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REVIEW 4 major objections 5 minor 72 references

Implicit Regularization for Multi-label Feature Selection

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that replacing the explicit l2,1 penalty with a Hadamard-product parameterization plus a latent label embedding yields a multi-label feature selector that suffers less extra bias and may lead to benign overfitting.

desk verdict Novel combination of Hadamard implicit regularization with label embedding for multi-label feature selection, but the central convergence claim is asserted, not proved, and the algorithm contradicts its own assumption. read the letter →

arxiv 2411.11436 v2 pith:5BGILTIF submitted 2024-11-18 cs.LG cs.AI

Dou El Kefel Mansouri , Khalid Benabdeslem , Seif-Eddine Benkabou This is my paper · ORCID
classification cs.LGcs.AI
keywords multi-labelfeatureselectionimplicitregularizationHadamardproductparameterizationlatentsemanticanalysislabelembeddingbenignoverfittingl21normnonnegativematrixfactorization
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

Multi-label feature selection usually adds an explicit sparsity penalty such as the $\ell^2$,1 norm to a regression loss, and the paper argues that this extra term injects bias that limits accuracy. It proposes instead to write the coefficient matrix as the element-wise product $W = G \odot H$ and to guide selection by a low-dimensional latent embedding of the label matrix, so sparsity and stability emerge without a penalty term. The estimator is smooth, simple to optimize by alternating gradient descent, and fast on ten benchmark datasets. The paper's headline experimental claim is that this implicit-regularization estimator suffers much less extra bias than explicit-regularization baselines and can exhibit benign overfitting on a denoised version of the bibtex dataset.

What carries the argument

The central object is the Hadamard product parameterization $W = G \odot H$, which replaces the explicit $l_{2,1}$ penalty: instead of penalizing a single coefficient matrix, the method learns two matrices multiplied element-wise, so sparsity emerges when either factor has zero entries. The second mechanism is latent semantic label embedding, in which the label matrix is decomposed as $Y \approx VB$ with nonnegative $V$ and $B$, and the graph Laplacian term $\mathrm{tr}(V^T L V)$ enforces that instances close in input space have close latent semantics. The optimization alternates gradient updates for $G, H, V, B$ with a projection that keeps $V$ and $B$ nonnegative, and the final row norms of $G \odot H$ provide the feature ranking.

What would settle it

Run the alternating gradient updates from many random and nonnegative initializations on one fixed dataset and compare the resulting feature rankings and objective values; if the final $W = G \odot H$ or the zero-pattern of $G$ and $H$ changes materially with initialization, the claimed global-minimum guarantee and sparsity property fail, and a second check would be to test whether the benign-overfitting gap closes on several datasets besides bibtex.

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Extended reading notes

Core claim

The paper proposes that explicit sparsity-inducing penalties are unnecessary for multi-label feature selection: parameterizing the coefficient matrix as $W = G \odot H$ and adding a latent-label embedding term induces sparsity and stability implicitly. The estimator solves $\min_{G,H,V,B \ge 0} \|X(G \odot H) - V\|_F^2 + \alpha\|Y - VB\|_F^2 + \beta\,\mathrm{tr}(V^T L V)$, where $V$ is a low-dimensional nonnegative latent semantics matrix, $B$ its coefficient matrix, and $L$ the graph Laplacian built from input similarities. The Hadamard form smooths the original non-smooth problem, and the authors argue that under their assumptions the alternating gradient scheme converges to a global minimum, so the row norms of $\hat{W} = \hat{G} \odot \hat{H}$ rank the features. Experiments on ten multi-label benchmark datasets indicate the estimator is competitive with or better than explicit-regularization baselines on Hamming loss and macro-averaged AUC, often much faster, and can exhibit benign overfitting on a cleaned version of the bibtex dataset.

Load-bearing premise

The central claim rests on the unproven assertion that the non-convex objective has no misleading local optima, so the alternating gradient scheme's final $W = G \odot H$ is a global solution rather than an arbitrary stationary point.

Editorial extensions

If this is right

  • The Hadamard parameterization converts the non-smooth $l_{2,1}$-regularized problem into a smooth unconstrained objective, so multi-label feature selection can run with plain gradient updates and no proximal operators.
  • If the bias claim holds, practitioners can drop the penalty-strength hyperparameter and rely on $\alpha$ and $\beta$ that tune the label embedding and manifold terms instead.
  • The reported convergence in roughly three to ten iterations with per-iteration complexity $O(nml + nlq + n^2l)$ makes the method practical on high-dimensional multi-label data.
  • The benign-overfitting observation suggests that implicit regularization outside neural-network training can also close the train-validation gap, at least when the label space is first denoised by latent semantic embedding.

Reading between the lines

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

  • An implication the authors leave implicit is that the convergence argument leans on unverified saddle-point conditions; a direct check of the strict-saddle property for the full objective with the graph Laplacian and nonnegative factorization terms would decide whether the global-minimum claim generalizes beyond the cited linear-regression setting.
  • Because the paper ties sparsity to nonnegative initialization of $G$ or $H$, the algorithm's practical behavior may change if those matrices are initialized with negative entries, a sensitivity the paper only partially explores in its sparsity experiments.
  • The benign-overfitting demonstration uses a single dataset after reducing features to 30 percent; a systematic sweep across datasets, noise levels, and label cardinalities would show whether the phenomenon is intrinsic to the implicit regularizer or specific to that reduction.
  • The estimator suggests a general recipe of implicit regularization plus latent output embedding that could transfer to semi-supervised or online multi-label learning, directions the authors name as future work but do not pursue.
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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

4 major / 5 minor

Summary. The paper proposes mFSIR, a multi-label feature selection method based on implicit regularization via Hadamard product parameterization (W = G ⊙ H) and a latent semantic label embedding (V, B). The objective function in Eq. (8) replaces the explicit l2,1 penalty in Eq. (2) with an implicit regularizer, and the authors present an alternating gradient descent algorithm (Algorithm 1) with projected updates for V and B. The paper claims global convergence to a minimum (Lemma 3.3) and reports experiments on ten benchmark datasets comparing mFSIR against MIFS, MICO, GRRO, and LassoNet. It also includes a study (Section 4.3.7) suggesting that mFSIR may lead to benign overfitting on the bibtex dataset.

Significance. The combination of Hadamard-product implicit regularization with a latent label embedding for multi-label feature selection is a novel and potentially useful idea, and the paper addresses a real limitation of explicit penalties—extra bias. The experimental evaluation is broad, covering ten datasets and three evaluation metrics with statistical testing, which is a strength. However, the central convergence claim is not rigorously supported, and the benign-overfitting experiment does not directly demonstrate the proposed estimator's behavior. If the theoretical gap is closed and the experiments are sharpened, the approach could be a meaningful contribution to multi-label feature selection.

major comments (4)
  1. [Section 3.3, Lemma 3.3] Lemma 3.3 asserts that Eq. (8) converges to a global minimum, but no proof is supplied. The text only states that under Assumption 3 the objective has no local maxima, all local minima are global, and all saddle points are strict, citing [46]. These geometric conditions are not verified for the specific objective in Eq. (8), which couples a Hadamard-parameterized regression term, a nonnegative NMF term α||Y - VB||_F^2, and the graph-Laplacian regularizer β tr(V^T L V). Without a proof or a verification of these conditions, the final W = G ⊙ H may be an arbitrary stationary point, and the feature ranking lacks the claimed optimality. Please provide a rigorous proof or a weaker, provable convergence statement that is sufficient for the method's practical use.
  2. [Algorithm 1 / Assumption 2] There is a mismatch between the theory and the algorithm. Lemma 3.3 is stated under Assumption 2, which requires initial values of G or H to be nonnegative. However, Algorithm 1 initializes all four blocks from Uniform(-ϖ, ϖ) in line 1, which produces negative entries, and the updates for G and H in lines 3–4 are unconstrained gradient steps with no projection onto the nonnegative orthant. Thus the algorithm may not satisfy the assumption under which the global convergence lemma is stated. Figure 4 empirically shows that random versus nonnegative initialization yields different sparsity patterns, indicating that the final solution is initialization-dependent. Please align the algorithm with the assumption, for example by using nonnegative initialization or by extending the theoretical analysis to the actual initialization scheme.
  3. [Section 4.3.7] The benign-overfitting experiment does not support the abstract's claim that "the proposed estimator ... may lead to benign overfitting." The experiment trains a baseline classifier on the original bibtex data and on bibtex reduced by mFSIR, and observes that validation performance tracks training performance better on the reduced data. This demonstrates that feature-selection preprocessing can reduce overfitting—a well-known effect of dimensionality reduction—but it does not isolate the effect of the implicit regularizer or of the proposed estimator itself. To substantiate the claim, the authors should compare mFSIR against an explicit-regularization feature selector (e.g., MIFS) under the same preprocessing protocol, or directly study the training and test error of the fitted X(G ⊙ H) versus the latent semantics V. As written, the experiment is consistent with any feature-selection method and is not load-bearing for the benign-overfitting claim.
  4. [Section 4.3.2] The "extra bias" comparison is not well posed. Figure 3 plots the objective function value of mFSIR (Eq. (8)) against that of MIFS, which minimizes a different objective with an explicit l2,1 penalty. A lower value of a different objective does not establish that mFSIR has less bias. The paper should either define a quantitative bias measure (for instance, estimation error against known ground-truth coefficients in a simulated sparse setting) or compare both methods under a common task-oriented metric on the selected features. The current experiment is suggestive but does not directly support the claimed advantage in bias.
minor comments (5)
  1. [Eq. (1)] The definition of the Frobenius norm is malformed; the standard definition is ||X||_F = (∑_{i,j} X_{ij}^2)^{1/2}. Please correct the formula.
  2. [Section 4.3.1] The text says "number of selected instances" but should read "number of selected features."
  3. [Algorithm 1] The input list includes "Validation data: (X,Y)" but the validation set is never used in the procedure. Please remove it or explain its role in early stopping or hyperparameter selection.
  4. [Table 2] The caption defining the markers • and ◦ is ambiguous. Please clarify that • indicates mFSIR is statistically superior to the column method and ◦ indicates inferiority, and ensure the win/tie/loss counts are fully consistent with the markers.
  5. [Section 3.4, Lemma 3.4] The stated complexity O(nml + nlq + n^2l) is per iteration; Algorithm 1 runs for Tmax iterations, so the total cost is Tmax times this value. Please state this explicitly.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the core estimator is imported from external prior work and benchmarked externally; the only self-citation is non-load-bearing.

full rationale

The paper's central derivation chain is Eq. (2) to Eq. (8): the explicit l2,1 penalty is replaced by W = G ⊙ H and a latent label embedding V. The replacement rests on Lemma 3.1, which explicitly cites Hoff [31] for Hadamard-parametrization smoothing, and on [46]/[57] (Zhao, Yang, He) for the implicit-regularization behavior of gradient descent on the over-parametrized objective. These are external prior results, not self-citations, and the paper does not define W, G, or H in terms of the feature-selection output it later ranks; W = G ⊙ H is the final estimate and its row norms are the ranking, so there is no fitted-input-called-prediction loop. The label embedding V is estimated from the same label matrix Y used in evaluation, which is standard supervised feature selection rather than a reconstruction of the reported performance. The experiments are self-contained against external benchmarks (MULAN datasets; baselines MIFS, MICO, GRRO, LassoNet), so the empirical claims are not forced by construction. The only self-citation is [24] (Alalga, Benabdeslem, and Mansouri), used in Section 2.3 and Section 4.1 for the 3-3FS baseline and for standard Hamming-loss and ranking-loss formulas; it is not load-bearing for the implicit-regularization claim. Separately, Lemma 3.3 asserts global convergence under Assumption 2 without a proof, and Algorithm 1's random signed initialization seems inconsistent with Assumption 2's nonnegativity requirement; those are correctness and completeness concerns, not instances of circular reasoning under the given definitions.

Assumptions & free parameters 8 free parameters · 5 assumptions · 1 invented entities

The estimator depends on three explicit modeling assumptions, one cited smoothing result, and unverified landscape conditions. Several hyperparameters are unspecified. The only invented construct is the latent semantics matrix, which is a standard modeling choice rather than a new physical entity.

free parameters (8)
  • alpha = grid {1e-3,...,1e2}, per-dataset choice not reported
    Balances the label reconstruction term in Eq. (8).
  • beta = grid {1e-3,...,1e2}, per-dataset choice not reported
    Controls the graph Laplacian regularization in Eqs. (7) and (8).
  • l (latent dimension) = not specified (l < q)
    Dimension of the latent semantics matrices V and B in Assumption 3.
  • eta (step size) = not specified
    Step size in Algorithm 1; no value or schedule is given.
  • Tmax (max iterations) = not specified
    Stopping condition in Algorithm 1; a convergence criterion appears only in Section 4.3.2.
  • varpi (initial perturbation) = 1e-5
    Small random initialization to escape the saddle point at zero, set in Section 4.1.
  • p (nearest neighbors) = not specified
    Number of neighbors in the similarity graph of Eq. (6).
  • lambda (graph kernel width) = not specified
    Heat kernel width in the similarity graph of Eq. (6).
assumptions (5)
  • ad hoc to paper Assumption 1: The coefficient matrix W can be written as G ⊙ H for G,H in R^{m×q}.
    Introduced in Section 3.2.1 to replace the explicit l2,1 penalty with implicit regularization.
  • ad hoc to paper Assumption 2: Sparsity is ensured if the initial values of G or H are nonnegative.
    Section 3.2.1 and empirically illustrated in Figure 4, but no proof is provided that nonnegative initialization guarantees sparsity.
  • domain assumption Assumption 3: The label space decomposes as Y ≈ VB with V>=0, B>=0, and l<q.
    Standard nonnegative low-rank assumption, used to guide feature selection in Section 3.2.2.
  • standard math Lemma 3.1: Hadamard product parameterization smooths the non-smooth l2,1 problem (from [31]).
    Cited result, not reproved in this paper.
  • ad hoc to paper Landscape conditions from [46]: Eq. (8) has no local maxima, all saddles are strict, and small step size suffices for global convergence.
    Invoked in Lemmas 3.2 and 3.3 without verification for this specific objective with graph Laplacian and NMF terms.
invented entities (1)
  • Low-dimensional nonnegative latent semantics (V, B)
    purpose: Decompose the label matrix to guide feature selection and reduce label noise.
    Introduced in Assumption 3; V and B are estimated from Y itself through Eq. (7) and have no external falsifiable handle.

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Pith. "Pith review of Implicit Regularization for Multi-label Feature Selection." pith.science (2026). https://pith.science/paper/5BGILTIF

@misc{pith2026241111436,
  author       = {Pith},
  title        = {Pith review of: Implicit Regularization for Multi-label Feature Selection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5BGILTIF}},
  note         = {Machine review of arXiv:2411.11436}
}
abstract

In this paper, we address the problem of feature selection in the context of multi-label learning, by using a new estimator based on implicit regularization and label embedding. Unlike the sparse feature selection methods that use a penalized estimator with explicit regularization terms such as $l_{2,1}$-norm, MCP or SCAD, we propose a simple alternative method via Hadamard product parameterization. In order to guide the feature selection process, a latent semantic of multi-label information method is adopted, as a label embedding. Experimental results on some known benchmark datasets suggest that the proposed estimator suffers much less from extra bias, and may lead to benign overfitting.

Figures

Figures reproduced from arXiv: 2411.11436 by the authors.

Figure 1
Figure 1. Comparison of mFSIR against other methods with the Nemenyi [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Influence of selected feature number on four datasets [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Convergence curves of mFSIR and MIFS on four datasets [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Different sparsity behaviors on bibtex dataset. (a) repre￾sents the matrix Gˆ initialized by values of G superior or equal to zero. The subfigure is clearly sparse with columns containing the value zero (blue color). (b) represents the matrix Gˆ initialized by random v…
Figure 6
Figure 6. Figure 6: Spider Web Diagrams for stability index values considering [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Different overfitting behaviors on bibtex dataset. Left: training and validation (loss and Macro F1-score) over the original bibtex (without mFSIR). Right: training and validation (loss and Macro F1-score) over the reduced bibtex (with mFSIR, 30% of selected features).…

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Works this paper leans on

72 extracted references · 64 canonical work pages

  1. [46]

    High-Dimensional Linear Regression via Implicit Regularization

    P. Zhao, Y . Yang, and Q.-C. He, “Implicit regularization via hadamard product over-parametrization in high-dimensional linear regression,” arXiv preprint arXiv:1903.09367, 2019

    work page Pith review arXiv 1903

  2. [1]

    A tutorial on multilabel learning,

    E. Gibaja and S. Ventura, “A tutorial on multilabel learning,” ACM Computing Surveys (CSUR), vol. 47, no. 3, pp. 1–38, 2015

    work page 2015

  3. [2]

    Collaboration based multi-label learning,

    L. Feng, B. An, and S. He, “Collaboration based multi-label learning,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 33, 2019, pp. 3550–3557

    work page 2019

  4. [3]

    Large scale multi-label learning using gaussian processes,

    A. Panos, P. Dellaportas, and M. K. Titsias, “Large scale multi-label learning using gaussian processes,” Machine Learning, vol. 110, no. 5, pp. 965–987, 2021

    work page 2021

  5. [4]

    Markov blanket and markov boundary of multiple variables,

    X.-Q. Liu and X.-S. Liu, “Markov blanket and markov boundary of multiple variables,” The Journal of Machine Learning Research, vol. 19, no. 1, pp. 1658–1707, 2018. Fig. 5. Performance of mFSIR changes with varying hyper-parameter configurations α and β from {10−3,10−2,10−1,1,10,102}. Dataset: emotions; First and second row: hamming loss, ranking loss and ...

    work page 2018

  6. [5]

    Svm based multi-label learning with missing labels for image annotation,

    Y . Liu, K. Wen, Q. Gao, X. Gao, and F. Nie, “Svm based multi-label learning with missing labels for image annotation,” Pattern Recognition, vol. 78, pp. 307–317, 2018

    work page 2018

  7. [6]

    Exploiting weakly supervised visual patterns to learn from partial annotations,

    K. Kundu and J. Tighe, “Exploiting weakly supervised visual patterns to learn from partial annotations,” Advances in Neural Information Processing Systems, vol. 33, 2020

    work page 2020

  8. [7]

    Deep learning for extreme multi-label text classification,

    J. Liu, W.-C. Chang, Y . Wu, and Y . Yang, “Deep learning for extreme multi-label text classification,” in Proceedings of the 40th International 10 Fig. 7. Different overfitting behaviors on bibtex dataset. Left: training and validation (loss and Macro F1-score) over the original bibtex (without mFSIR). Right: training and validation (loss and Macro F1-sc...

    work page 2017

Show all 72 references
  1. [8]

    Memetic feature selection for mul- tilabel text categorization using label frequency difference,

    J. Lee, I. Yu, J. Park, and D.-W. Kim, “Memetic feature selection for mul- tilabel text categorization using label frequency difference,” Information Sciences, vol. 485, pp. 263–280, 2019

    2019

  2. [9]

    Exploiting medline for gene molecular function prediction via nmf based multi-label classification,

    S. J. Fodeh and A. Tiwari, “Exploiting medline for gene molecular function prediction via nmf based multi-label classification,” Journal of biomedical informatics, vol. 86, pp. 160–166, 2018

    2018

  3. [10]

    Identification of autistic risk candidate genes and toxic chemicals via multilabel learning,

    Z.-A. Huang, J. Zhang, Z. Zhu, E. Q. Wu, and K. C. Tan, “Identification of autistic risk candidate genes and toxic chemicals via multilabel learning,” IEEE Transactions on Neural Networks and Learning Systems, 2020

    2020

  4. [11]

    Multi-label causal feature selection

    X. Wu, B. Jiang, K. Yu, H. Chen, and C. Miao, “Multi-label causal feature selection.” in AAAI, 2020, pp. 6430–6437

    2020

  5. [12]

    Analysis and optimization of loss functions for multiclass, top-k, and multilabel classification,

    M. Lapin, M. Hein, and B. Schiele, “Analysis and optimization of loss functions for multiclass, top-k, and multilabel classification,” IEEE transactions on pattern analysis and machine intelligence, vol. 40, no. 7, pp. 1533–1554, 2017

    2017

  6. [13]

    Topic-based algorithm for multilabel learning with missing labels,

    J. Ma and T. W. Chow, “Topic-based algorithm for multilabel learning with missing labels,” IEEE transactions on neural networks and learning systems, vol. 30, no. 7, pp. 2138–2152, 2018

    2018

  7. [14]

    Joint feature selection and classification for multilabel learning,

    J. Huang, G. Li, Q. Huang, and X. Wu, “Joint feature selection and classification for multilabel learning,” IEEE transactions on cybernetics, vol. 48, no. 3, pp. 876–889, 2017

    2017

  8. [15]

    Catego- rizing feature selection methods for multi-label classification,

    R. B. Pereira, A. Plastino, B. Zadrozny, and L. H. Merschmann, “Catego- rizing feature selection methods for multi-label classification,” Artificial Intelligence Review, vol. 49, no. 1, pp. 57–78, 2018

    2018

  9. [16]

    Multi-view multi-label learning with sparse feature selection for image annotation,

    Y . Zhang, J. Wu, Z. Cai, and S. Y . Philip, “Multi-view multi-label learning with sparse feature selection for image annotation,” IEEE Transactions on Multimedia, 2020

    2020

  10. [17]

    P. E. Hart, D. G. Stork, and R. O. Duda, Pattern classification. Wiley Hoboken, 2000

    2000

  11. [18]

    Wrappers for feature subset selection,

    R. Kohavi and G. H. John, “Wrappers for feature subset selection,” Artificial intelligence, vol. 97, no. 1-2, pp. 273–324, 1997

    1997

  12. [19]

    Regression shrinkage and selection via the lasso,

    R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 58, no. 1, pp. 267–288, 1996

    1996

  13. [20]

    Efficient and robust feature selec- tion via joint l2, 1-norms minimization,

    F. Nie, H. Huang, X. Cai, and C. Ding, “Efficient and robust feature selec- tion via joint l2, 1-norms minimization,” Advances in neural information processing systems, vol. 23, pp. 1813–1821, 2010

    2010

  14. [21]

    Multilabel dimensionality reduction via dependence maximization,

    Y . Zhang and Z.-H. Zhou, “Multilabel dimensionality reduction via dependence maximization,” ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 4, no. 3, pp. 1–21, 2010

    2010

  15. [22]

    Multi-label informed feature selection

    L. Jian, J. Li, K. Shu, and H. Liu, “Multi-label informed feature selection.” in IJCAI, 2016, pp. 1627–1633

    2016

  16. [23]

    Mlaco: A multi-label feature selection algorithm based on ant colony optimization,

    M. Paniri, M. B. Dowlatshahi, and H. Nezamabadi-Pour, “Mlaco: A multi-label feature selection algorithm based on ant colony optimization,” Knowledge-Based Systems, vol. 192, p. 105285, 2020

    2020

  17. [24]

    3-3fs: ensemble method for semi-supervised multi-label feature selection,

    A. Alalga, K. Benabdeslem, and D. E. K. Mansouri, “3-3fs: ensemble method for semi-supervised multi-label feature selection,” Knowledge and Information Systems, vol. 63, no. 11, pp. 2969–2999, 2021

    2021

  18. [25]

    Integrating global and local feature selection for multi-label learning,

    Z. Zhang, L. Liu, J. Li, and X. Wu, “Integrating global and local feature selection for multi-label learning,” ACM Transactions on Knowledge Discovery from Data (TKDD), 2022

    2022

  19. [26]

    Sparse feature selection based on l2, 1/2-matrix norm for web image annotation,

    C. Shi, Q. Ruan, S. Guo, and Y . Tian, “Sparse feature selection based on l2, 1/2-matrix norm for web image annotation,” Neurocomputing, vol. 151, pp. 424–433, 2015

    2015

  20. [27]

    Feature selection with mcp2 regularization,

    Y . Shi, J. Miao, and L. Niu, “Feature selection with mcp2 regularization,” Neural Computing and Applications , vol. 31, no. 10, pp. 6699–6709, 2019

    2019

  21. [28]

    Variable selection via nonconcave penalized likelihood and its oracle properties,

    J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,”Journal of the American statistical Association, vol. 96, no. 456, pp. 1348–1360, 2001

    2001

  22. [29]

    Learning from examples as an inverse problem,

    E. D. Vito, L. Rosasco, A. Caponnetto, U. D. Giovannini, and F. Odone, “Learning from examples as an inverse problem,” Journal of Machine Learning Research, vol. 6, no. May, pp. 883–904, 2005

    2005

  23. [30]

    On early stopping in gradient descent learning,

    Y . Yao, L. Rosasco, and A. Caponnetto, “On early stopping in gradient descent learning,” Constructive Approximation, vol. 26, no. 2, pp. 289– 315, 2007

    2007

  24. [31]

    Lasso, fractional norm and structured sparse estimation using a hadamard product parametrization,

    P. D. Hoff, “Lasso, fractional norm and structured sparse estimation using a hadamard product parametrization,” Computational Statistics & Data Analysis, vol. 115, pp. 186–198, 2017

    2017

  25. [32]

    Benign overfitting and noisy features,

    Z. Li, W. J. Su, and D. Sejdinovic, “Benign overfitting and noisy features,” Journal of the American Statistical Association , pp. 1–13, 2022

    2022

  26. [33]

    Implicit regularization leads to benign overfitting for sparse linear regression,

    M. Zhou and R. Ge, “Implicit regularization leads to benign overfitting for sparse linear regression,” arXiv preprint arXiv:2302.00257, 2023

    2023 arXiv

  27. [34]

    The implicit bias of benign overfitting,

    O. Shamir, “The implicit bias of benign overfitting,” Journal of Machine Learning Research, vol. 24, no. 113, pp. 1–40, 2023

    2023

  28. [35]

    Indexing by latent semantic analysis,

    S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer, and R. Harshman, “Indexing by latent semantic analysis,” Journal of the American society for information science , vol. 41, no. 6, pp. 391–407, 1990. 11

    1990

  29. [36]

    An introduction to latent semantic analysis,

    T. K. Landauer, P. W. Foltz, and D. Laham, “An introduction to latent semantic analysis,” Discourse processes, vol. 25, no. 2-3, pp. 259–284, 1998

    1998

  30. [37]

    Latent semantic analysis,

    S. T. Dumais, “Latent semantic analysis,” Annual review of information science and technology, vol. 38, no. 1, pp. 188–230, 2004

    2004

  31. [38]

    Exploiting multilabel information for noise- resilient feature selection,

    L. Jian, J. Li, and H. Liu, “Exploiting multilabel information for noise- resilient feature selection,” ACM Transactions on Intelligent Systems and Technology (TIST), vol. 9, no. 5, pp. 1–23, 2018

    2018

  32. [39]

    Joint multi-label classification and label correlations with missing labels and feature selection,

    Z.-F. He, M. Yang, Y . Gao, H.-D. Liu, and Y . Yin, “Joint multi-label classification and label correlations with missing labels and feature selection,” Knowledge-Based Systems, vol. 163, pp. 145–158, 2019

    2019

  33. [40]

    Robust multi-label feature selection with dual-graph regularization,

    J. Hu, Y . Li, W. Gao, and P. Zhang, “Robust multi-label feature selection with dual-graph regularization,” Knowledge-Based Systems, p. 106126, 2020

    2020

  34. [41]

    Manifold learning with structured subspace for multi-label feature selection,

    Y . Fan, J. Liu, P. Liu, Y . Du, W. Lan, and S. Wu, “Manifold learning with structured subspace for multi-label feature selection,” Pattern Recogni- tion, vol. 120, p. 108169, 2021

    2021

  35. [42]

    Multi-label feature selection via manifold regu- larization and dependence maximization,

    R. Huang and Z. Wu, “Multi-label feature selection via manifold regu- larization and dependence maximization,” Pattern Recognition, vol. 120, p. 108149, 2021

    2021

  36. [43]

    Understanding deep learning (still) requires rethinking generalization,

    C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals, “Understanding deep learning (still) requires rethinking generalization,” Communications of the ACM, vol. 64, no. 3, pp. 107–115, 2021

    2021

  37. [44]

    Measuring saturation in neural networks,

    A. Rakitianskaia and A. Engelbrecht, “Measuring saturation in neural networks,” in 2015 IEEE Symposium Series on Computational Intelli- gence. IEEE, 2015, pp. 1423–1430

    2015

  38. [45]

    Implicit regularization for optimal sparse recovery,

    T. Vaskevicius, V . Kanade, and P. Rebeschini, “Implicit regularization for optimal sparse recovery,” in Advances in Neural Information Processing Systems, 2019, pp. 2972–2983

    2019

  39. [47]

    The interplay between implicit bias and benign overfitting in two-layer linear networks,

    N. S. Chatterji, P. M. Long, and P. L. Bartlett, “The interplay between implicit bias and benign overfitting in two-layer linear networks,”Journal of machine learning research, vol. 23, no. 263, pp. 1–48, 2022

    2022

  40. [48]

    Multi-label informed latent semantic indexing,

    K. Yu, S. Yu, and V . Tresp, “Multi-label informed latent semantic indexing,” in Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval, 2005, pp. 258–265

    2005

  41. [49]

    Latent semantic aware multi-view multi-label classification,

    C. Zhang, Z. Yu, Q. Hu, P. Zhu, X. Liu, and X. Wang, “Latent semantic aware multi-view multi-label classification,” in Thirty-second AAAI conference on artificial intelligence, 2018, pp. –

    2018

  42. [50]

    Estimating attributes: Analysis and extensions of relief,

    I. Kononenko, “Estimating attributes: Analysis and extensions of relief,” in European conference on machine learning. Springer, 1994, pp. 171– 182

    1994

  43. [51]

    Multi-label relieff and f- statistic feature selections for image annotation,

    D. Kong, C. Ding, H. Huang, and H. Zhao, “Multi-label relieff and f- statistic feature selections for image annotation,” in 2012 IEEE confer- ence on computer vision and pattern recognition . IEEE, 2012, pp. 2352–2359

    2012

  44. [52]

    Prototype and feature selection by sampling and random mutation hill climbing algorithms,

    D. B. Skalak, “Prototype and feature selection by sampling and random mutation hill climbing algorithms,” in Machine Learning Proceedings

  45. [53]

    Multiple svm-rfe for gene selection in cancer classification with expression data,

    K.-B. Duan, J. C. Rajapakse, H. Wang, and F. Azuaje, “Multiple svm-rfe for gene selection in cancer classification with expression data,” IEEE transactions on nanobioscience, vol. 4, no. 3, pp. 228–234, 2005

    2005

  46. [54]

    Least angle regression,

    B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” The Annals of statistics, vol. 32, no. 2, pp. 407–499, 2004

    2004

  47. [55]

    Variable- size cooperative coevolutionary particle swarm optimization for feature selection on high-dimensional data,

    X.-F. Song, Y . Zhang, Y .-N. Guo, X.-Y . Sun, and Y .-L. Wang, “Variable- size cooperative coevolutionary particle swarm optimization for feature selection on high-dimensional data,” IEEE Transactions on Evolutionary Computation, vol. 24, no. 5, pp. 882–895, 2020

    2020

  48. [56]

    Nonnegative laplacian embedding guided subspace learning for unsupervised feature selection,

    Y . Zhang, Q. Wang, D.-w. Gong, and X.-f. Song, “Nonnegative laplacian embedding guided subspace learning for unsupervised feature selection,” Pattern Recognition, vol. 93, pp. 337–352, 2019

    2019

  49. [57]

    High-Dimensional Linear Regression via Implicit Regularization,

    P. Zhao, Y . Yang, and Q.-C. He, “High-Dimensional Linear Regression via Implicit Regularization,” Biometrika, vol. 109, no. 4, p. 1033–1046,

  50. [58]

    Orthogonal nonnegative matrix t-factorizations for clustering,

    C. Ding, T. Li, W. Peng, and H. Park, “Orthogonal nonnegative matrix t-factorizations for clustering,” in Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, 2006, pp. 126–135

    2006

  51. [59]

    Unsupervised feature selection for multi- cluster data,

    D. Cai, C. Zhang, and X. He, “Unsupervised feature selection for multi- cluster data,” in Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining , 2010, pp. 333– 342

    2010

  52. [60]

    Mutual information based multi-label feature selection via constrained convex optimization,

    Z. Sun, J. Zhang, L. Dai, C. Li, C. Zhou, J. Xin, and S. Li, “Mutual information based multi-label feature selection via constrained convex optimization,” Neurocomputing, vol. 329, pp. 447–456, 2019

    2019

  53. [61]

    Multi-label feature selection via global relevance and redundancy optimization

    J. Zhang, Y . Lin, M. Jiang, S. Li, Y . Tang, and K. C. Tan, “Multi-label feature selection via global relevance and redundancy optimization.” in IJCAI, 2020, pp. 2512–2518

    2020

  54. [62]

    Lassonet: A neural network with feature sparsity,

    I. Lemhadri, F. Ruan, L. Abraham, and R. Tibshirani, “Lassonet: A neural network with feature sparsity,” Journal of Machine Learning Research, vol. 22, no. 127, pp. 1–29, 2021. [Online]. Available: http://jmlr.org/papers/v22/20-848.html

    2021

  55. [63]

    Multi-label classification: An overview,

    G. Tsoumakas and I. Katakis, “Multi-label classification: An overview,” International Journal of Data Warehousing and Mining (IJDWM), vol. 3, no. 3, pp. 1–13, 2007

    2007

  56. [64]

    Robust multi-label learning with pro loss,

    M. Xu, Y .-F. Li, and Z.-H. Zhou, “Robust multi-label learning with pro loss,” IEEE Transactions on Knowledge and Data Engineering , vol. 32, no. 8, pp. 1610–1624, 2019

    2019

  57. [65]

    A unified view of multi-label performance measures,

    X.-Z. Wu and Z.-H. Zhou, “A unified view of multi-label performance measures,” in International Conference on Machine Learning . PMLR, 2017, pp. 3780–3788

    2017

  58. [66]

    Improving pairwise ranking for multi-label image classification,

    Y . Li, Y . Song, and J. Luo, “Improving pairwise ranking for multi-label image classification,” inProceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 3617–3625

    2017

  59. [67]

    Bilabel-specific features for multi-label classification,

    M.-L. Zhang, J.-P. Fang, and Y .-B. Wang, “Bilabel-specific features for multi-label classification,” ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 16, no. 1, pp. 1–23, 2021

    2021

  60. [68]

    Ml-knn: A lazy learning approach to multi-label learning,

    M.-L. Zhang and Z.-H. Zhou, “Ml-knn: A lazy learning approach to multi-label learning,” Pattern recognition, vol. 40, no. 7, pp. 2038–2048, 2007

    2007

  61. [69]

    Statistical comparisons of classifiers over multiple data sets,

    J. Dem ˇsar, “Statistical comparisons of classifiers over multiple data sets,” Journal of Machine Learning Research, vol. 7, pp. 1–30, 2006

    2006

  62. [70]

    Online multi-label streaming feature selection based on neighborhood rough set,

    J. Liu, Y . Lin, Y . Li, W. Weng, and S. Wu, “Online multi-label streaming feature selection based on neighborhood rough set,” Pattern Recognition, vol. 84, pp. 273–287, 2018

    2018

  63. [1994]

    Elsevier, 1994, pp. 293–301

    1994

  64. [2022]

    Available: https://doi.org/10.1093/biomet/asac010

    [Online]. Available: https://doi.org/10.1093/biomet/asac010

    doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.