e.g., 90% vs 99%) in the supplement would strengthen robustness claims.
  5. Throughout: a few typos and spacing issues (e.g., “BYMARIONKERIOUI”, “HÉLÈNERUFFIEUX”, “bσ”, “dCPV”) should be cleaned in production; also standardize “two-step” vs “two-steps”.
  6. Related work: briefly position against other multi-subject functional clustering / mixture-of-FPCA approaches beyond the single-subject Bayesian curve clustering cited (Heard et al., Ma et al., Angelini et al.), so the novelty boundary is sharper for AoS readers.

Circularity Check

1 steps flagged · score 1.0 of 10

Minor self-citation of a uniqueness theorem from overlapping authors; the central joint-inference recovery claims rest on independent Monte-Carlo simulations, not on that citation.

  1. uniqueness imported from authors [Section 2.1, paragraph after Eq. (3)]
    "The decomposition in Equation (2) is unique up to a change of sign of the scores and eigenfunctions, provided all eigenfunctions are distinct (see, e.g., Theorem 3.1, Nolan, Richardson and Ruffieux, 2025). This property allows for an initial estimation of the decomposition without imposing any constraint on the scores and latent functions"

    Uniqueness of the Karhunen–Loève decomposition (up to sign) is imported from a theorem whose authors overlap with the present paper and is then used to justify unconstrained variational estimation plus post-hoc orthonormalisation. While the fact itself is standard, the paper treats the self-cited theorem as the warrant for its inference strategy; the step is minor because the central recovery claims do not depend on this uniqueness.

full rationale

The paper's load-bearing comparative claim (joint PFPCA recovers the true partition in 27 % of hard-regime replicates versus 1 % for UFPCA+K-medoids) is an external simulation result, not algebraically forced by any fitted constant or by a self-cited uniqueness statement. The model extends the authors' earlier Bayesian MFPCA variational machinery, but the new mixture layer, joint updates, annealing schedule, and simulation design are self-contained and do not reduce to those priors by construction. The single minor self-citation of a uniqueness theorem is used only to justify unconstrained estimation followed by post-processing; it is not required for the recovery percentages or the application findings. No fitted-input-called-prediction, self-definitional loop, or ansatz smuggling appears. Score 1 reflects the presence of one non-load-bearing self-citation of uniqueness while the derivation chain of the main claims remains independent.

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

The central comparative claim rests on standard functional-data theory (Karhunen–Loève), a mean-field variational family, an overfitted Dirichlet mixture with a specific concentration, Gaussian measurement errors, and a handful of algorithmic hyper-parameters chosen by the authors. No new physical entities are postulated; the only free parameters that materially affect the reported recovery rates are the annealing schedule, the Dirichlet concentration and the initial over-specification of Q and L.

free parameters (4)
  • initial annealing temperature T and number of annealed iterations
    Default T=2 and 100 iterations are chosen empirically; the paper notes that too few annealed steps degrade partitioning (Section 3.2).
  • Dirichlet concentration α_q = 1/Q (or Q^{-1})
    Controls sparsity of the overfitted mixture; recommended value is justified by literature and a sensitivity check in the supplement (Section 3.3).
  • maximum number of groups Q and FPCA components L
    Set “conservatively large” (default 10) and then pruned by empty-group counting and cumulative variance explained; the final reported partition depends on these ceilings.
  • Gamma hyper-parameters a_ε = b_ε = 10 (and analogous for spline precisions)
    Default values that encourage decreasing variance explained by successive components; not estimated from data.
assumptions (4)
  • standard math Multivariate Karhunen–Loève expansion exists and a finite truncation of L components is adequate
    Invoked in Section 2.1 to justify the MFPCA representation inside each mixture component.
  • ad hoc to paper Mean-field factorisation of the variational posterior (independence of means, eigenfunctions and scores)
    Equation (6) and surrounding text; required for closed-form coordinate-ascent updates.
  • domain assumption Gaussian measurement errors and Gaussian priors on scores and spline coefficients
    Likelihood and prior statements in Section 2.2; standard but load-bearing for conjugacy of the variational updates.
  • domain assumption Overfitted mixture with α < 1 asymptotically recovers the true number of groups
    Cited from Rousseau & Mengersen (2011) and used to justify pruning empty components (Section 3.3).
invented entities (1)
  • Partition FPCA (PFPCA) hierarchical model
    purpose: Simultaneously partitions variables and performs MFPCA inside each group so that scores are shared only within coherent subsets
    The model itself is the methodological contribution; it is not an unobserved physical object but a new statistical construct whose utility is demonstrated by simulation and one real-data example.

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Cite this review

Pith. "Pith review of Modeling Time-course Gene Expression Data through Bayesian Partition Functional Principal Component Analysis." pith.science (2026). https://pith.science/paper/IOIZIIRO

@misc{pith2026260711558,
  author       = {Pith},
  title        = {Pith review of: Modeling Time-course Gene Expression Data through Bayesian Partition Functional Principal Component Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IOIZIIRO}},
  note         = {Machine review of arXiv:2607.11558}
}
read the original abstract

High-dimensional biomarkers such as gene expression levels are now routinely measured over time, allowing biological processes to be studied dynamically rather than through cross-sectional snapshots. However, existing methods do not adequately address the central applied challenges posed by such data: simultaneously reducing dimensionality, quantifying inter-individual variability and uncovering temporal structure shared across biomarkers. We introduce Partition Functional Principal Component Analysis (PFPCA), a Bayesian model that jointly learns shared temporal patterns and clusters variables according to their latent dynamics. PFPCA combines a mixture model with multivariate functional principal component analysis performed within each group. We develop a scalable mean-field variational algorithm for joint inference of functional principal component loadings, individual-level scores, group assignments and partition sizes. Simulations show clear gains from joint inference: PFPCA recovers both the partition and the latent functional structure more accurately than a two-step baseline. In the most challenging settings, PFPCA retrieves the true partition in 27% of replicates compared with 1% for the two-step baseline. Applied to longitudinal gene-expression data from individuals experimentally infected with H3N2 influenza virus, PFPCA identifies groups of genes with coordinated activation patterns and reveals temporal signatures associated with immune-response dynamics and symptom status.

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Works this paper leans on

27 extracted references · 8 canonical work pages

  1. [1]

    and PENSKY, M

    ANGELINI, C., DECANDITIIS, D. and PENSKY, M. (2012). Clustering time-course microarray data using func- tional Bayesian infinite mixture model.Journal of Applied Statistics39129–149. https://doi.org/10.1080/ 02664763.2011.578620

    arXiv 2012

  2. [2]

    and HOCHBERG, Y

    BENJAMINI, Y. and HOCHBERG, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.Journal of the Royal Statistical Society. Series B (Methodological)57289–300. Publisher: [Royal Statistical Society, Oxford University Press]

    1995

  3. [3]

    BISHOP, C. M. (2006).Pattern recognition and machine learning.Information science and statistics. Springer, New York

    2006

  4. [4]

    M., KUCUKELBIR, A

    BLEI, D. M., KUCUKELBIR, A. and MCAULIFFE, J. D. (2017). Variational Inference: A Review for Statisti- cians.Journal of the American Statistical Association112859–877. https://doi.org/10.1080/01621459.2017. 1285773 18

    doi:10.1080/01621459.2017 2017

  5. [5]

    and JACQUES, J

    BOUVEYRON, C. and JACQUES, J. (2011). Model-based clustering of time series in group-specific func- tional subspaces.Advances in Data Analysis and Classification5281–300. https://doi.org/10.1007/ s11634-011-0095-6

    2011

  6. [6]

    CAI, J., GOUDIE, R. J. B., STARR, C. and TOM, B. D. M. (2024). Dynamic factor analysis with dependent Gaussian processes for high-dimensional gene expression trajectories.Biometrics80ujae131. https://doi.org/ 10.1093/biomtc/ujae131

    work page doi:10.1093/biomtc/ujae131 2024

  7. [7]

    S., LUCAS, J., DUNSON, D

    CHEN, M., ZAAS, A., WOODS, C., GINSBURG, G. S., LUCAS, J., DUNSON, D. and CARIN, L. (2011). Pre- dicting Viral Infection From High-Dimensional Biomarker Trajectories.Journal of the American Statistical Association1061259–1279. https://doi.org/10.1198/jasa.2011.ap10611 FRÜHWIRTH-SCHNATTER, S. and MALSINER-WALLI, G. (2019). From here to infinity: sparse fin...

    work page doi:10.1198/jasa.2011.ap10611 2011

  8. [8]

    and SCHRACK, J

    GOLDSMITH, J., ZIPUNNIKOV, V. and SCHRACK, J. (2015). Generalized Multilevel Function-on-Scalar Regres- sion and Principal Component Analysis.Biometrics71344–353. https://doi.org/10.1111/biom.12278

    doi:10.1111/biom.12278 2015

Show all 27 references
  1. [9]

    and GREVEN, S

    HAPP, C. and GREVEN, S. (2018). Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains.Journal of the American Statistical Association113649–659. https: //doi.org/10.1080/01621459.2016.1273115

    2018 doi

  2. [10]

    A., HOLMES, C

    HEARD, N. A., HOLMES, C. C. and STEPHENS, D. A. (2006). A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves.Journal of the American Statistical Association10118–29. https...

    2006

  3. [11]

    and ARABIE, P

    HUBERT, L. and ARABIE, P. (1985). Comparing partitions.Journal of Classification2193–218. https://doi.org/ 10.1007/BF01908075

    1985 doi

  4. [12]

    and ZUCKNICK, M

    ICKSTADT, K., SCHÄFER, M. and ZUCKNICK, M. (2018). Toward Integrative Bayesian Analysis in Molecular Biology.Annual Review of Statistics and Its Application5141–167. https://doi.org/10.1146/ annurev-statistics-031017-100438

    2018

  5. [13]

    and PREDA, C

    JACQUES, J. and PREDA, C. (2014). Model-based clustering for multivariate functional data.Computational Statistics & Data Analysis7192–106. https://doi.org/10.1016/j.csda.2012.12.004

    2014 doi

  6. [14]

    and DESMÉE, S

    KERIOUI, M., BERTRAND, J., BRUNO, R., MERCIER, F., GUEDJ, J. and DESMÉE, S. (2022). Modelling the as- sociation between biomarkers and clinical outcome: an introduction to nonlinear joint models.British Journal of Clinical Pharmacology. https://doi.org/10.1111/bcp.15200

    2022 doi

  7. [15]

    KIRKPATRICK, S., GELATT, C. D. and VECCHI, M. P. (1983). Optimization by Simulated Annealing.Science 220671–680. https://doi.org/10.1126/science.220.4598.671

    1983 doi

  8. [16]

    LU, Z. (2024). Clustering Longitudinal Data: A Review of Methods and Software Packages.International Statis- tical Review. Publisher: Wiley. https://doi.org/10.1111/insr.12588

    2024 doi

  9. [17]

    and LIU, J

    MA, P., ZHONG, W., FENG, Y. and LIU, J. S. (2008). Bayesian Functional Data Clustering for Temporal Mi- croarray Data.International Journal of Plant Genomics20081–4. https://doi.org/10.1155/2008/231897

    2008 doi

  10. [18]

    and WAND, M

    MENICTAS, M. and WAND, M. (2013). Variational inference for marginal longitudinal semiparametric regres- sion.Stat261–71. https://doi.org/10.1002/sta4.18

    2013 doi

  11. [19]

    H., GOLDSMITH, J

    NOLAN, T. H., GOLDSMITH, J. and RUPPERT, D. (2025). Bayesian Functional Principal Components Analysis via Variational Message Passing with Multilevel Extensions.Bayesian Analysis20. https://doi.org/10.1214/ 23-BA1393

    2025

  12. [20]

    H., RICHARDSON, S

    NOLAN, T. H., RICHARDSON, S. and RUFFIEUX, H. (2025). Efficient Bayesian functional principal component analysis of irregularly-observed multivariate curves.Computational Statistics & Data Analysis203108094. https://doi.org/10.1016/j.csda.2024.108094

    2025 doi

  13. [21]

    PAPASTAMOULIS, P. (2018). Overfitting Bayesian mixtures of factor analyzers with an unknown number of components.Computational Statistics & Data Analysis124220–234. https://doi.org/10.1016/j.csda.2018.03. 007

    2018 doi

  14. [22]

    and LIQUET, B

    PROUST-LIMA, C., PHILIPPS, V. and LIQUET, B. (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: TheRPackagelcmm.Journal of Statistical Software78. https://doi.org/10. 18637/jss.v078.i02 PÉLABON, C., HILDE, C. H., EINUM, S. and GAMELON, M. (2...

    2017 doi

  15. [23]

    RAMSAY, J. (2005). Functional Data Analysis. InEncyclopedia of Statistics in Behavioral Science1 ed. (B. S. Everitt and D. C. Howell, eds.) Wiley. https://doi.org/10.1002/0470013192.bsa239

    2005 doi

  16. [24]

    and MENGERSEN, K

    ROUSSEAU, J. and MENGERSEN, K. (2011). Asymptotic Behaviour of the Posterior Distribution in Overfitted Mixture Models.Journal of the Royal Statistical Society Series B: Statistical Methodology73689–710. https: //doi.org/10.1111/j.1467-9868.2011.00781.x BAYESIAN PARTITION FUNC...

    2011 doi

  17. [25]

    C., HAGER, J., INSHAW, J., FAIRFAX, B

    RUFFIEUX, H., DAVISON, A. C., HAGER, J., INSHAW, J., FAIRFAX, B. P., RICHARDSON, S. and BOTTOLO, L. (2020). A global-local approach for detecting hotspots in multiple-response regression.The Annals of Applied Statistics14. https://doi.org/10.1214/20-AOAS1332

    2020 doi

  18. [26]

    and NAKANO, R

    UEDA, N. and NAKANO, R. (1998). Deterministic annealing EM algorithm.Neural Networks11271–282. https: //doi.org/10.1016/S0893-6080(97)00133-0

    1998 doi

  19. [27]

    WAND, M. P. and ORMEROD, J. T. (2008). ON SEMIPARAMETRIC REGRESSION WITH O’SULLIV AN PENALIZED SPLINES.Australian & New Zealand Journal of Statistics50179–198. https://doi.org/10.1111/ j.1467-842X.2008.00507.x

    2008 arXiv

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