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arxiv: 2604.14949 · v2 · submitted 2026-04-16 · 📊 stat.ML · cs.LG

Unsupervised feature selection using Bayesian Tucker decomposition

Y-h. Taguchi , Yoh-ichi Mototake This is my paper

Pith reviewed 2026-05-10 10:00 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords Bayesian Tucker decompositionunsupervised feature selectiontensor decompositionGaussian residualsgene expression profilessynthetic datasetscoupled maps
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The pith

Bayesian Tucker decomposition with Gaussian residuals enables unsupervised feature selection across synthetic and real datasets.

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

The paper proposes Bayesian Tucker decomposition where residuals follow a Gaussian distribution, modeled analogously to linear regression. This supports an unsupervised feature selection procedure that the authors test on synthetic datasets, global coupled maps with randomized coupling strengths, and gene expression profiles. The resulting method is presented as promising and expected to align with prior Tucker decomposition approaches to feature extraction. A sympathetic reader would see value in a probabilistic framing that extends tensor methods to label-free high-dimensional data analysis.

Core claim

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD based unsupervs

What carries the argument

Bayesian Tucker decomposition (BTuD) with Gaussian residual assumption that supports unsupervised feature selection through tensor factorization.

If this is right

  • The method performs unsupervised feature selection on various synthetic datasets.
  • It succeeds on global coupled maps with randomized coupling strength.
  • It applies successfully to gene expression profiles.
  • The BTuD-based approach is expected to coincide with prior Tucker decomposition based unsupervised feature extraction.
  • The procedure is promising for a wide range of problems previously addressed by TD methods.

Where Pith is reading between the lines

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

  • The Gaussian residual framing could be tested for robustness gains in other noisy tensor data settings beyond the reported cases.
  • Because the method aligns with earlier TD results, it may serve as a probabilistic bridge to unify deterministic and Bayesian tensor feature selection pipelines.
  • Extensions to additional high-dimensional domains such as imaging or time-series tensors would be a direct next test of the approach.

Load-bearing premise

Modeling the residual as Gaussian produces a meaningfully different or improved unsupervised feature selection procedure compared with conventional higher-order orthogonal iteration Tucker decomposition.

What would settle it

Direct head-to-head comparison of selected features or downstream task performance on the same gene expression profiles using BTuD versus standard higher-order orthogonal iteration Tucker decomposition; large divergence or inferior results would disprove the success and coincidence claims.

read the original abstract

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed and successfully applied to a wide range of problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes Bayesian Tucker decomposition (BTuD) in which residuals are modeled as Gaussian, analogous to linear regression. An algorithm is presented for performing BTuD, but the text states that this decomposition is consistent with the conventional higher-order orthogonal iteration (HOOI) procedure. The BTuD is then used for unsupervised feature selection and applied to synthetic datasets, global coupled maps with randomized coupling, and gene expression profiles. The paper concludes that the method is promising and explicitly notes that BTuD-based feature selection is expected to coincide with previously proposed tensor-decomposition-based unsupervised feature selection.

Significance. If the reported applications hold and the equivalence to prior work is properly contextualized, the manuscript could offer a modest unifying perspective by framing Tucker decomposition in Bayesian terms with Gaussian residuals. However, because the paper itself states that the conventional HOOI already produces consistent results and that the feature-selection outcomes coincide with earlier non-Bayesian TD methods, the Bayesian component does not appear to introduce new algorithmic behavior or improved predictions. No machine-checked proofs, reproducible code, or falsifiable predictions beyond the equivalence are highlighted. The significance is therefore limited to a probabilistic reinterpretation rather than a substantive advance in unsupervised feature selection.

major comments (3)
  1. [Abstract] Abstract: The central claim that BTuD constitutes a 'newly proposed' unsupervised feature selection method is directly contradicted by the statements that 'the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation' and that 'BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed.' This equivalence means reported successes on synthetic data, coupled maps, and gene expression cannot be attributed to the Bayesian residual model.
  2. [Abstract and §3] Abstract and §3 (method): The Gaussian residual assumption is presented as analogous to linear regression, yet no derivation or independent test is supplied showing that this assumption produces a distinct decomposition or feature-selection ranking compared with standard HOOI. The claim that BTuD enables successful feature selection therefore rests on a procedure the manuscript acknowledges is not meaningfully different from prior work.
  3. [Abstract] Abstract: The assertion of successful application to 'various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles' supplies no quantitative metrics, error bars, baseline comparisons against standard HOOI or other feature-selection methods, or ablation of the Bayesian component, leaving the empirical support for any added value unverified.
minor comments (2)
  1. [Introduction] The manuscript should clarify in the introduction whether the Bayesian formulation is intended as a new algorithm or solely as a probabilistic interpretation of existing HOOI results.
  2. [§2] Notation for the Tucker core tensor, factor matrices, and residual variance should be introduced with explicit equations before the algorithm description to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below, acknowledging where the abstract phrasing may overstate novelty given the stated equivalence to HOOI, and outlining revisions to improve clarity and empirical support.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that BTuD constitutes a 'newly proposed' unsupervised feature selection method is directly contradicted by the statements that 'the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation' and that 'BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed.' This equivalence means reported successes on synthetic data, coupled maps, and gene expression cannot be attributed to the Bayesian residual model.

    Authors: We agree that the abstract's use of 'newly proposed' for the unsupervised feature selection method is imprecise in light of the explicit statements on consistency with HOOI and expected coincidence with prior TD-based feature selection. The intended contribution is the Bayesian formulation with Gaussian residuals, which provides a probabilistic reinterpretation analogous to linear regression. However, this does not yield distinct point estimates or rankings. We will revise the abstract to emphasize the Bayesian perspective as a unifying framework rather than a new algorithmic method, while retaining the applications as demonstrations of the decomposition's utility. revision: yes

  2. Referee: [Abstract and §3] Abstract and §3 (method): The Gaussian residual assumption is presented as analogous to linear regression, yet no derivation or independent test is supplied showing that this assumption produces a distinct decomposition or feature-selection ranking compared with standard HOOI. The claim that BTuD enables successful feature selection therefore rests on a procedure the manuscript acknowledges is not meaningfully different from prior work.

    Authors: The Gaussian residual model is motivated directly by the linear regression analogy to justify the objective function for the decomposition. As noted in the manuscript, this leads to an optimization that is solved consistently by the conventional HOOI procedure, so we do not claim or demonstrate a distinct decomposition or altered feature rankings. The Bayesian framing may support future extensions (e.g., uncertainty quantification via posteriors), but no such tests are provided here. We will add a clarifying sentence in §3 to explicitly state that the current implementation produces results equivalent to HOOI and that any added value would require further development beyond the present work. revision: partial

  3. Referee: [Abstract] Abstract: The assertion of successful application to 'various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles' supplies no quantitative metrics, error bars, baseline comparisons against standard HOOI or other feature-selection methods, or ablation of the Bayesian component, leaving the empirical support for any added value unverified.

    Authors: The abstract provides a high-level summary of the applications; the full manuscript contains the detailed experimental results on these datasets. Given the acknowledged equivalence to HOOI, we recognize that quantitative metrics, error bars, direct baseline comparisons, and ablations of the Bayesian component are necessary to substantiate any incremental benefit. We will expand the results section with tables reporting performance metrics, comparisons to standard HOOI and other feature-selection baselines, and an explicit statement that the Bayesian component does not alter the observed feature selections in the current implementation. revision: yes

Circularity Check

1 steps flagged

BTuD is explicitly stated to coincide with conventional HOOI Tucker decomposition, so the Gaussian residual model yields no distinct feature selection procedure.

specific steps
  1. renaming known result [Abstract]
    "Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. ... BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed and successfully applied to a wide range of problems."

    The paper claims BTuD enables successful unsupervised feature selection on various datasets as a new method with Gaussian residuals, but states that its Tucker decomposition is consistent with conventional HOOI and that the feature selection coincides with prior TD methods. The claimed successes therefore reduce to the outputs of the previously proposed non-Bayesian procedure by the paper's own admission, with no independent grounding or distinct predictions from the Bayesian component.

full rationale

The paper's central claim of successful unsupervised feature selection via the newly proposed BTuD reduces directly to the performance of prior non-Bayesian TD methods. The abstract acknowledges that the implementation is consistent with conventional HOOI and that BTuD-based FE is expected to coincide with previously proposed TD-based FE. This equivalence means the reported successes on synthetic data, coupled maps, and gene expression profiles are not attributable to the Bayesian Gaussian residual model (presented as analogous to linear regression) but are the same as earlier results. The Bayesian framing adds no distinct algorithmic behavior or new predictions, rendering the method a renaming of known results rather than an independent advance.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the model rests on the unelaborated assumption that residuals are Gaussian and that the resulting feature selection matches prior non-Bayesian tensor methods.

free parameters (1)
  • Gaussian residual variance
    Invoked by the analogy to linear regression but no value or estimation procedure is stated.
axioms (1)
  • domain assumption Residuals after Tucker decomposition obey a Gaussian distribution
    Stated directly in the abstract as the basis for the Bayesian formulation.

pith-pipeline@v0.9.0 · 5411 in / 1219 out tokens · 38348 ms · 2026-05-10T10:00:49.626900+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Unsupervised and Semi- Supervised Learning

    Taguchi, Y.-h.: Unsupervised Feature Extraction Applied to Bioinformatics: A PCA Based and TD Based Approach, 2nd edn. Unsupervised and Semi- Supervised Learning. Springer, Switzerland (2024)

    work page 2024

  2. [2]

    Springer, Cham, Switzerland (2023)

    Cheng, L., Chen, Z., Wu, Y.-C.: Bayesian Tensor Decomposition for Signal Processing and Machine Learning, 1st edn. Springer, Cham, Switzerland (2023)

    work page 2023

  3. [3]

    In: Balcan, M.F., Weinberger, K.Q

    Kanagawa, H., Suzuki, T., Kobayashi, H., Shimizu, N., Tagami, Y.: Gaus- sian process nonparametric tensor estimator and its minimax optimality. In: Balcan, M.F., Weinberger, K.Q. (eds.) Proceedings of The 33rd Interna- tional Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 48, pp. 1632–1641. PMLR, New York, New York, USA (20...

    work page 2016

  4. [4]

    In: Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N., Weinberger, K.Q

    Wimalawarne, K., Sugiyama, M., Tomioka, R.: Multitask learning meets tensor factorization: task imputation via convex optimization. In: Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N., Weinberger, K.Q. (eds.) Advances in Neu- ral Information Processing Systems, vol. 27. Curran Associates, Inc., ??? (2014). https://proceedings.neurips.cc/paper files/...

    work page 2014

  5. [5]

    SN Computer Science3(3), 225 (2022) https://doi.org/10.1007/ s42979-022-01119-8

    Takayama, H., Zhao, Q., Hontani, H., Yokota, T.: Bayesian Tensor Comple- tion and Decomposition with Automatic CP Rank Determination Using MGP Shrinkage Prior. SN Computer Science3(3), 225 (2022) https://doi.org/10.1007/ s42979-022-01119-8

    work page 2022

  6. [6]

    https://arxiv.org/abs/1505.02343

    Zhao, Q., Zhang, L., Cichocki, A.: Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion (2015). https://arxiv.org/abs/1505.02343

    work page internal anchor Pith review arXiv 2015

  7. [7]

    Journal of Chemometrics 23(7-8), 352–363 (2009) https://doi.org/10.1002/cem.1223 https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/cem.1223

    Mørup, M., Hansen, L.K.: Automatic relevance determi- nation for multi-way models. Journal of Chemometrics 23(7-8), 352–363 (2009) https://doi.org/10.1002/cem.1223 https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/cem.1223

    work page doi:10.1002/cem.1223 2009

  8. [8]

    IEEE Transactions on Signal Processing71, 4077–4091 (2023) https://doi

    Tong, X., Cheng, L., Wu, Y.-C.: Bayesian tensor tucker completion with a flexible core. IEEE Transactions on Signal Processing71, 4077–4091 (2023) https://doi. org/10.1109/TSP.2023.3327845 23

    work page doi:10.1109/tsp.2023.3327845 2023

  9. [9]

    Journal of the Royal Statistical Society

    Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society. Series B (Statistical Methodology)61(3), 611–622 (1999). Accessed 2024-09-16

    work page 1999

  10. [10]

    Information Science and Statistics

    Bishop, C.M.: Pattern Recognition and Machine Learning, 1st edn. Information Science and Statistics. Springer, New York, NY (2006)

    work page 2006

  11. [11]

    In: Proceedings of 3rd International Con- ference on Document Analysis and Recognition, vol

    Ho, T.K.: Random decision forests. In: Proceedings of 3rd International Con- ference on Document Analysis and Recognition, vol. 1, pp. 278–282 (1995). IEEE

    work page 1995

  12. [12]

    The Annals of Statistics13(1), 70–84 (1985)

    Hartigan, J.A., Hartigan, P.M.: The dip test of unimodality. The Annals of Statistics13(1), 70–84 (1985). Accessed 2025-01-07

    work page 1985

  13. [13]

    2012 The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory.Brazilian Journal of Physics42, 146–165

    Barata, J.C.A., Hussein, M.S.: The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory. Brazilian Journal of Physics42(1-2), 146–165 (2012) https: //doi.org/10.1007/s13538-011-0052-z

    work page doi:10.1007/s13538-011-0052-z 2012

  14. [14]

    Journal of Statistical Software87(10), 1–31 (2018) https://doi.org/10.18637/jss.v087.i10

    Li, J., Bien, J., Wells, M.T.: rTensor: An R package for multidimensional array (tensor) unfolding, multiplication, and decomposition. Journal of Statistical Software87(10), 1–31 (2018) https://doi.org/10.18637/jss.v087.i10

    work page doi:10.18637/jss.v087.i10 2018

  15. [15]

    Kaneko, K.: Globally coupled chaos violates the law of large numbers but not the central-limit theorem. Phys. Rev. Lett.65, 1391–1394 (1990) https://doi.org/10. 1103/PhysRevLett.65.1391

    work page 1990

  16. [16]

    https://arxiv.org/abs/2304.06522

    Mototake, Y.-i., Taguchi, Y.-h.: Signal identification without signal formulation (2023). https://arxiv.org/abs/2304.06522

    work page arXiv 2023

  17. [17]

    iScience23(2), 100791 (2020) https://doi.org/10.1016/j.isci.2019.100791

    Kozawa, S., Sagawa, F., Endo, S., De Almeida, G.M., Mitsuishi, Y., Sato, T.N.: Predicting human clinical outcomes using mouse multi-organ transcriptome. iScience23(2), 100791 (2020) https://doi.org/10.1016/j.isci.2019.100791

    work page doi:10.1016/j.isci.2019.100791 2020

  18. [18]

    Frontiers in Genetics11(2020) https://doi.org/ 10.3389/fgene.2020.00695

    Taguchi, Y.-h., Turki, T.: Universal nature of drug treatment responses in drug-tissue-wide model-animal experiments using tensor decomposition-based unsupervised feature extraction. Frontiers in Genetics11(2020) https://doi.org/ 10.3389/fgene.2020.00695

    work page doi:10.3389/fgene.2020.00695 2020

  19. [19]

    Scientific Reports12(1), 17438 (2022) https: //doi.org/10.1038/s41598-022-21474-z 24

    Taguchi, Y.-h., Turki, T.: Adapted tensor decomposition and PCA based unsuper- vised feature extraction select more biologically reasonable differentially expressed genes than conventional methods. Scientific Reports12(1), 17438 (2022) https: //doi.org/10.1038/s41598-022-21474-z 24

    work page doi:10.1038/s41598-022-21474-z 2022