Pith. sign in

REVIEW 5 major objections 5 minor 49 references

Sparse minimum Redundancy Maximum Relevance for feature selection

T0 review · 5 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A penalized mRMR criterion can mark inactive features by zero coefficients and control false discoveries with a knockoff filter.

desk verdict Competent HSIC-LASSO extension with SCAD/MCP and knockoffs, but the headline claim that zero coefficients identify conditionally inactive features is not proven; the theorems only recover the support of the mRMR loss minimizer. read the letter →

arxiv 2508.18901 v1 pith:LGM6MGLH submitted 2025-08-26 stat.ML cs.LGstat.ME

Peter Naylor , Benjamin Poignard , Héctor Climente-González , Makoto Yamada This is my paper · ORCID
classification stat.MLcs.LGstat.ME MSC 62F1262H2062J07
keywords featurescreeningmRMRnon-convexpenalizationfalsediscoveryrateknockofffiltersparsistencyHSICprojectioncorrelation
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 tries to establish that feature screening can be made redundancy-aware and FDR-controlled at the same time. It proposes a continuous, penalized version of the minimum Redundancy Maximum Relevance criterion, where the estimated coefficient for each feature is positive if the feature is relevant and zero if it is inactive. The paper proves that, with non-convex SCAD or MCP penalties, the zero pattern of the population mRMR solution is recovered consistently, and that adding a knockoff filter after a screening step controls the false discovery rate. If correct, the practical payoff is a feature selection method where the user sets a target FDR instead of guessing how many features to keep.

What carries the argument

The engine is the penalized mRMR loss L_v,n(θ), a continuous relaxation of the discrete mRMR selection problem, regularized by a non-convex penalty such as SCAD or MCP. The feature-feature dependence matrix D_XX enters as a design-like quadratic form, and the association measures are V-statistic estimators—normalized HSIC and squared projection correlation—that make the loss an explicit least-squares or tensor least-squares problem. A data-splitting knockoff procedure supplies the FDR control, with the importance score defined as the difference between the fitted coefficient of an original feature and its knockoff copy.

What would settle it

Simulate a design with a duplicated or near-duplicated feature, e.g. X_2 = X_1 exactly while Y depends only on X_1, and run SmRMR with SCAD and MCP at large n. Since D_XX is singular or nearly singular, Assumption 3.2 fails; recording whether the redundant coefficient is consistently set to zero and whether the knockoff threshold still controls FDR across seeds would reveal exactly where the guarantee breaks.

Watch

Extended reading notes

Core claim

The central claim is that the sparse mRMR estimator, defined as the penalized continuous relaxation of the classic mRMR objective, consistently recovers the support of the population mRMR coefficients, so zero entries correctly identify the inactive features. Theorems 3.5 and 3.6 establish consistency and sparsistency under SCAD or MCP penalties, with the LASSO failing the sparsistency rate condition. Theorem 4.1 then shows that, conditional on a screening event where all truly active features survive the first data-splitting stage, the knockoff+ threshold controls the FDR of the selected set. The method can be built with either normalized HSIC or squared projection correlation as the depend

Load-bearing premise

The load-bearing premise is Assumption 3.2: the feature-feature dependence matrix D_XX must have all eigenvalues bounded away from zero and infinity, which fails when features are strongly or perfectly redundant—even though handling redundancy is the stated motivation of the method.

Editorial extensions

If this is right

  • Under SCAD or MCP penalties, the zero coefficients of the SmRMR estimator can be trusted, with probability tending to one, to mark the features that the population mRMR criterion treats as inactive.
  • After screening, users can select features by setting an FDR level rather than by fixing the number of features to retain, which removes a common calibration step in feature screening pipelines.
  • Because the loss is a least-squares or tensor least-squares problem, the method can reuse standard solvers for LASSO, SCAD, and MCP, including local linear approximation algorithms.
  • Empirically, SmRMR reaches accuracy comparable to HSIC-LASSO while selecting substantially fewer features, which lowers the observed FDR in the reported simulations and real-data benchmarks.

Reading between the lines

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

  • I read the theory as implying that the screening power comes from the feature-feature quadratic term: when two features are strongly redundant, the penalty can set one to zero even if both are marginally relevant, something marginal screening alone cannot do.
  • The paper asserts rather than proves that zero entries of the population mRMR coefficients coincide with the causal inactive set I of Section 2.1; the theorems show the estimator recovers the zero pattern of the mRMR solution, not that this pattern equals conditional independence with Y.
  • A natural extension is to apply the same screening-plus-knockoff structure with other dependence measures or with adaptive weights, since the proofs only need V-statistic estimators with the same sub-exponential deviation tail.
  • The eigenvalue bound on D_XX suggests the guarantee is weakest exactly in the regime of perfect or near-perfect feature redundancy, which is the regime mRMR was originally designed to address; testing with duplicated or near-duplicated features would map where the theory stops and the heuristics begin.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes a sparse continuous relaxation of mRMR feature screening, called SmRMR, in which a penalty (Lasso, SCAD, or MCP) is applied to a quadratic loss built from pairwise dependence estimates (HSIC or projection correlation). The main theoretical claims are: (i) consistency of a local minimizer of the penalized criterion (Thm 3.5), (ii) sparsistency, i.e. recovery of zero coefficients of the population pseudo-true parameter (Thm 3.6), and (iii) conditional FDR control after a two-stage knockoff procedure (Thm 4.1). Experiments on synthetic and real datasets compare SmRMR with HSIC-LASSO and report accuracy, TPR, FDR, and number of selected features. Code is provided.

Significance. If the claims were fully established, the paper would contribute a redundancy-aware screening method with an FDR guarantee, extending HSIC-LASSO in a useful direction. The authors provide reproducible code, a wide experimental study, and proofs that follow the standard Fan-Li / Loh-Wainwright template for penalized M-estimation. The most valuable and defensible part is the support-recovery analysis for the pseudo-true mRMR parameter and the conditional FDR statement for a valid knockoff construction. However, the paper's central advertised claim — that zero coefficients identify the conditional-independence inactive set of Section 2.1 — is never proved, and several assumptions are in tension with the method's motivation. These issues are load-bearing for the paper as written.

major comments (5)
  1. [Sections 1, 2.3, 3 (Thms 3.5–3.6)] The paper claims that zero coefficients in the estimated parameter correspond to the inactive features I = {k : F(Y|X) does not functionally depend on X_k}. What is actually proved is that the penalized estimator recovers the support of the pseudo-true parameter θ_n0 defined in Assumption 3.1 as the minimizer of L(θ) = -Σθ_k D(X_k,Y) + (1/2)Σθ_k θ_l D(X_k,X_l). No proposition establishes {k : θ_n0,k=0} = I. Since D is a marginal dependence measure, a conditionally inactive feature can be marginally dependent on Y through active features, and the redundancy term can drive its coefficient to zero even when it is conditionally active. The heuristic in Section 2.3 only gives inequalities involving bD_v(X_k,Y) and redundancy terms, not conditional independence. Consequently Theorem 3.6 concerns 'non-relevant' features for the mRMR loss, not the inactive set named in the abstract; the FDR theo
  2. [Assumption 3.1, Section 3] Assumption 3.1 states that an open neighbourhood of θ_n0 is contained in R_+^{p_n} and that the stationarity equality -D(X_k,Y)+Σ_l D(X_k,X_l)θ_n0,l = 0 holds for every k. If θ_n0 has zero coordinates (as required for sparsistency and as assumed by the sparsity structure before Theorem 3.5), no Euclidean open neighbourhood of θ_n0 is contained in the non-negative orthant. The correct first-order condition at a boundary zero is a variational inequality / directional derivative condition, not equality. The proof of Theorem 3.6 uses the equality form of Assumption 3.1 for zero coordinates, so the current assumptions are internally inconsistent with the very sparsity pattern the theorems are meant to establish. This needs to be repaired, e.g. by formulating boundary KKT conditions and adapting the proofs.
  3. [Assumption 3.2, Theorems 3.5–3.6, Section 1] Assumption 3.2 requires 0 < μ ≤ λ_min(D_XX) ≤ λ_max(D_XX) < μ < ∞. This excludes situations where two features are perfectly or nearly redundant, since then D_XX is singular or ill-conditioned. But redundancy among features is the exact motivation of mRMR, and the paper's own DGPs include correlated features (e.g. DGPs 1.c, 3.c with c=0.5). Moreover, Theorem 3.5 requires p_n^2 s_n log(p_n) = o(n), which forces p_n ≪ sqrt(n) when s_n ≥ 1. This is incompatible with the paper's stated ultra-high-dimensional setting (p ≫ n) and with experiments such as n=100, p=5000. The theory should either be restricted to moderate-dimensional problems or extended with screening theory and restricted-eigenvalue-type conditions; in its present form, the main theorems do not cover the regime the method is designed for.
  4. [Section 4, Section 5.1.2, Theorem 4.1] The FDR guarantee in Theorem 4.1 relies on the knockoff exchangeability property (via Lemma 1 of Liu et al. [2022]). But the implementation in Section 5.1.2 uses second-order Model-X knockoffs with the equicorrelated construction. For non-Gaussian X and for kernel-based statistics that depend on the full joint distribution, second-order knockoffs are not exact knockoffs, so the sign-flip property required for W_k may fail. Thus the theorem does not justify the FDR numbers reported in the experiments unless exact Model-X knockoffs or an appropriate second-order-sufficient statistic is established. In addition, Theorem 4.1 is conditional on the screening event E_n = {S_n ⊆ hat S_0,n, 2s_0,n < n_1}; the experiments evaluate FDR with respect to the causal active set S, not S_n = {k : θ_n0,k ≠ 0}. The authors should make this distinction explicit and, if the causal claim is retained, connect
  5. [Section 5.3, SmRMR2] The paper acknowledges that the modified procedure SmRMR2, which returns at least one feature, has FDR not controlled in every situation. This is a clear and honest statement, but it means the headline FDR control in the abstract and in parts of the experimental section applies only to the unmodified procedure; the figures and tables mix both variants. The authors should separate the two regimes and clearly label where the theoretical guarantee applies, especially because SmRMR2 is used for real-data benchmarking.
minor comments (5)
  1. [Section 2.3] Typo: 'righ-derivative' should be 'right-derivative'. The subdifferential of the LASSO at θ_k=0 under the non-negative constraint is stated as {z_k : z_k ≤ 1}; for the non-negative constrained problem the relevant subgradient interval should also reflect the sign constraint (z_k ∈ [0,1] when θ_k=0 in the one-sided sense). Please clarify.
  2. [Section 5.1.2] 'Bayes optimization' should be 'Bayesian optimization'. Also 'fine-tuning the LARS penalty' is unclear; LARS does not normally have a penalty tuning parameter.
  3. [Algorithm 1] The stopping criterion 'while s ≠ m and ||bθ(s) − bθ(s−1)|| < ε' combines a fixed iteration cap with a convergence check; as written, if s reaches m the loop exits regardless of convergence. State explicitly whether convergence is required before m iterations.
  4. [Section 4, Eq. (4.1)] The objective G_{v,n} includes cross terms only between original variables and only between knockoff variables, but no cross term X_k with tilde X_l. This is a modelling choice; a sentence explaining why the cross term is omitted would help, since a fully quadratic model would normally include it.
  5. [Appendix A] Lemma A.2's proof invokes 'Lemma S.2 of Liu et al. [2022]' without stating the lemma or its conditions. Since the paper otherwise provides self-contained proofs, please state the lemma or give a direct argument for the normalized HSIC deviation.

Circularity Check

2 steps flagged · score 6.0 of 10

Zero-coefficient support is equated with the conditional-inactive set only by definition; theorems prove recovery of the pseudo-true mRMR parameter's support, not of the inactive set I.

  1. self definitional [Abstract and Section 3 (sparsity assumption before Theorem 3.5); Section 2.1 defines I by conditional independence.]
    "Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, ... where the parameters estimated as zero coefficients represent the set of inactive features. ... Without loss of generality, we assume ... θn0,k = 0 for k > sn with sn the cardinality of the true sparse support, defined as Sn := {k = 1, . . . , pn : θn0,k ̸= 0}: this is the sparsity assumption."

    Section 2.1 defines the inactive set I by conditional independence: F(Y|X1,...,Xp) does not functionally depend on Xk. But θn0 is defined only as the minimizer of L(θ)=−ΣθkD(Xk,Y)+(1/2)ΣθkθlD(Xk,Xl). No proposition proves {k:θn0,k=0}=I; Section 2.3's heuristic gives only a bound involving bDv(Xk,Y) and redundancy terms, not conditional independence. Thus Theorem 3.6, which recovers the zero coordinates of θn0, is a consistency statement for the SmRMR loss's own pseudo-true support. Calling these zeros 'inactive features' makes the abstract's central claim 'zero coefficients ... represent the set of inactive features' true by definition rather than by derivation.

  2. self definitional [Section 4, around the knockoff statistic definition and Theorem 4.1; proof in Appendix B.3.]
    "As pointed out by Barber and Candès [2015], the properties of the Wk imply that card (k ∈ Sc_n : cWk ≥ t) d= card (k ∈ Sc_n : cWk ≤ −t) ... where Sn := {k = 1, . . . , pn : θn0,k ̸= 0}."

    The FDR theorem controls false discoveries among Sc_n, and Sc_n is explicitly defined as the complement of the pseudo-true mRMR support {θn0,k≠0}. The screening event En is Sn⊆bS0,n, again with Sn=θn0's support. Since no result identifies Sc_n with the conditional-inactive set I from Section 2.1, the advertised 'discard inactive features while controlling FDR' is a guarantee about the method's own fitted zero set. The external knockoff lemma is independent and valid, but its conclusion is attached to a self-defined target, so the FDR control for the paper's inactive features is partly definitional.

full rationale

The estimation theory is largely self-contained: Theorem 3.5 proves consistency of the penalized estimator for the pseudo-true minimizer θn0 of the mRMR loss, and Theorem 3.6 proves sparsistency for θn0's zero coordinates using deviation inequalities from Liu et al. and Gretton et al., plus standard sparse-M-estimation arguments. The knockoff FDR step invokes the external Barber-Candès / Liu et al. lemmas rather than the authors' own prior results. Self-citations (HSIC-LASSO, kernel knockoffs) are contextual and not load-bearing. The circularity is in the advertised target: the abstract and Section 3 call θn0's zero coordinates 'inactive features,' but inactive features were defined in Section 2.1 by conditional independence. The paper never shows that the support of θn0 equals I; indeed, D(Xk,Y) is a marginal dependence measure, so conditionally inactive features can have positive marginal D(Xk,Y) through correlation with active features. Consequently, the central claim that zero coefficients identify inactive features, and the FDR guarantee relative to Sc_n={θn0,k=0}, reduce by construction to properties of the fitted objective's own support. This is partial circularity: the core estimation rates are independent, but the paper's headline identification claim is definitional rather than derived. The eigenvalue Assumption 3.2 and the conditional-independence gap are correctness risks, not additional circularity.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The paper leans on the standard sparse M-estimation assumption package (bounded eigenvalues, penalty regularity, min-signal) and imports the knockoff theorem from Barber-Candès and Liu et al. The only paper-specific target is the pseudo-true theta_0 of the mRMR loss; the link from theta_0 zeros to causal inactivity is an unproved identification assumption. No new entities are introduced.

free parameters (4)
  • lambda_n (regularization) = 0.01 (screening); CV-optimized (knockoff)
    Controls sparsity; theory assumes rate conditions, practice tunes or defaults.
  • alpha (FDR level) = 0.3 default; incremented in SmRMR2
    User threshold; adaptive increment (SmRMR2) voids FDR control.
  • Gaussian kernel width = median heuristic
    Affects all HSIC dependence estimates.
  • s_0 / p_max = (n-1)/2
    Screening set size needed to satisfy 2 s0 < n1 for knockoff construction.
assumptions (8)
  • domain assumption Assumption 3.1: unique pseudo-true theta_0 minimizes L(theta) on R_+^p and satisfies the orthogonality condition
    Defines the target parameter; needed for all subsequent rates.
  • domain assumption Assumption 3.2: eigenvalues of D_XX bounded below and above by positive constants
    Fails with strongly redundant or duplicated features, the paper's motivating case.
  • domain assumption Assumption 3.3: penalty derivative conditions: a_n = O(n^-1/2), b_n -> 0
    Standard Fan-Peng conditions for SCAD/MCP and LASSO.
  • domain assumption Assumption 3.4: min nonzero theta_0j / lambda_n -> infinity
    Minimum signal strength; required for zero recovery.
  • ad hoc to paper Screening event E_n = {S_n subset of hat S0,n, 2 s0,n < n1}
    FDR theorem 4.1 is conditional on this event; no guarantee it holds.
  • ad hoc to paper Zero coefficients of theta_0 correspond to inactive features (conditional independence)
    Asserted in Section 2.3; never proven. A redundant active feature can have zero theta_0.
  • domain assumption Non-negative symmetric kernels bounded by 1
    Used for the deviation inequality in Lemma A.2.
  • standard math Knockoff sufficiency and anti-symmetry (Lemma 1 of Liu et al. 2022)
    Imported external result; gives the sign-flip property used for FDR control.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Sparse minimum Redundancy Maximum Relevance for feature selection." pith.science (2026). https://pith.science/paper/LGM6MGLH

@misc{pith2026250818901,
  author       = {Pith},
  title        = {Pith review of: Sparse minimum Redundancy Maximum Relevance for feature selection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LGM6MGLH}},
  note         = {Machine review of arXiv:2508.18901}
}
read the original abstract

We propose a feature screening method that integrates both feature-feature and feature-target relationships. Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, which is the continuous version of the classic mRMR penalized by a non-convex regularizer, and where the parameters estimated as zero coefficients represent the set of inactive features. We establish the conditions under which zero coefficients are correctly identified to guarantee accurate recovery of inactive features. We introduce a multi-stage procedure based on the knockoff filter enabling the penalized mRMR to discard inactive features while controlling the false discovery rate (FDR). Our method performs comparably to HSIC-LASSO but is more conservative in the number of selected features. It only requires setting an FDR threshold, rather than specifying the number of features to retain. The effectiveness of the method is illustrated through simulations and real-world datasets. The code to reproduce this work is available on the following GitHub: https://github.com/PeterJackNaylor/SmRMR.

Figures

Figures reproduced from arXiv: 2508.18901 by the authors.

Figure 1
Figure 1. Overview of the proposed method 5.1.1 Screening step The screening step is essential in the high-dimensional setting. Indeed, if n < 2p, we can not build the knockoff features that lead to the knockoff filter essential for controlling the FDR. Therefore, in the same vein as in Barber and Candès [2019], we split the data in two where a fraction n0 of the data is used to reduce the set of features to the set Sb0 and t… view at source ↗
Figure 2
Figure 2. Screening step in details, DR is a boolean variable indicating if Data Recycling will be used. 5.1.2 Knockoff filter After applying the screening step to the high-dimensional data, we have X(1) ∈ R n1×p with n1 > 2p and we can apply the knockoff filter on X(1). We show a summarizing panel of this step in [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Knockoff feature steps in details 16 [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Results for the non-linear DGP. For HSIC, we use the Gaussian kernel. [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: Real-world biological datasets application with SmRMR and HSIC-LASSO. [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 47 canonical work pages

  1. [1]

    Ultrahigh dimensional feature screening via RKHS embeddings

    Krishnakumar Balasubramanian, Bharath Sriperumbudur, and Guy Lebanon. Ultrahigh dimensional feature screening via RKHS embeddings. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, 31: 0 126--134, 2013

    work page 2013

  2. [2]

    Barber and Emmanuel J

    Rina F. Barber and Emmanuel J. Cand\`es. Controlling the false discovery rate via knockoffs. The Annals of Statistics, 43 0 (5): 0 2055--2085, 2015

    work page

  3. [3]

    Barber and Emmanuel J

    Rina F. Barber and Emmanuel J. Cand\`es. A knockoff filter for high-dimensional selective inference. The Annals of Statistics, 47 0 (5): 0 2504--2537, 2019

    work page 2019

  4. [4]

    Cand \`e s, Yingying Fan, Lucas Janson, and Jinchi Lv

    Emmanuel J. Cand \`e s, Yingying Fan, Lucas Janson, and Jinchi Lv. Panning for gold: Model-free knockoffs for high-dimensional controlled variable selection, volume 1610. Department of Statistics, Stanford University Stanford, CA, USA, 2016

    work page 2016

  5. [5]

    Cand \`e s, Yingying Fan, Lucas Janson, and Jinchi Lv

    Emmanuel J. Cand \`e s, Yingying Fan, Lucas Janson, and Jinchi Lv. Panning for gold: 'model-x' knockoffs for high-dimensional controlled variable selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80 0 (3): 0 551–577, 2018

    work page 2018

  6. [6]

    Block hsic lasso: model-free biomarker detection for ultra-high dimensional data

    H \'e ctor Climente-Gonz \'a lez, Chlo \'e -Agathe Azencott, Samuel Kaski, and Makoto Yamada. Block hsic lasso: model-free biomarker detection for ultra-high dimensional data. Bioinformatics, 35 0 (14): 0 i427--i435, 2019

    work page 2019

  7. [7]

    Global sensitivity analysis with dependence measures

    S\'ebastien Da Veiga. Global sensitivity analysis with dependence measures. Journal of Statistical Computation and Simulation, 85 0 (7): 0 1283--1305, 2015

    work page 2015

  8. [8]

    Bayesian optimization for machine learning : A practical guidebook

    Ian Dewancker, Michael McCourt, and Scott Clark. Bayesian optimization for machine learning : A practical guidebook. CoRR, abs/1612.04858, 2016. URL http://arxiv.org/abs/1612.04858

    arXiv 2016

Show all 49 references
  1. [9]

    CVXPY : A P ython-embedded modeling language for convex optimization

    Steven Diamond and Stephen Boyd. CVXPY : A P ython-embedded modeling language for convex optimization. Journal of Machine Learning Research, 17 0 (83): 0 1--5, 2016

    2016

  2. [10]

    Least angle regression

    Bradley Efron, Trevor Hastie, Iain Johnstone, and Robert Tibshirani. Least angle regression. The Annals of Statistics, 32 0 (2): 0 407--499, 2004

    2004

  3. [11]

    Variable selection via nonconcave penalized likelihood and its oracle properties

    Jianqing Fan and Runze Li. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96 0 (456): 0 1348--1360, 2001

    2001

  4. [12]

    Sure independence screening for ultrahigh dimensional feature space

    Jianqing Fan and Jinchi Lv. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70 0 (5): 0 849--911, 2008

    2008

  5. [13]

    Nonconcave penalized likelihood with a diverging number of parameters

    Jianqing Fan and Heng Peng. Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics, 32 0 (3): 0 928--961, 2004

    2004

  6. [14]

    Network exploration via the adaptive lasso and scad penalties

    Jianqing Fan, Yang Feng, and Wu Yichao. Network exploration via the adaptive lasso and scad penalties. The Annals of Applied Statistics, 3 0 (2): 0 521--541, 2009

    2009

  7. [15]

    Strong oracle optimality of folded concave penalized estimation

    Jianqing Fan, Lingzhou Xue, and Hui Zou. Strong oracle optimality of folded concave penalized estimation. The Annals of statistics, 42 0 (3): 0 819, 2014

    2014

  8. [16]

    Rank: Large-scale inference with graphical nonlinear knockoffs

    Yingying Fan, Emre Demirkaya, Gaorong Li, and Jinchi Lv. Rank: Large-scale inference with graphical nonlinear knockoffs. Journal of the American Statistical Association, 115 0 (529): 0 362--379, 2020

    2020

  9. [17]

    Fermanian and Benjamin Poignard

    Jean-D. Fermanian and Benjamin Poignard. Sparse m-estimators in semi-parametric copula models. Bernoulli, 30 0 (3): 0 2475--2500, 2024

    2024

  10. [18]

    Sriperumbudur

    Kenji Fukumizu, Arthur Gretton, Gert Lanckriet, Bernhard Schölkopf, and Bharath K. Sriperumbudur. Kernel choice and classifiability for rkhs embeddings of probability cistributions. Advances in Neural Information Processing Systems, 22, 2009

    2009

  11. [19]

    Type s error rates for classical and bayesian single and multiple comparison procedures

    Andrew Gelman and Francis Tuerlinckx. Type s error rates for classical and bayesian single and multiple comparison procedures. Computational statistics, 15 0 (3): 0 373--390, 2000

    2000

  12. [20]

    Measuring statistical dependence with H ilbert- S chmidt norms

    Arthur Gretton, Olivier Bousquet, Alex Smola, and Bernhard Sch \"o lkopf. Measuring statistical dependence with H ilbert- S chmidt norms. International Conference on Algorithmic Learning Theory, pages 63--77, 2005 a

    2005

  13. [21]

    Kernel methods for measuring independence

    Arthur Gretton, Ralf Herbrich, Alexander Smola, Olivier Bousquet, and Bernhard Schölkopf. Kernel methods for measuring independence. Journal of Machine Learning Research, 6: 0 2075--2129, 2005 b

  14. [22]

    Teo, Le Song, Bernhard Sch \"o lkopf, and Alex Smola

    Arthur Gretton, Kenji Fukumizu, Choon H. Teo, Le Song, Bernhard Sch \"o lkopf, and Alex Smola. A kernel statistical test of independence. Advances in Neural Information Processing Systems, 20: 0 585--592, 2007

    2007

  15. [23]

    Structure-based design and classifications of small molecules regulating the circadian rhythm period

    Seref Gul, Fatih Rahim, Safak Isin, Fatma Yilmaz, Nuri Ozturk, Metin Turkay, and Ibrahim Halil Kavakli. Structure-based design and classifications of small molecules regulating the circadian rhythm period. Scientific Reports, 11 0 (1), September 2021. ISSN 2045-2322

    2021

  16. [24]

    An introduction to variable and feature selection

    Isabelle Guyon and Andr\' e Elisseeff. An introduction to variable and feature selection. Journal of Machine Learning Research, 3: 0 1157--1182, 2003

    2003

  17. [25]

    Sparsistency and rates of convergence in large covariance matrix estimation

    Clifford Lam and Jianqing Fan. Sparsistency and rates of convergence in large covariance matrix estimation. The Annals of Statistics, 37 0 (6B): 0 4254--4278, 2009

    2009

  18. [26]

    Trevino, Jiliang Tang, and Huan Liu

    Jundong Li, Kewei Cheng, Suhang Wang, Fred Morstatter, Robert P. Trevino, Jiliang Tang, and Huan Liu. Feature selection: A data perspective. ACM Comput. Surv., 50 0 (6), dec 2017. ISSN 0360-0300

    2017

  19. [27]

    Feature screening via distance correlation learning

    Runze Li, Wei Zhong, and Liping Zhu. Feature screening via distance correlation learning. Journal of the American Statistical Association, 107 0 (499): 0 1129--1139, 2012

    2012

  20. [28]

    Model-free feature screening and fdr control with knockoff features

    Wanjun Liu, Yuan Ke, Jingyuan Liu, and Runze Li. Model-free feature screening and fdr control with knockoff features. Journal of the American Statistical Association, 117 0 (537): 0 428--443, 2022

    2022

  21. [29]

    Loh and Martin J

    Poh-L. Loh and Martin J. Wainwright. Support recovery without incoherence: A case for nonconvex regularization. The Annals of Statistics, 45 0 (6): 0 2455--2482, 2017

    2017

  22. [30]

    Yang Lu, Yingying Fan, Jinchi Lv, and William S. Noble. Deeppink: Reproducible feature selection in deep neural networks. Advances in Neural Information Processing Systems, 31: 0 8676--8686, 2018

    2018

  23. [31]

    The kolmogorov filter for variable screening in high dimensional binary classification

    Qing Mai and Hui Zou. The kolmogorov filter for variable screening in high dimensional binary classification. Biometrika, 100 0 (1): 0 229--234, 2013

    2013

  24. [32]

    The fused kolmogorov filter: A nonparametric model-free screening method

    Qing Mai and Hui Zou. The fused kolmogorov filter: A nonparametric model-free screening method. The Annals of Statistics, 43 0 (4): 0 1471--1497, 2015

    2015

  25. [33]

    Prediction of treatment response in triple negative breast cancer from whole slide images

    Peter Naylor, Tristan Lazard, Guillaume Bataillon, Marick La \'e , Anne Vincent-Salomon, Anne-Sophie Hamy, Fabien Reyal, and Thomas Walter. Prediction of treatment response in triple negative breast cancer from whole slide images. Frontiers in Signal Processing, 2: 0 851809, 2022

    2022

  26. [34]

    Feature selection based on mutual information: Criteria of max-dependency, max-relevance, and min-redundancy

    Hanchuan Peng, Fuhui Long, and Chris Ding. Feature selection based on mutual information: Criteria of max-dependency, max-relevance, and min-redundancy. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27: 0 1226--1237, 2005

    2005

  27. [35]

    Fermanian

    Benjamin Poignard and Jean-D. Fermanian. The finite sample properties of sparse m-estimators with pseudo-observations. Annals of the Institute of Statistical Mathematics, 74: 0 1--31, 2022

    2022

  28. [36]

    Sparse hilbert-schmidt independence criterion regression

    Benjamin Poignard and Makoto Yamada. Sparse hilbert-schmidt independence criterion regression. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, 108: 0 538--548, 2020

    2020

  29. [37]

    Feature screening with kernel knockoffs

    Benjamin Poignard, Peter Naylor, Hector Climente-Gonz\'alez, and Makoto Yamada. Feature screening with kernel knockoffs. Proceedings of the Twenty Fith International Conference on Artificial Intelligence and Statistics, 151: 0 1935--1974, 2022

    1935

  30. [38]

    Cand\`es

    Yaniv Romano, Matteo Sesia, and Emmanuel J. Cand\`es. Deep knockoffs. Journal of the American Statistical Association, 115 0 (532): 0 1861--1872, 2020

    2020

  31. [39]

    Serfling

    Robert J. Serfling. Approximation theorems of mathematical statistics. New York: Wiley, 1980

    1980

  32. [40]

    Feature selection via dependence maximization

    Le Song, Alex Smola, Arthur Gretton, Justin Bedo, and Karsten Borgwardt. Feature selection via dependence maximization. Journal of Machine Learning Research, 13: 0 1393--1434, 2012

    2012

  33. [41]

    Compositional knockoff filter for high-dimensional regression analysis of microbiome data

    Arun Srinivasan, Lingzhou Xue, and Xiang Zhan. Compositional knockoff filter for high-dimensional regression analysis of microbiome data. Biometrics, 77 0 (3): 0 984--995, 2021

    2021

  34. [42]

    Sz \'e kely and Maria L

    Gabor J. Sz \'e kely and Maria L. Rizzo. Brownian distance covariance. The Annals of Applied Statistics, 3 0 (4): 0 1236--1265, 2009

    2009

  35. [43]

    Sz \'e kely, Maria L

    G \'a bor J. Sz \'e kely, Maria L. Rizzo, and Nail K. Bakirov. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35 0 (6): 0 2769--2794, 2007

    2007

  36. [44]

    Peixin Tian, Yiqian Hu, Zhonghua Liu, and Yan D. Zhang. Grace-ako: a novel and stable knockoff filter for variable selection incorporating gene network structures. BMC bioinformatics, 23 0 (1): 0 478, 2022

    2022

  37. [45]

    Regression shrinkage and selection via the lasso

    Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 58 0 (1): 0 267--288, 1996

    1996

  38. [46]

    Xing, and Masashi Sugiyama

    Makoto Yamada, Wittawat Jitkrittum, Leonid Sigal, Eric P. Xing, and Masashi Sugiyama. High-dimensional feature selection by feature-wise kernelized lasso. Neural computation, 26 0 (1): 0 185--207, 2014

    2014

  39. [47]

    Cun-H. Zhang. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38 0 (2): 0 894--942, 2010

    2010

  40. [48]

    Projection correlation between two random vectors

    Liping Zhu, Kai Xu, Runze Li, and Wei Zhong. Projection correlation between two random vectors. Biometrika, 104 0 (4): 0 829--843, 2017

    2017

  41. [49]

    One-step sparse estimates in nonconcave penalized likelihood models

    Hui Zou and Runze Li. One-step sparse estimates in nonconcave penalized likelihood models. The Annals of Statistics, 36 0 (4): 0 1509--1533, 2008

    2008

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.