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REVIEW 3 major objections 4 minor 1 cited by

LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read LEARNER claims that penalizing differences between source and target latent row and column spaces in a rank-r factorization gives a better estimate of a target population's signal matrix than a target-only truncated SVD, with the benefit…

desk verdict A genuinely new transfer-learning estimator for low-rank matrices with reproducible code; the correlated-noise simulations need a clean re-run before the main claim is fully nailed. read the letter →

arxiv 2412.20605 v2 pith:BXLVOJYH submitted 2024-12-29 stat.ME stat.COstat.ML

Sean McGrath , Cenhao Zhu , Ryan O'Dea , Min Guo , Rui Duan This is my paper · ORCID
classification stat.MEstat.COstat.ML
keywords transferlearninglow-rankmatrixestimationlatentspacespenalizedoptimizationtruncatedsingularvaluedecompositioncross-validationgenome-wideassociationstudies
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

This paper proposes LEARNER, a transfer-learning estimator that reconstructs a low-rank signal matrix in a target population by borrowing strength from a source population with a similar latent structure. The central claim is that penalizing differences between the estimated latent row and column spaces of the two populations, rather than assuming identical factor matrices, produces more accurate target estimates than the conventional target-only truncated SVD. The authors support that claim with simulations in which LEARNER often improves on the target-only benchmark, with the improvement increasing as the source signal-to-noise ratio grows, and with a genome-wide association study re-analysis where LEARNER had the lowest held-out mean squared error among the compared methods. If the claim holds, well-studied populations can be used to sharpen estimates in underpowered target populations without forcing the two populations to share identical factor structures.

What carries the argument

The central object is the penalized objective of Equation (2): two projection penalties $P^\perp(\hat U_1)U$ and $P^\perp(\hat V_1)V$ that measure how much of the target factor matrices lies outside the source latent row and column spaces, plus a balancing penalty $\|U^\top U - V^\top V\|_F^2$. The source projections are obtained from a truncated SVD of $Y_1$, and ScreeNOT chooses the shared rank $r$. The objective is minimized by alternating gradient descent (Algorithm 1), with $\lambda_1$ and $\lambda_2$ chosen by four-fold cross-validation on held-out entries of $Y_0$; a tuning-free special case, D-LEARNER, replaces the optimization with the direct projection $P(\hat U_1)Y_0 P(\hat V_1)$ when the latent spaces are assumed identical.

What would settle it

Simulate a target and source with the same rank and noise level but with orthogonal latent row and column spaces, and give the source a high signal-to-noise ratio; if LEARNER's cross-validated estimate still beats the target-only truncated SVD in Frobenius error, the penalty is not preventing negative transfer as claimed.

Watch

Extended reading notes

Core claim

LEARNER solves a penalized low-rank factorization of the observed target matrix $Y_0$: $$(U,V) \mapsto \|UV^\top - Y_0\|$_F^{2}$ + \lambda_1 \|P^\perp(\hat U_1)U\|$_F^{2}$ + \lambda_1\|P^\perp(\hat V_1)V\|$_F^{2}$ + \lambda_2\|U^\top U - V^\top V\|$_F^{2}$,$$ where $\hat U_1,\hat V_1$ come from the rank-$r$ truncated SVD of the source matrix $Y_1$ and $P^\perp(\cdot)$ projects onto the orthogonal complement of the estimated source latent space. The first two terms penalize target factors that lie outside the source row and column spaces; the last term balances the scales of $U$ and $V$. The estimator interpolates between the target-only SVD ($\lambda_1=0$) and the source-only SVD (large $\lambda_1$), and cross-validation selects the interpolation point. The paper's claim is that this interpolation adapts to the heterogeneity between populations and that, in the settings tested, it frequently delivers a lower Frobenius-norm error than the target-only SVD, increasingly so as the source signal-to-noise ratio rises.

Load-bearing premise

The method assumes the source and target signal matrices have the same rank, and that applying ScreeNOT to the source data returns the true rank of the target matrix.

Editorial extensions

If this is right

  • A well-powered source population can be used to reduce estimation error in a target population with weaker data, with the benefit growing as the source signal-to-noise ratio increases.
  • Because the penalties are tuned by cross-validation, the method can reduce information borrowing when the populations diverge, offering a defense against negative transfer.
  • LEARNER nests the two standard benchmarks: target-only SVD at $\lambda_1 = 0$ and source-only SVD as $\lambda_1$ grows, so it can continuously adapt between them.
  • The empirical comparison indicates the framework transfers to GWAS summary statistics, where the latent-space transfer improved holdout error over target-only and source-only SVD.

Reading between the lines

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

  • A natural extension the authors leave implicit: when several source populations are available, their estimated projection matrices could be pooled before fitting LEARNER, which would stabilize the penalty targets; the discussion notes this possibility but does not develop it.
  • The correlated-noise results, where ScreeNOT selected a rank of 5 instead of the true 4 in every scenario, suggest that rank misspecification can be as consequential as tuning-parameter choice in real applications, and that the external-dataset tuning variant described in the supplementary material deserves priority when noise is correlated.
  • One testable prediction: LEARNER's advantage over target-only SVD should be largest when the source and target share the same row and column spaces but the source has much lower noise, and should vanish or reverse when the latent spaces are orthogonal; this can be checked in the paper's own simulation setup.
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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 / 4 minor

Summary. The paper proposes LEARNER, a transfer-learning method for estimating a low-rank target matrix by borrowing strength from a source matrix. The estimator solves a penalized low-rank approximation problem in which differences between the estimated latent row and column spaces of the source and target populations are penalized. The method is implemented through alternating minimization, with cross-validation for the two regularization parameters and ScreeNOT for rank selection. The authors evaluate LEARNER on 48 independent-noise and 36 correlated-noise simulation scenarios, compare it with target-only truncated SVD and a direct-projection variant D-LEARNER, and apply it to GWAS summary statistics from BioBank Japan with source data from UK Biobank and FinnGen. The main claimed finding is that LEARNER often outperforms target-only truncated SVD, especially when the source signal is strong and the latent spaces are similar.

Significance. If the empirical claims hold, LEARNER is a practical and adaptable addition to the transfer-learning toolbox for low-rank matrix estimation in biomedical settings. The paper is commendable for shipping reproducible code and R and Python packages, for evaluating many simulation scenarios, and for including a real GWAS application with cross-validation. The idea of penalizing projection-matrix differences rather than matching individual singular vectors is a sensible way to allow flexible latent-space similarity. The method is not circular: cross-validation for lambda_1 and lambda_2 is standard model selection. The main weakness is that the empirical support is substantially weakened by the acknowledged rank misspecification in the correlated-noise simulations, and the optimization algorithm lacks convergence guarantees, so the contribution is primarily empirical and needs those issues cleaned up before the central claim can be accepted.

major comments (3)
  1. [Section 3.2.2, Figure 2] In every correlated-noise scenario, ScreeNOT selected rank 5 instead of the true rank 4 for LEARNER and D-LEARNER, while the target-only SVD benchmark was given the true rank (Section 3.1.1). Since the paper's headline claim is about the full Algorithm 2 pipeline, this block of simulations does not cleanly support the claim as stated for the method as presented. I agree that the misspecification is likely conservative for LEARNER, but it still leaves the quantitative magnitude of the advantage unestablished. Please re-run these scenarios with oracle rank 4 for all methods, or at least report LEARNER results with both estimated and oracle rank, so that the effect of rank misspecification is explicit.
  2. [Section 2.3.1, Algorithm 1] The estimator is defined as the output of alternating minimization on a non-convex objective, but the paper offers no convergence guarantee for this specific objective. The passage relies on analogies to other low-rank problems, yet the objective here contains nonstandard projection penalties and a scale-balancing term, so it is not immediate that the cited results apply. Since the reported estimates depend on the local solution reached, please provide convergence diagnostics (objective trajectories, multiple random initializations) and, if possible, a formal stationarity or local-convergence result; otherwise it is unclear that the numerical solution is a meaningful minimizer.
  3. [Section 2.3.3 and Supplementary Section 1.2] The main correlated-noise simulation results use the cross-validation tuning rule that the authors themselves state is suboptimal under correlated noise, while the supplementary external-dataset rule is reported to perform considerably better. This means the abstract's "often outperforms the benchmark" claim is demonstrated for the version of LEARNER whose tuning is acknowledged to be suboptimal, and the better-performing variant appears only in the supplement. The main text should either include the external-dataset variant in the primary correlated-noise comparison or explicitly qualify the scope of the abstract claim to the cross-validated version.
minor comments (4)
  1. [Section 5, Discussion] The list of possible extensions is numbered inconsistently: it starts with "First," continues with "Second," then uses "Additionally," and then jumps to "Fourth." Please renumber for clarity.
  2. [Section 2.1, Eq. (2)] The factorization notation would be clearer if the identifiability conditions on U and V were stated explicitly; as written, the same product U V^T can be rescaled without changing Theta_0, which is relevant to the role of lambda_2.
  3. [Section 3.1.2] The statement that the rank selection method "correctly selected the rank in each iteration" would be more informative if the number of repetitions yielding the correct rank were reported, especially since Section 3.2.2 reports failure in every repetition.
  4. [Algorithm 1] The normalized gradient step uses a scenario-dependent step size c, but the sensitivity of the results to c is not reported; a brief sensitivity check or a discussion of how c was chosen would increase confidence in the numerical results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LEARNER is defined by an optimization objective, tuning is selected by standard cross-validation, and all empirical claims are compared against external benchmarks.

full rationale

The derivation chain is self-contained. The LEARNER estimator is defined in Eq. (2) as the minimizer of a penalized Frobenius objective; no parameter in that objective is fitted to the quantity being predicted. The penalties lambda_1 and lambda_2 are selected in Section 2.3.3 by four-fold cross-validation on held-out entries of Y0, which is standard model selection rather than a circular reduction: the held-out MSE in Eq. (5) evaluates the estimator on data not used to fit it. The rank r is selected by ScreeNOT applied to Y1 (Section 2.3.4), an external method from Donoho et al. (2023); the paper's assumption that source and target share r is an explicit modeling assumption, not an output of the method. The simulation results are empirical comparisons against the target-only truncated SVD benchmark, and the BBJ application compares methods on held-out entries. The only notable concern is the acknowledged rank misspecification under correlated noise: Section 3.2.2 states that 'the rank selection method ... incorrectly selected a rank of 5 (recall that the true rank was 4) in each iteration in each of the scenarios.' This is a validity/fairness limitation that works against LEARNER (since the benchmark uses the true rank), and it does not reduce any prediction to its inputs. Self-citations in the introduction are background references and are not load-bearing for the method's validity. No equation in the paper equals its input by construction, and no fitted parameter is renamed as a prediction. Therefore the score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method rests on the low-rank-plus-noise model, the shared-rank assumption, and the assumption that projection-space similarity is the right transferable quantity. The only data-fitted quantities are the tuning parameters lambda_1, lambda_2, and the rank r, all selected by standard model-selection procedures. No new entities are introduced.

free parameters (3)
  • lambda_1 = selected by cross-validation (grid 10^0 to 10^4 in simulations, 10^1 to 10^4 in application)
    Controls the strength of the penalty on differences between target and source latent row/column spaces; chosen to minimize held-out MSE.
  • lambda_2 = selected by cross-validation (grid 10^-2 to 10^1 in simulations, 10^-2 to 10^1 in application)
    Balances the norms of U and V to avoid scale-ambiguity local minima; also selected by CV.
  • rank r = selected by ScreeNOT applied to Y1
    Assumed shared between source and target; ScreeNOT thresholding on source singular values.
assumptions (4)
  • domain assumption The observed matrices follow Y_k = Theta_k + Z_k with mean-zero noise (Eq. 1).
    Section 2.1; the entire estimation problem is posed as low-rank signal plus noise.
  • domain assumption Source and target share the same rank r.
    Section 2.1 and Section 2.3.4; used to justify applying ScreeNOT to Y1 for the target rank.
  • domain assumption The latent row and column spaces of source and target are similar enough that penalizing their differences improves target estimation.
    Section 2.3; the central modeling assumption that transfer via projection penalties is beneficial.
  • ad hoc to paper Alternating minimization on the non-convex objective converges to a near-global solution.
    Section 2.3.1; the paper cites refs [28-31] for local-minima guarantees without verifying their conditions.

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Cite this review

Pith. "Pith review of LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation." pith.science (2026). https://pith.science/paper/BXLVOJYH

@misc{pith2026241220605,
  author       = {Pith},
  title        = {Pith review of: LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BXLVOJYH}},
  note         = {Machine review of arXiv:2412.20605}
}
read the original abstract

Low-rank matrix estimation is a fundamental problem in statistics and machine learning with applications across biomedical sciences, including genetics, medical imaging, drug discovery, and electronic health record data analysis. In the context of heterogeneous data generated from diverse sources, a key challenge lies in leveraging data from a source population to enhance the estimation of a low-rank matrix in a target population of interest. We propose an approach that leverages similarity in the latent row and column spaces between the source and target populations to improve estimation in the target population, which we refer to as LatEnt spAce-based tRaNsfer lEaRning (LEARNER). LEARNER is based on performing a low-rank approximation of the target population data which penalizes differences between the latent row and column spaces between the source and target populations. We present a cross-validation approach that allows the method to adapt to the degree of heterogeneity across populations. We conducted extensive simulations which found that LEARNER often outperforms the benchmark approach that only uses the target population data, especially as the signal-to-noise ratio in the source population increases. We also performed an illustrative application and empirical comparison of LEARNER and benchmark approaches in a re-analysis of summary statistics from a genome-wide association study in the BioBank Japan cohort. LEARNER is implemented in the R package learner and the Python package learner-py.

Figures

Figures reproduced from arXiv: 2412.20605 by the authors.

Figure 1
Figure 1. Simulation results in the rectangular matrix settings with i [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Simulation results under the correlated noise scenarios. Th [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Heatmaps of P(Vˆ 0) (top left panel) and P(Vˆ 1) (top right panel) and 500 randomly selected subset of rows and columns of P(Uˆ 0) (bottom left panel) and P(Uˆ 1) (bottom right panel). The phenotypes are ordered based on their ICD-10 category, and the variants are ordered based on their chromosome and position number. in Section 2.3. We also applied a missing value SVD approach – also referred to as hard thresholdin… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Heatmaps of the matrix of phenotype (left panel) and variant (right [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 1
Figure 1. Figure 1: Simulation results in the square matrix settings with inde [PITH_FULL_IMAGE:figures/full_fig_p023_1.png]
Figure 2
Figure 2. Figure 2: Simulation results under the correlated noise settings, wh [PITH_FULL_IMAGE:figures/full_fig_p025_2.png]
Figure 3
Figure 3. Figure 3: Scree plot based on the source population data. [PITH_FULL_IMAGE:figures/full_fig_p027_3.png]
Figure 4
Figure 4. Figure 4: Heatmap of the matrix of variant contribution scores in the target pop [PITH_FULL_IMAGE:figures/full_fig_p027_4.png]
Figure 5
Figure 5. Figure 5: Heatmap of the matrix of phenotype contribution scores in the targe [PITH_FULL_IMAGE:figures/full_fig_p028_5.png]
Figure 6
Figure 6. Figure 6: Heatmap of the held-out MSE for each candidate ( [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]
Figure 7
Figure 7. Figure 7: Convergence of the numerical optimization algorithm for solving t [PITH_FULL_IMAGE:figures/full_fig_p030_7.png]
Figure 8
Figure 8. Figure 8: Heatmap of the LEARNER and D-LEARNER estimates of Θ [PITH_FULL_IMAGE:figures/full_fig_p031_8.png]
Figure 9
Figure 9. Figure 9: Heatmaps of 500 randomly selected subset of rows and columns of [PITH_FULL_IMAGE:figures/full_fig_p032_9.png]
Figure 10
Figure 10. Figure 10: Heatmaps of the matrix of phenotype (left panels) and variant (righ [PITH_FULL_IMAGE:figures/full_fig_p033_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

46 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    Components of genetic associations across 2,138 phenotypes in the uk biobank highlight adipocyte biology

    Yosuke Tanigawa, Jiehan Li, Johanne M Justesen, Heiko Horn, Matthew Aguirre, Christopher DeBoever, Chris Chang, Balasubramanian Narasimhan, Kasper Lage, Trevor Hastie, et al. Components of genetic associations across 2,138 phenotypes in the uk biobank highlight adipocyte biology. Nature communications , 10(1):4064, 2019

    work page 2019

  2. [2]

    A cross-population atlas of genetic associations for 220 human phenotypes

    Saori Sakaue, Masahiro Kanai, Yosuke Tanigawa, Juha Karjalainen, Mitja Kurki, Seizo Koshiba, Akira Narita, Takahiro Konuma, Kenichi Yamamoto, Masato Akiyama, et al. A cross-population atlas of genetic associations for 220 human phenotypes. Nature genetics , 53(10):1415--1424, 2021

    work page 2021

  3. [3]

    Low-rank plus sparse matrix decomposition for accelerated dynamic mri with separation of background and dynamic components

    Ricardo Otazo, Emmanuel Candes, and Daniel K Sodickson. Low-rank plus sparse matrix decomposition for accelerated dynamic mri with separation of background and dynamic components. Magnetic resonance in medicine , 73(3):1125--1136, 2015

    work page 2015

  4. [4]

    Computational drug repositioning using low-rank matrix approximation and randomized algorithms

    Huimin Luo, Min Li, Shaokai Wang, Quan Liu, Yaohang Li, and Jianxin Wang. Computational drug repositioning using low-rank matrix approximation and randomized algorithms. Bioinformatics , 34(11):1904--1912, 2018

    work page 1904

  5. [5]

    Inference of dependency knowledge graph for electronic health records

    Zhiwei Xu, Ziming Gan, Doudou Zhou, Shuting Shen, Junwei Lu, and Tianxi Cai. Inference of dependency knowledge graph for electronic health records. arXiv preprint arXiv:2312.15611 , 2023

    work page arXiv 2023

  6. [6]

    The approximation of one matrix by another of lower rank

    Carl Eckart and Gale Young. The approximation of one matrix by another of lower rank. Psychometrika , 1(3):211--218, 1936

    work page 1936

  7. [7]

    The truncated svd as a method for regularization

    Per Christian Hansen. The truncated svd as a method for regularization. BIT Numerical Mathematics , 27:534--553, 1987

    work page 1987

  8. [8]

    Principal component analysis for special types of data

    Ian T Jolliffe. Principal component analysis for special types of data . Springer, 2002

    2002

Show all 46 references
  1. [9]

    Learning the parts of objects by non-negative matrix factorization

    Daniel D Lee and H Sebastian Seung. Learning the parts of objects by non-negative matrix factorization. nature , 401(6755):788--791, 1999

    1999

  2. [10]

    Plaid models for gene expression data

    Laura Lazzeroni and Art Owen. Plaid models for gene expression data. Statistica sinica , pages 61--86, 2002

    2002

  3. [11]

    Genomics, health disparities, and missed opportunities for the nation’s research agenda

    Kathleen McGlone West, Erika Blacksher, and Wylie Burke. Genomics, health disparities, and missed opportunities for the nation’s research agenda. Jama , 317(18):1831--1832, 2017

    2017

  4. [12]

    Current clinical use of polygenic scores will risk exacerbating health disparities

    Alicia R Martin, Masahiro Kanai, Yoichiro Kamatani, Yukinori Okada, Benjamin M Neale, and Mark J Daly. Current clinical use of polygenic scores will risk exacerbating health disparities. Nature genetics , 51(4):584, 2019

    2019

  5. [13]

    A roadmap to increase diversity in genomic studies

    Segun Fatumo, Tinashe Chikowore, Ananyo Choudhury, Muhammad Ayub, Alicia R Martin, and Karoline Kuchenbaecker. A roadmap to increase diversity in genomic studies. Nature medicine , 28(2):243--250, 2022

    2022

  6. [14]

    A survey of transfer learning

    Karl Weiss, Taghi M Khoshgoftaar, and DingDing Wang. A survey of transfer learning. Journal of Big data , 3:1--40, 2016

    2016

  7. [15]

    Deep transfer learning for reducing health care disparities arising from biomedical data inequality

    Yan Gao and Yan Cui. Deep transfer learning for reducing health care disparities arising from biomedical data inequality. Nature communications , 11(1):5131, 2020

    2020

  8. [16]

    Commute: communication-efficient transfer learning for multi-site risk prediction

    Tian Gu, Phil H Lee, and Rui Duan. Commute: communication-efficient transfer learning for multi-site risk prediction. Journal of biomedical informatics , 137:104243, 2023

    2023

  9. [17]

    Targeting underrepresented populations in precision medicine: A federated transfer learning approach

    Sai Li, Tianxi Cai, and Rui Duan. Targeting underrepresented populations in precision medicine: A federated transfer learning approach. The Annals of Applied Statistics , 17(4):2970--2992, 2023

    2023

  10. [18]

    Heterogeneous component analysis

    Shigeyuki Oba, Motoaki Kawanabe, Klaus-Robert M \"u ller, and Shin Ishii. Heterogeneous component analysis. Advances in Neural Information Processing Systems , 20, 2007

    2007

  11. [19]

    Distributed estimation of principal eigenspaces

    Jianqing Fan, Dong Wang, Kaizheng Wang, and Ziwei Zhu. Distributed estimation of principal eigenspaces. Annals of statistics , 47(6):3009, 2019

    2019

  12. [20]

    Target pca: Transfer learning large dimensional panel data

    Junting Duan, Markus Pelger, and Ruoxuan Xiong. Target pca: Transfer learning large dimensional panel data. Journal of Econometrics , page 105521, 2023

    2023

  13. [21]

    Personalized pca: Decoupling shared and unique features

    Naichen Shi and Raed Al Kontar. Personalized pca: Decoupling shared and unique features. Journal of Machine Learning Research , 25(41):1--82, 2024

    2024

  14. [22]

    Knowledge transfer across multiple principal component analysis studies

    Zeyu Li, Kangxiang Qin, Yong He, Wang Zhou, and Xinsheng Zhang. Knowledge transfer across multiple principal component analysis studies. arXiv preprint arXiv:2403.07431 , 2024

    2024 arXiv

  15. [23]

    Optimal transfer learning for missing not-at-random matrix completion

    Akhil Jalan, Yassir Jedra, Arya Mazumdar, Soumendu Sundar Mukherjee, and Purnamrita Sarkar. Optimal transfer learning for missing not-at-random matrix completion. arXiv preprint arXiv:2503.00174 , 2025

    2025 arXiv

  16. [24]

    Group-sparse matrix factorization for transfer learning of word embeddings

    Kan Xu, Xuanyi Zhao, Hamsa Bastani, and Osbert Bastani. Group-sparse matrix factorization for transfer learning of word embeddings. In International Conference on Machine Learning , pages 11603--11612. PMLR, 2021

    2021

  17. [25]

    Understanding alternating minimization for matrix completion

    Moritz Hardt. Understanding alternating minimization for matrix completion. In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science , pages 651--660. IEEE, 2014

    2014

  18. [26]

    Predicting drug-disease associations by using similarity constrained matrix factorization

    Wen Zhang, Xiang Yue, Weiran Lin, Wenjian Wu, Ruoqi Liu, Feng Huang, and Feng Liu. Predicting drug-disease associations by using similarity constrained matrix factorization. BMC bioinformatics , 19:1--12, 2018

    2018

  19. [27]

    Scmfmda: predicting microrna-disease associations based on similarity constrained matrix factorization

    Lei Li, Zhen Gao, Yu-Tian Wang, Ming-Wen Zhang, Jian-Cheng Ni, Chun-Hou Zheng, and Yansen Su. Scmfmda: predicting microrna-disease associations based on similarity constrained matrix factorization. PLoS computational biology , 17(7):e1009165, 2021

    2021

  20. [28]

    Nonconvex low rank matrix factorization via inexact first order oracle

    Tuo Zhao, Zhaoran Wang, and Han Liu. Nonconvex low rank matrix factorization via inexact first order oracle. Advances in Neural Information Processing Systems , 458:461--462, 2015

    2015

  21. [29]

    Matrix completion has no spurious local minimum

    Rong Ge, Jason D Lee, and Tengyu Ma. Matrix completion has no spurious local minimum. Advances in neural information processing systems , 29, 2016

    2016

  22. [30]

    No spurious local minima in nonconvex low rank problems: A unified geometric analysis

    Rong Ge, Chi Jin, and Yi Zheng. No spurious local minima in nonconvex low rank problems: A unified geometric analysis. In International conference on machine learning , pages 1233--1242. PMLR, 2017

    2017

  23. [31]

    The non-convex geometry of low-rank matrix optimization

    Qiuwei Li, Zhihui Zhu, and Gongguo Tang. The non-convex geometry of low-rank matrix optimization. Information and Inference: A Journal of the IMA , 8(1):51--96, 2019

    2019

  24. [32]

    The bellkor solution to the netflix grand prize

    Yehuda Koren. The bellkor solution to the netflix grand prize. Netflix prize documentation , 81(2009):1--10, 2009

    2009

  25. [33]

    Matrix factorization techniques for recommender systems

    Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recommender systems. Computer , 42(8):30--37, 2009

    2009

  26. [34]

    Screenot: Exact mse-optimal singular value thresholding in correlated noise

    David Donoho, Matan Gavish, and Elad Romanov. Screenot: Exact mse-optimal singular value thresholding in correlated noise. The Annals of Statistics , 51(1):122--148, 2023

    2023

  27. [35]

    Overview of the biobank japan project: Study design and profile

    Akiko Nagai, Makoto Hirata, Yoichiro Kamatani, Kaori Muto, Koichi Matsuda, Yutaka Kiyohara, Toshiharu Ninomiya, Akiko Tamakoshi, Zentaro Yamagata, Taisei Mushiroda, et al. Overview of the biobank japan project: Study design and profile. Journal of epidemiology , 27(Supplement\...

    2017

  28. [36]

    The uk biobank resource with deep phenotyping and genomic data

    Clare Bycroft, Colin Freeman, Desislava Petkova, Gavin Band, Lloyd T Elliott, Kevin Sharp, Allan Motyer, Damjan Vukcevic, Olivier Delaneau, Jared O’Connell, et al. The uk biobank resource with deep phenotyping and genomic data. Nature , 562(7726):203--209, 2018

    2018

  29. [37]

    Finngen provides genetic insights from a well-phenotyped isolated population

    Mitja I Kurki, Juha Karjalainen, Priit Palta, Timo P Sipil \"a , Kati Kristiansson, Kati M Donner, Mary P Reeve, Hannele Laivuori, Mervi Aavikko, Mari A Kaunisto, et al. Finngen provides genetic insights from a well-phenotyped isolated population. Nature , 613(7944):508--518, 2023

    2023

  30. [38]

    The varimax criterion for analytic rotation in factor analysis

    Henry F Kaiser. The varimax criterion for analytic rotation in factor analysis. Psychometrika , 23(3):187--200, 1958

    1958

  31. [39]

    Spectral regularization algorithms for learning large incomplete matrices

    Rahul Mazumder, Trevor Hastie, and Robert Tibshirani. Spectral regularization algorithms for learning large incomplete matrices. The Journal of Machine Learning Research , 11:2287--2322, 2010

    2010

  32. [40]

    softImpute: Matrix Completion via Iterative Soft-Thresholded SVD , 2021

    Trevor Hastie and Rahul Mazumder. softImpute: Matrix Completion via Iterative Soft-Thresholded SVD , 2021. R package version 1.4-1

    2021

  33. [41]

    Heteroskedastic pca: Algorithm, optimality, and applications

    Anru R Zhang, T Tony Cai, and Yihong Wu. Heteroskedastic pca: Algorithm, optimality, and applications. The Annals of Statistics , 50(1):53--80, 2022

    2022

  34. [42]

    The dyson equalizer: Adaptive noise stabilization for low-rank signal detection and recovery

    Boris Landa and Yuval Kluger. The dyson equalizer: Adaptive noise stabilization for low-rank signal detection and recovery. Information and Inference: A Journal of the IMA , 14(1):iaae036, 2025

    2025

  35. [43]

    The international genome sample resource (igsr) collection of open human genomic variation resources

    Susan Fairley, Ernesto Lowy-Gallego, Emily Perry, and Paul Flicek. The international genome sample resource (igsr) collection of open human genomic variation resources. Nucleic Acids Research , 48(D1):D941--D947, 10 2019

    2019

  36. [44]

    Plink: a tool set for whole-genome association and population-based linkage analyses

    Shaun Purcell, Benjamin Neale, Kathe Todd-Brown, Lori Thomas, Manuel AR Ferreira, David Bender, Julian Maller, Pamela Sklar, Paul IW De Bakker, Mark J Daly, et al. Plink: a tool set for whole-genome association and population-based linkage analyses. The American journal of hum...

    2007

  37. [45]

    A global reference for human genetic variation

    The 1000 Genomes Project Consortium . A global reference for human genetic variation. Nature , 526(7571):68--74, 2015

    2015

  38. [46]

    The International Genome Sample Resource (IGSR) collection of open human genomic variation resources

    Susan Fairley, Ernesto Lowy-Gallego, Emily Perry, and Paul Flicek. The International Genome Sample Resource (IGSR) collection of open human genomic variation resources. Nucleic acids research , 48(D1):D941--D947, 2020

    2020

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.