Pith. sign in

REVIEW 2 major objections 4 minor 44 references

spar: Sparse Projected Averaged Regression in R

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper presents the R package spar, the first implementation of sparse projected averaged regression for generalized linear models, together with an S3-class framework that lets users plug in custom screening and projection procedures.

desk verdict Solid software paper for an existing ensemble method; the package looks real and well-designed, but the default CV procedure leaks validation information into screening and needs fixing or a warning before the reported results are taken at face value. read the letter →

arxiv 2411.17808 v1 pith:7CJDKYUJ submitted 2024-11-26 stat.CO stat.ME

Roman Parzer , Laura Vana-Gür , Peter Filzmoser This is my paper · ORCID
classification stat.COstat.ME MSC 62-0462J0762J12
keywords randomprojectionvariablescreeningensemblelearninggeneralizedlinearmodelshigh-dimensionalregressionsparseprojectedaveragedRpackageS3classes
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 presents spar, an R package that implements sparse projected averaged regression (SPAR) for generalized linear models when predictors vastly outnumber observations. Each member of the ensemble screens the predictor set, projects the survivors to a random low-dimensional space, fits a penalized GLM, and thresholds the resulting coefficients, then the members are averaged back in the original variable space. The package's central claims are first implementation and extensibility: the screening, projection, and marginal-model steps are all S3 classes, so users can supply their own procedures through constructor functions. The default projection is data-driven, replacing random diagonal entries of a sparse embedding with small-penalty ridge coefficients, which the authors say keeps the true coefficients approximately recoverable after projection. The practical payoff would be computationally feasible high-dimensional GLM fitting whose coefficients remain interpretable in terms of the original predictors.

What carries the argument

The load-bearing object is the SPAR ensemble loop: per-model screening, random projection, penalized GLM fit, coefficient thresholding, and averaging. The identity that gives the default its interpretability is the data-driven sparse embedding rp_cw(data = TRUE), where random diagonal entries are swapped for minimal-penalty ridge coefficients so the true beta is claimed to lie approximately in the projection's span. Around these sit the three S3 classes—'screencoef' for screening coefficients, 'randomprojection' for projection matrices, and 'sparmodel' for marginal models—each exposing a generate_fun component that the main spar() and spar.cv() functions invoke, which is what makes any of the steps replaceable.

What would settle it

Run spar() on the package's included simulated data, which explicitly provides the true coefficient vector, and compare rp_cw(data = TRUE) with a data-agnostic projection such as rp_gaussian(): if the data-driven default does not produce closer coefficient recovery or better variable ranking, the approximate-span premise is unsupported. A second check is to search the package ecosystem for an existing GLM ensemble that already performs screening, random projection, and averaging, which would directly test the first-implementation claim.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that spar is the first implementation of the SPAR algorithm for GLMs, and that its S3 architecture delivers genuine extensibility. The algorithm works model by model: screen to at most 2n predictors based on a screening coefficient, project the selected variables to a random dimension chosen between log(p) and n/2, estimate a (possibly L2-penalized) GLM on the projected data, map the coefficients back to original variables, and threshold small entries before averaging across M models. The distinctive default is rp_cw(data = TRUE), a Clarkson-Woodruff-style sparse embedding whose random diagonal entries are replaced by ridge coefficients from a minimal penalty; the paper states this construction approximately captures the true regression coefficients in the span of the projection. The paper demonstrates extensibility by wrapping a SIRS screening coefficient from another package and by building a Cannings-Samworth-style random projection that selects among Haar matrices by validation error.

Load-bearing premise

The load-bearing premise is that replacing the random diagonal entries of the projection with small-penalty ridge coefficients keeps the true regression coefficients approximately recoverable after projection, a property this paper cites from its technical reports rather than proving or verifying here.

Editorial extensions

If this is right

  • For p >> n data, no ensemble member ever fits a model on more than 2n screened variables projected to at most n/2 dimensions, so the algorithm stays computationally tractable where a direct GLM fit is infeasible or unstable.
  • Because coefficients are averaged in the original variable space after thresholding, the resulting object supports standard coef and predict methods and yields per-predictor effects rather than effects on uninterpretable projected features.
  • The S3 framework allows new screening and projection methods to be dropped in without touching the core loop; the paper shows this by adding a SIRS-based screening coefficient and a validation-selected Haar projection.
  • The cross-validation routine can tune both the number of ensemble models and the threshold level, including a one-standard-error rule that returns a sparser coefficient vector with nearly the same validation performance.
  • The internal L2 penalty on marginal models is especially useful for binomial families, where it reduces separation problems during the ensemble fit.

Reading between the lines

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

  • Beyond the paper, the same S3 machinery could house non-GLM base learners such as Cox proportional hazards or quantile regression by defining a new marginal-model class; the authors do not implement these, but nothing in the loop prevents it.
  • Beyond the paper, the cross-validation shortcut of holding random projections fixed across folds and updating only the data-dependent parts means reported CV results should be read as conditional on that fixed-projection choice; full per-fold updates could change the measured performance.
  • Beyond the paper, the package's own simulated example, which ships with the true coefficients, could power a routine diagnostic: comparing estimated and true coefficients after fitting would make the approximate-span property observable rather than assumed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper describes the R package "spar", which implements sparse projected averaged regression (SPAR) for high-dimensional generalized linear models. The algorithm combines marginal screening, random projection, per-model penalized GLM fitting, thresholding, and averaging. The package provides S3 classes for screening coefficients and random projections, including a data-driven projection (rp_cw) that is claimed to approximately preserve the true coefficient vector. The paper gives an algorithmic description, package documentation, two extensibility examples, and two real-data illustrations on the Isomap faces data and the Darwin Alzheimer's handwriting data.

Significance. If the implementation is correct, the package would be a useful contribution because it offers a flexible, extensible framework for combining screening and random projection in GLM ensembles, and the S3 class design is a genuine strength that lowers the barrier for users to plug in custom procedures. The paper also gives credit to the source algorithms and clearly attributes the data-driven projection to earlier technical reports by the same authors. However, the paper currently lacks any independent empirical verification of the algorithm's recovery or predictive properties, and the cross-validation implementation as described has a selection-leakage problem that undermines the main model-selection tool. These issues are fixable, but they are load-bearing for the paper's central claims.

major comments (2)
  1. [Section 3.3 and Section 6] The cross-validation procedure in spar.cv leaks validation information into the screening step. Section 3.1 states that spar.cv generates inds and RPMs by first calling spar() on the whole data set, and then passes these predefined objects to spar() in each fold. However, Algorithm 2.4 specifies that screening is an internal step: Step 3 computes screening coefficients and Step 4.1 selects the screened index set from the data. Reusing full-data screening indices in every fold means the validation-fold responses influence which predictors enter each training-fold model, so the cross-validated measure K(M, nu) is not an unbiased estimate of generalization error for the full screening-then-projection pipeline. The optional update_rpm_w_data() refreshes only the data-dependent entries in the projection matrices; it does not regenerate the screening indices. This is particularly serious because spar.cv is the package's only model-selection tool and is used in Sections 5.1 and 5.2 to choose (M, nu). The paper should either recompute screening coefficients and indices on each training fold inside the CV loop, or explicitly document and justify this as an approximate CV scheme, with a simulation demonstrating that the leakage has negligible effect on the selected parameters.
  2. [Section 3.3, Section 6, and Section 5] The paper's default projection rp_cw(data=TRUE) is repeatedly claimed to approximately capture the true regression coefficients in the span of the projection, and Section 6 asserts that SPAR with this projection performs effectively across different degrees of sparsity. These claims are supported only by citations to the authors' technical reports (Parzer et al. 2024a,b); the manuscript itself contains no simulation with known coefficients, no comparison with existing high-dimensional estimators, and no runtime benchmark. Because the recovery property is the main justification for the default projection and for the interpretability of the resulting coefficients, the paper should include at least one synthetic-data experiment that checks coefficient recovery under the implemented rp_cw(data=TRUE), and ideally a small comparison against a baseline such as glmnet to demonstrate that the implementation reproduces the expected prediction behavior. Without such verification, a reader cannot distinguish implementation errors from expected algorithm behavior.
minor comments (4)
  1. [Figure 1] The caption says the plot uses a fixed optimal number of models M = 20, but the text and the printed output for the faces example report the smallest CV measure at nummod=10. The caption should be corrected to M = 10.
  2. [Section 3.1] In the two function signatures, the default for the measure argument is shown as c("deviance", "mse", "mae", "class", "1-auc"), while the explanatory text says the default is "deviance". This inconsistency should be fixed so that the documentation matches the actual R default.
  3. [Section 2.1] The equation for the marginal likelihood screening coefficient reads "ˆ\omega_j =: argmin" but the notation appears to be reversed; it should be "\hat\omega_j := \argmin" or simply "\hat\omega_j = \argmin".
  4. [Section 6] The conclusion contains the sentence "The package provides an implementation an algorithm" which is missing a word; it should read "an implementation of an algorithm".

Circularity Check

2 steps flagged · score 5.0 of 10

Partial circularity: spar.cv's reported validation measure uses full-data screening indices, making the CV evaluation self-referential, and the flagship data-driven projection's recovery property is imported from the authors' own technical reports.

  1. fitted input called prediction [Section 3.1 (spar.cv description), compared with Algorithm Step 6 in Section 2.4; used in Sections 5.1 and 5.2]
    "It relies on spar() as a workhorse, which is called for each fold. The random projections for each model are held fixed throughout the cross-validation to reduce the computational burden. This is possible by calling spar() in each fold with a predefined inds and RPMs argument, which are generated by first calling spar() on the whole data set, before starting the cross-validation procedure."

    The algorithm in Section 2.4 defines cross-validation in Step 6 as "repeating steps 1 to 4" per fold, and Step 4.1 selects the screened index set I_k from screening coefficients computed on the fitting data. In spar.cv, however, inds are precomputed from a whole-data spar() fit and passed unchanged into every fold, so the held-out fold's responses have already influenced which predictors enter the training model. The reported CV measure (e.g., "Smallest CV-Meas 19.4" in Section 5.1) is therefore not an unbiased estimate of generalization error for the full screening-then-projection pipeline; it is a self-referential validation score that has seen the validation data through the screening indices.

  2. self citation load bearing [Section 2.2 (Random projection tools); relied on in Section 3.3 (rp_cw default) and Section 6 (Conclusion)]
    "This method has the advantage of approximately capturing the true beta in the span of the random projection, i.e., it ensures that the true regression coefficients can be recovered approximately after the projection."

    The default data-driven projection rp_cw(data=TRUE), used in the Section 5 examples, is the package's flagship construction precisely because of this span/recovery property, and the property is asserted only with citations to the authors' own Parzer et al. (2024a,b) technical reports. The present paper contains no proof, simulation, or independent verification of the property; the conclusion repeats it as a demonstrated advantage. This is not a within-paper derivation loop, and the cited reports may themselves contain proofs, but as presented the load-bearing methodological premise of the package's default projection reduces to an unexamined self-citation.

full rationale

The core SPAR implementation and S3 extensibility are self-contained: the package code is available on GitHub, the examples are reproducible, and no fitted constant is relabeled as a theoretical prediction. However, the cross-validated selection loop is methodologically self-referential: Algorithm Step 6 requires screening to be repeated within each fold, while spar.cv fixes inds from a whole-data spar() call and reuses them in every fold, so the held-out responses influence the screened predictor sets. Consequently, the CV measures and 1se sparsity choices reported in Sections 5.1 and 5.2 are not honest out-of-sample evaluations of the full screening-then-projection pipeline. Additionally, the flagship rp_cw(data=TRUE) choice is justified by a span/recovery property cited only to the authors' own Parzer et al. (2024a,b) technical reports, with no proof in this paper. These two issues make the paper partially circular in its validation narrative, but the package's core implementation content remains independent.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central algorithm contributes no new parameters beyond the package defaults; all key statistical assumptions come from prior literature, mostly the authors' own technical reports. The free parameters are algorithmic design choices rather than fitted scientific constants.

free parameters (3)
  • screening set size (nscreen) = 2n by default
    Section 3.2: nscreen defaults to 2n; when p > 2n the algorithm keeps exactly 2n predictors per model. This fixed multiple of n is a hand-chosen design decision, not derived.
  • projected dimension bounds (mslow, msup) = log(p) and n/2 by default
    Section 3.3 and Section 2.4: m_k is drawn uniformly from {log(p), ..., n/2}; the lower and upper endpoints are user-supplied defaults chosen by the authors, not implied by a theorem.
  • marginal ridge penalty (minimal lambda) = default glmnet minimal lambda, lambda.min.ratio = 0.001 in examples
    Section 2.3 and Section 5: a small L2 penalty is added for stability; the exact amount is delegated to glmnet's lambda path, so it is data-dependent and not fixed by a stated principle.
assumptions (6)
  • standard math Random projection matrices satisfying the Johnson-Lindenstrauss lemma approximately preserve all pairwise distances.
    Section 2.2 invokes the JL lemma (Johnson and Lindenstrauss 1984) and sub-Gaussian constructions as the basis for reducing the predictor dimension.
  • domain assumption Marginal screening coefficients have the sure screening property under stated technical conditions.
    Section 2.1 relies on Fan and Lv (2007) and Fan and Song (2010) to justify that top-ranked marginal predictors contain the active set with probability tending to one.
  • domain assumption The response follows a GLM in the reproductive exponential dispersion family after projection.
    Section 2.3 specifies the model for the projected predictors; all uncertainty statements and loss measures are conditional on this family being correct.
  • ad hoc to paper The data-driven random projection approximately captures the true coefficient vector in its span.
    Section 2.2 and 3.3: 'it ensures that the true regression coefficients can be recovered approximately after the projection.' This is the key assumption inherited from the authors' Parzer et al. (2024a,b) technical reports and not proved in this paper.
  • ad hoc to paper Averaging over thresholds and random screening/projection ensembles yields a valid predictive model.
    Section 2.4 defines thresholding and averaging; the statistical validity of the ensemble predictor is taken from Mukhopadhyay and Dunson (2020) and Parzer et al. (2024a), not derived here.
  • ad hoc to paper Projected dimension around n/2 with a small ridge penalty prevents separation and stabilizes estimation.
    Section 2.3 recommends m at most n/2 and employs an L2 penalty 'especially for the binomial family'; this is a heuristic added for numerical stability.

how reviews work

0 comments
Cite this review

Pith. "Pith review of spar: Sparse Projected Averaged Regression in R." pith.science (2026). https://pith.science/paper/7CJDKYUJ

@misc{pith2026241117808,
  author       = {Pith},
  title        = {Pith review of: spar: Sparse Projected Averaged Regression in R},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7CJDKYUJ}},
  note         = {Machine review of arXiv:2411.17808}
}
read the original abstract

Package spar for R builds ensembles of predictive generalized linear models with high-dimensional predictors. It employs an algorithm utilizing variable screening and random projection tools to efficiently handle the computational challenges associated with large sets of predictors. The package is designed with a strong focus on extensibility. Screening and random projection techniques are implemented as S3 classes with user-friendly constructor functions, enabling users to easily integrate and develop new procedures. This design enhances the package's adaptability and makes it a powerful tool for a variety of high-dimensional applications.

Figures

Figures reproduced from arXiv: 2411.17808 by the authors.

Figure 1
Figure 1. Plot of mean squared error over a grid of threshold values [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 2
Figure 2. Coefficient plot for all variables and all [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗
Figure 3
Figure 3. Left: Image corresponding to one observation in the [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Average number of active variables for the grid of thresholding values [PITH_FULL_IMAGE:figures/full_fig_p026_4.png]
Figure 5
Figure 5. Figure 5: Coefficient plot for all variables and all considered [PITH_FULL_IMAGE:figures/full_fig_p027_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 24 canonical work pages

  1. [1]

    Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins

    Achlioptas D (2003). Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins. Journal of Computer and System Sciences, 66(4), 671--687. ISSN 0022-0000. doi:10.1016/S0022-0000(03)00025-4. Special Issue on PODS 2001

    doi:10.1016/s0022-0000(03)00025-4 2003

  2. [2]

    RandPro : Random Projection with Classification

    Aghila G, Siddharth R (2020). RandPro : Random Projection with Classification . doi:10.32614/CRAN.package.RandPro. R package version 0.2.2

    work page doi:10.32614/cran.package.randpro 2020

  3. [3]

    The Fast Johnson--Lindenstrauss Transform and Approximate Nearest Neighbors

    Ailon N, Chazelle B (2009). The Fast Johnson--Lindenstrauss Transform and Approximate Nearest Neighbors. SIAM Journal on computing, 39(1), 302--322. doi:10.1137/060673096

    doi:10.1137/060673096 2009

  4. [4]

    R.matlab : Read and Write MAT Files and Call MATLAB from Within R

    Bengtsson H (2022). R.matlab : Read and Write MAT Files and Call MATLAB from Within R . doi:10.32614/CRAN.package.R.matlab. R package version 3.7.0

    work page doi:10.32614/cran.package.r.matlab 2022

  5. [5]

    Random-projection ensemble classification

    Cannings TI, Samworth RJ (2017). Random-projection ensemble classification. Journal of the Royal Statistical Society Series B: Statistical Methodology, 79(4), 959--1035. doi:10.1111/rssb.12228

    work page doi:10.1111/rssb.12228 2017

  6. [6]

    RPEnsemble : Random Projection Ensemble Classification

    Cannings TI, Samworth RJ (2021). RPEnsemble : Random Projection Ensemble Classification . R package version 0.5, 10.32614/CRAN.package.RPEnsemble

    work page doi:10.32614/cran.package.rpensemble 2021

  7. [7]

    MFSIS : Model-Free Sure Independent Screening Procedures

    Cheng X, Wang H, Zhu L, Zhong W, Zhou H (2024). MFSIS : Model-Free Sure Independent Screening Procedures . doi:10.32614/CRAN.package.MFSIS. R package version 0.2.1

    work page doi:10.32614/cran.package.mfsis 2024

  8. [8]

    High dimensional variable selection via tilting

    Cho H, Fryzlewicz P (2012). High dimensional variable selection via tilting. Journal of the Royal Statistical Society Series B: Statistical Methodology, 74(3), 593--622. doi:10.1111/j.1467-9868.2011.01023.x

    arXiv 2012

Show all 44 references
  1. [9]

    Diagnosing Alzheimer’s disease from on-line handwriting: A novel dataset and performance benchmarking

    Cilia ND, De Gregorio G, De Stefano C, Fontanella F, Marcelli A, Parziale A (2022). Diagnosing Alzheimer’s disease from on-line handwriting: A novel dataset and performance benchmarking. Engineering Applications of Artificial Intelligence, 111, 104822. ISSN 0952-1976. doi:10.1...

    2022

  2. [10]

    Low Rank Approximation and Regression in Input Sparsity Time

    Clarkson KL, Woodruff DP (2013). Low Rank Approximation and Regression in Input Sparsity Time. In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC '13, p. 81–90. Association for Computing Machinery, New York, NY, USA. ISBN 9781450320290. doi:10....

    2013

  3. [12]

    Nonparametric independence screening in sparse ultra-high-dimensional additive models

    Fan J, Feng Y, Song R (2011). Nonparametric independence screening in sparse ultra-high-dimensional additive models. Journal of the American Statistical Association, 106(494), 544--557. doi:10.1198/jasa.2011.tm09779

    2011 doi

  4. [13]

    High-dimensional variable selection for Cox’s proportional hazards model

    Fan J, Feng Y, Wu Y (2010). High-dimensional variable selection for Cox’s proportional hazards model. In Borrowing strength: Theory powering applications--a Festschrift for Lawrence D. Brown, volume 6, pp. 70--87. Institute of Mathematical Statistics. doi:10.1214/10-IMSCOLL606

    2010 doi

  5. [14]

    Sure Independence Screening for Ultra-High Dimensional Feature Space

    Fan J, Lv J (2007). Sure Independence Screening for Ultra-High Dimensional Feature Space. Journal of the Royal Statistical Society Series B: Statistical Methodology, B 70. doi:10.1111/j.1467-9868.2008.00674.x

    2007

  6. [15]

    Ultrahigh dimensional feature selection: beyond the linear model

    Fan J, Samworth R, Wu Y (2009). Ultrahigh dimensional feature selection: beyond the linear model. The Journal of Machine Learning Research, 10, 2013--2038. ://jmlr.csail.mit.edu/papers/v10/fan09a.html

    2009

  7. [16]

    Sure independence screening in generalized linear models with NP -dimensionality

    Fan J, Song R (2010). Sure independence screening in generalized linear models with NP -dimensionality. The Annals of Statistics, 38(6), 3567 -- 3604. doi:10.1214/10-AOS798

    2010 doi

  8. [17]

    The Johnson-Lindenstrauss Lemma and the Sphericity of Some Graphs

    Frankl P, Maehara H (1988). The Johnson-Lindenstrauss Lemma and the Sphericity of Some Graphs. Journal of Combinatorial Theory, Series B, 44(3), 355--362. ISSN 0095-8956. doi:10.1016/0095-8956(88)90043-3

    1988 doi

  9. [18]

    SPCAvRP : Sparse Principal Component Analysis via Random Projections (SPCAvRP)

    Gataric M, Wang T, Samworth RJ (2019). SPCAvRP : Sparse Principal Component Analysis via Random Projections (SPCAvRP) . R package version 0.4, 10.32614/CRAN.package.SPCAvRP

    2019 doi

  10. [19]

    Extensions of Lipschitz Maps into a Hilbert Space

    Johnson W, Lindenstrauss J (1984). Extensions of Lipschitz Maps into a Hilbert Space. Contemporary Mathematics, 26, 189--206. doi:10.1090/conm/026/737400

    1984 doi

  11. [20]

    Sufficient Variable Screening With High-Dimensional Controls

    Ke C (2023). Sufficient Variable Screening With High-Dimensional Controls. Electronic Journal of Statistics, 17(2), 2139 -- 2179. doi:10.1214/23-EJS2150

    2023 doi

  12. [21]

    Very Sparse Random Projections

    Li P, Hastie TJ, Church KW (2006). Very Sparse Random Projections. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '06, p. 287–296. Association for Computing Machinery, New York, NY, USA. ISBN 1595933395. doi:10.1145/1...

    2006

  13. [22]

    VariableScreening : High-Dimensional Screening for Semiparametric Longitudinal Regression

    Li R, Huang L, Dziak J (2022). VariableScreening : High-Dimensional Screening for Semiparametric Longitudinal Regression . doi:10.32614/CRAN.package.VariableScreening. R package version 0.2.1

    2022 doi

  14. [23]

    Feature Screening via Distance Correlation Learning

    Li R, Zhong W, Zhu L (2012). Feature Screening via Distance Correlation Learning. Journal of the American Statistical Association, 107(499), 1129--1139. doi:10.1080/01621459.2012.695654

    2012

  15. [24]

    Robust Model-Free Feature Screening via Quantile Correlation

    Ma X, Zhang J (2016). Robust Model-Free Feature Screening via Quantile Correlation. Journal of Multivariate Analysis, 143, 472--480. doi:10.1016/j.jmva.2015.10.010

    2016 doi

  16. [25]

    The Kolmogorov Filter for Variable Screening in High-Dimensional Binary Classification

    Mai Q, Zou H (2013). The Kolmogorov Filter for Variable Screening in High-Dimensional Binary Classification. Biometrika, 100(1), 229--234. doi:10.1093/biomet/ass062

    2013 doi

  17. [26]

    The Fused Kolmogorov Filter: A Nonparametric Model-Free Screening Method

    Mai Q, Zou H (2015). The Fused Kolmogorov Filter: A Nonparametric Model-Free Screening Method. The Annals of Statistics, 43(4), 1471 -- 1497. doi:10.1214/14-AOS1303

    2015 doi

  18. [27]

    On Variants of the Johnson--Lindenstrauss Lemma

    Matou s ek J (2008). On Variants of the Johnson--Lindenstrauss Lemma. Random Structures & Algorithms, 33(2), 142--156. doi:10.1002/rsa.20218

    2008 doi

  19. [28]

    Targeted Random Projection for Prediction From High-Dimensional Features

    Mukhopadhyay M, Dunson DB (2020). Targeted Random Projection for Prediction From High-Dimensional Features . Journal of the American Statistical Association, 115(532), 1998--2010. doi:10.1080/01621459.2019.1677240

    2020

  20. [29]

    Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models

    Parzer R, Filzmoser P, Vana-Gür L (2024 a ). Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models. Technical Report 2410.00971, arXiv.org E-Print Archive. doi:10.48550/arXiv.2410.00971

    2024 doi

  21. [30]

    Sparse Data-Driven Random Projection in Regression for High-Dimensional Data

    Parzer R, Filzmoser P, Vana-Gür L (2024 b ). Sparse Data-Driven Random Projection in Regression for High-Dimensional Data . Technical Report 2312.00130, arXiv.org E-Print Archive. doi:10.48550/arXiv.2312.00130

    2024 doi arXiv

  22. [31]

    Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, et al. (2011). scikit-learn : Machine Learning in Python . Journal of Machine Learning Research, 12(Oct), 2825--2830. ://www.jmlr.org/papers/v12/pedregosa11a.html

    2011

  23. [32]

    cellWise : Analyzing Data with Cellwise Outliers

    Raymaekers J, Rousseeuw P (2023). cellWise : Analyzing Data with Cellwise Outliers . doi:10.32614/CRAN.package.cellWise. R package version 2.5.3

    2023 doi

  24. [33]

    R : A Language and Environment for Statistical Computing

    R Core Team (2024). R : A Language and Environment for Statistical Computing . R Foundation for Statistical Computing, Vienna, Austria. ://www.R-project.org/

    2024

  25. [34]

    Asymmetric Random Projections

    Ryder N, Karnin Z, Liberty E (2019). Asymmetric Random Projections. Technical Report 1906.09489, arXiv.org E-Print Archive. doi:10.48550/arXiv.1906.09489

    2019 doi arXiv

  26. [35]

    SIS : An R Package for Sure Independence Screening in Ultrahigh-Dimensional Statistical Models

    Saldana DF, Feng Y (2018). SIS : An R Package for Sure Independence Screening in Ultrahigh-Dimensional Statistical Models. Journal of Statistical Software, 83(2), 1--25. doi:10.18637/jss.v083.i02

    2018 doi

  27. [36]

    RandPro -- A Practical Implementation of Random Projection-Based Feature Extraction for High Dimensional Multivariate Data Analysis in R

    Siddharth R, Aghila G (2020). RandPro -- A Practical Implementation of Random Projection-Based Feature Extraction for High Dimensional Multivariate Data Analysis in R . SoftwareX, 12, 100629. ISSN 2352-7110. doi:10.1016/j.softx.2020.100629

    2020

  28. [37]

    Random Projections for Large-Scale Regression, pp

    Thanei GA, Heinze C, Meinshausen N (2017). Random Projections for Large-Scale Regression, pp. 51--68. Springer International Publishing, Cham. doi:10.1007/978-3-319-41573-4_3

    2017 doi

  29. [38]

    RaSEn : Random Subspace Ensemble Classification and Variable Screening

    Tian Y, Feng Y (2021). RaSEn : Random Subspace Ensemble Classification and Variable Screening . doi:10.32614/CRAN.package.RaSEn. R package version 3.0.0

    2021 doi

  30. [39]

    van Rossum G, et al. (2011). Python Programming Language . ://www.python.org

    2011

  31. [40]

    High-dimensional Ordinary Least-squares Projection for Screening Variables

    Wang X, Leng C (2016). High-dimensional Ordinary Least-squares Projection for Screening Variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78, 589–611. doi:10.1111/rssb.12127

    2016 doi

  32. [41]

    Conditional Distance Correlation

    Wang X, Pan W, Hu W, Tian Y, Zhang H (2015). Conditional Distance Correlation. Journal of the American Statistical Association, 110(512), 1726--1734. doi:10.1080/01621459.2014.993081

    2015

  33. [42]

    Model-Free Feature Screening and FDR Control With Knockoff Features

    Wanjun Liu Yuan Ke JL, Li R (2022). Model-Free Feature Screening and FDR Control With Knockoff Features. Journal of the American Statistical Association, 117(537), 428--443. doi:10.1080/01621459.2020.1783274

    2022

  34. [43]

    ggplot2 : Elegant Graphics for Data Analysis

    Wickham H (2016). ggplot2 : Elegant Graphics for Data Analysis . Springer-Verlag New York. ISBN 978-3-319-24277-4. ://ggplot2.tidyverse.org

    2016

  35. [44]

    The Sparse MLE for Ultrahigh-Dimensional Feature Screening

    Xu C, Chen J (2014). The Sparse MLE for Ultrahigh-Dimensional Feature Screening. Journal of the American Statistical Association, 109(507), 1257--1269. doi:10.1080/01621459.2013.879531

    2014

  36. [45]

    Model-Free Feature Screening for Ultrahigh-Dimensional Data

    Zhu LP, Li L, Li R, Zhu LX (2011). Model-Free Feature Screening for Ultrahigh-Dimensional Data. Journal of the American Statistical Association, 106(496), 1464--1475. doi:10.1198/jasa.2011.tm10563

    2011 doi

Pith tools

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