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arxiv: 2405.03063 · v2 · submitted 2024-05-05 · 🧮 math.ST · cs.IT· cs.LG· math.IT· stat.ME· stat.ML· stat.TH

Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection

Jingbo Liu This is my paper

Pith reviewed 2026-05-24 01:02 UTC · model grok-4.3

classification 🧮 math.ST cs.ITcs.LGmath.ITstat.MEstat.MLstat.TH
keywords debiased lassostabilityvariable selectionresamplingconditional randomization testknockoff filterhigh-dimensional statisticsproportional regime
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The pith

A stability-based update to the generalized debiased Lasso approximates the estimator accurately for all but a vanishing fraction of coordinates under sub-Gaussian designs.

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

The paper proposes a generalized debiased Lasso estimator defined through a stability principle. When one column of the design matrix is perturbed, the estimator admits a simple update formula computed directly from the original solution. Under sub-Gaussian designs with well-conditioned covariance in the proportional growth regime, this approximation is asymptotically accurate for all but a vanishing fraction of coordinates. The result matters because it cuts the cost of repeated estimations in resampling procedures for variable selection. The proof relies on concentration and anti-concentration bounds, while establishing full distributional limits such as Gaussianity remains open under the same conditions.

Core claim

A generalized debiased Lasso estimator based on a stability principle admits a simple update formula when a single column of the design matrix is perturbed. Under sub-Gaussian designs with well-conditioned covariance, in the proportional growth regime, the approximation is asymptotically accurate for all but a vanishing fraction of coordinates. The proof uses concentration and anti-concentration arguments to control error terms and sign changes, while comparable distributional limits remain open.

What carries the argument

The stability principle that supplies a simple update formula for the generalized debiased Lasso when one design column is perturbed.

If this is right

  • The approximation significantly reduces the computational cost of resampling-based variable selection procedures.
  • It applies to the conditional randomization test.
  • It supports a local knockoff filter.
  • The stability approximation holds in settings where full Gaussian distributional limits are still open.

Where Pith is reading between the lines

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

  • Similar stability updates might be constructible for other high-dimensional penalized estimators beyond the Lasso.
  • The cost reduction could extend to other resampling schemes such as bootstrap or cross-validation in high dimensions.
  • Numerical checks in finite samples could test how quickly the vanishing fraction disappears as n grows.
  • The gap between stable approximation and open distributional limits suggests stability may be provable under weaker conditions than full asymptotics.

Load-bearing premise

The design matrix satisfies sub-Gaussian tail bounds and has a well-conditioned covariance matrix, with analysis restricted to the proportional growth regime.

What would settle it

A sub-Gaussian design matrix with well-conditioned covariance for which the stability approximation error fails to vanish for a non-vanishing fraction of coordinates when p/n approaches a constant.

Figures

Figures reproduced from arXiv: 2405.03063 by Jingbo Liu.

Figure 1
Figure 1. Figure 1: Comparison of βˆ (j)U j (cross) and its approximation error βˆ (j)U j −γ˜j (circle) for ρ = 0. have Σ = 1 apϵ  I − ϵ−1 1+ϵ−1p E  . We then generate α with a random set of s coordinates equal to Aval/ √ n (Aval > 0 being a parameter to be specified), and the rest coordinates equal to 0. The observation is Y = Aα + w, where w ∼ N (0, σI). We compare the performance of 6 variable selection methods in [PITH… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of βˆ (j)U j (cross) and its approximation error βˆ (j)U j −γ˜j (circle) for ρ = 0.5. As s = 20 is relatively small in this setting, there are a few instances of FDR overflow for Knockoff-db, due to fluctuations. Meanwhile, the power achieved by the local knockoff filter and CRT are better than the knockoff filter, with or without debiasing. In [PITH_FULL_IMAGE:figures/full_fig_p065_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of βˆ (j)U j (cross) and its approximation error βˆ (j)U j −γ˜j (circle) for ρ = 0.95. close to E (the matrix consisting of 1’s), the knockoff filter fails in the high-dimensional limit, regardless of the choice of the knockoff mechanism, whereas methods based on more relaxed local exchangeability conditions (such as local knockoff and CRT) remains powerful. H.4 FDR control with Riboflavin data … view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of βˆ (j) j (cross) and its approximation error (circle) for ρ = 0. we use the best linear estimator A:\jΣ −1 \j Σ\jj for the µ:j in the definition of the debiased estimator. The FDR and power cannot be precisely evaluated since we do not know the ground truth. To tackle this issue, we first use cross-validated Lasso to obtain α for the observed Y , and then generate new Y = Aα + w, where the no… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of βˆ (j) j (cross) and its approximation error (circle) for ρ = 0.5. vector. For this dataset, we have n = 2026, p = 163, and sparsity level s = 79. For the knockoff function, we use the implementation from the official package. The results are shown in [PITH_FULL_IMAGE:figures/full_fig_p068_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of βˆ (j) j (cross) and its approximation error (circle) for ρ = 0.95. I Proofs and implementation details for variable se lection I.1 Proof of Lemma 11 Set a = √ 1 2 S 1/2 e where e = (1, . . . , 1)⊤. From ∥s∥1 = s ⊤S −1 s ≥ 1 2 s ⊤Es = 1 2 ∥s∥ 2 1 we obtain ∥a∥ 2 = 1 2 ∥s∥1 ≤ 1. Moreover, (I − 1 2 S 1/2ES1/2 ) −1 = (I − aa⊤) −1 (276) = I + 1 1 − ∥a∥ 2 2 aa⊤. (277) 69 [PITH_FULL_IMAGE:figures/… view at source ↗
read the original abstract

We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under sub-Gaussian designs with well-conditioned covariance, this approximation is asymptotically accurate for all but a vanishing fraction of coordinates in the proportional growth regime. The proof relies on concentration and anti-concentration arguments to control error terms and sign changes. In contrast, establishing comparable distributional limits (e.g., Gaussianity) under similar assumptions remains open. As an application, we show that the approximation significantly reduces the computational cost of resampling-based variable selection procedures, including the conditional randomization test and a local knockoff filter.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 1 minor

Summary. The manuscript proposes a generalized debiased Lasso estimator grounded in a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under sub-Gaussian designs with well-conditioned covariance, this approximation is asymptotically accurate for all but a vanishing fraction of coordinates in the proportional growth regime. The proof relies on concentration and anti-concentration arguments to control error terms and sign changes. As an application, the approximation significantly reduces the computational cost of resampling-based variable selection procedures, including the conditional randomization test and a local knockoff filter.

Significance. If the central asymptotic accuracy result holds, this work provides a computationally efficient method for approximating the debiased Lasso under column perturbations, which has direct implications for scalable resampling-based inference in high dimensions. The approach leverages standard concentration tools in a novel way for stability updates. The authors' note that stronger distributional limits remain open demonstrates appropriate caution. This contributes to the field by offering practical speedups without sacrificing the core statistical properties under the stated assumptions. The manuscript includes applications to established procedures like CRT and knockoffs, enhancing its relevance.

minor comments (1)
  1. [Abstract] Abstract: A brief parenthetical reference to the specific concentration inequalities employed in the proof would help readers quickly gauge the technical level.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, significance assessment, and recommendation to accept the manuscript. We appreciate the recognition of the stability-based update formula, its asymptotic accuracy under the stated assumptions, and the computational benefits for resampling procedures such as the CRT and local knockoffs.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via concentration arguments

full rationale

The paper derives the stability-based update formula and its asymptotic accuracy from concentration and anti-concentration inequalities applied to sub-Gaussian designs in the proportional regime. No step reduces a claimed prediction or result to a fitted parameter, self-definition, or load-bearing self-citation. The update is presented as following directly from the perturbed Lasso solution, with error control shown via standard tail bounds rather than by construction or renaming. The abstract explicitly flags that stronger limits like Gaussianity remain open, confirming the argument does not smuggle in its own conclusion. This is the normal case of an independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard high-dimensional statistics assumptions rather than new free parameters or invented entities.

axioms (2)
  • domain assumption Design matrix entries are sub-Gaussian with well-conditioned covariance
    Invoked to guarantee the asymptotic accuracy of the stability approximation.
  • domain assumption Proportional growth regime (p/n → constant)
    Required for the vanishing-fraction accuracy statement.

pith-pipeline@v0.9.0 · 5656 in / 1249 out tokens · 23810 ms · 2026-05-24T01:02:16.748375+00:00 · methodology

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Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages · 1 internal anchor

  1. [1]

    Generalization error in high-dimensional perceptrons: Approaching bayes error with convex optimization

    Benjamin Aubin, Florent Krzakala, Yue Lu, and Lenka Zdeborov \'a . Generalization error in high-dimensional perceptrons: Approaching bayes error with convex optimization. Advances in Neural Information Processing Systems, 33: 0 12199--12210, 2020

    work page 2020

  2. [2]

    A leave-one-out approach to approximate message passing

    Zhigang Bao, Qiyang Han, and Xiaocong Xu. A leave-one-out approach to approximate message passing. arXiv preprint arXiv:2312.05911, 2023

    work page arXiv 2023

  3. [3]

    Cand\'es

    Rina Foygel 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 2055

  4. [4]

    Second-order stein: Sure for sure and other applications in high-dimensional inference

    Pierre C Bellec and Cun-Hui Zhang. Second-order stein: Sure for sure and other applications in high-dimensional inference. The Annals of Statistics, 49 0 (4): 0 1864--1903, 2021

    work page 1903

  5. [5]

    De-biasing the lasso with degrees-of-freedom adjustment

    Pierre C Bellec and Cun-Hui Zhang. De-biasing the lasso with degrees-of-freedom adjustment. Bernoulli, 28 0 (2): 0 713--743, 2022

    work page 2022

  6. [6]

    Debiasing convex regularized estimators and interval estimation in linear models

    Pierre C Bellec and Cun-Hui Zhang. Debiasing convex regularized estimators and interval estimation in linear models. The Annals of Statistics, 51 0 (2): 0 391--436, 2023

    work page 2023

  7. [7]

    Controlling the false discovery rate: a practical and powerful approach to multiple testing

    Yoav Benjamini and Yosef Hochberg. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal statistical society: series B (Methodological), 57 0 (1): 0 289--300, 1995

    work page 1995

  8. [8]

    Proximity of probability distributions in terms of fourier--stieltjes transforms

    Sergei Germanovich Bobkov. Proximity of probability distributions in terms of fourier--stieltjes transforms. Russian Mathematical Surveys, 71 0 (6): 0 1021, 2016

    work page 2016

  9. [9]

    Concentration of empirical distribution functions with applications to non-iid models

    SG Bobkov and F G \"o tze. Concentration of empirical distribution functions with applications to non-iid models. Bernoulli, 16 0 (4): 0 1385--1414, 2010

    work page 2010

  10. [10]

    Covering the sphere by equal spherical balls

    K \'a roly B \"o r \"o czky and Gergely Wintsche. Covering the sphere by equal spherical balls. Discrete and Computational Geometry: The Goodman-Pollack Festschrift, pages 235--251, 2003

    work page 2003

  11. [11]

    Inequalities

    S Boucheron, G Lugosi, and P Massart. Inequalities. a nonasymptotic theory of independence, 2013

    work page 2013

  12. [12]

    Algorithmic stability and generalization performance

    Olivier Bousquet and Andr \'e Elisseeff. Algorithmic stability and generalization performance. Advances in neural information processing systems, 13, 2000

    work page 2000

  13. [13]

    Statistical significance in high-dimensional linear models

    Peter B \"u hlmann. Statistical significance in high-dimensional linear models. Bernoulli, pages 1212--1242, 2013

    work page 2013

  14. [14]

    High-dimensional statistics with a view toward applications in biology

    Peter B \"u hlmann, Markus Kalisch, and Lukas Meier. High-dimensional statistics with a view toward applications in biology. Annual Review of Statistics and Its Application, 1: 0 255--278, 2014

    work page 2014

  15. [15]

    Panning for gold: model-x knockoffs for high dimensional controlled variable selection

    Emmanuel Cand\'es, 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

  16. [16]

    The lasso with general gaussian designs with applications to hypothesis testing

    Michael Celentano, Andrea Montanari, and Yuting Wei. The lasso with general gaussian designs with applications to hypothesis testing. The Annals of Statistics, 51 0 (5): 0 2194--2220, 2023

    work page 2023

  17. [17]

    Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization

    Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma, and Yuling Yan. Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization. SIAM journal on optimization, 30 0 (4): 0 3098--3121, 2020

    work page 2020

  18. [18]

    Double/debiased/neyman machine learning of treatment effects

    Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, and Whitney Newey. Double/debiased/neyman machine learning of treatment effects. American Economic Review, 107 0 (5): 0 261--265, 2017

    work page 2017

  19. [19]

    Double/debiased machine learning for treatment and structural parameters

    Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21 0 (1): 0 C1--C68, 2018

    work page 2018

  20. [20]

    High dimensional robust m-estimation: Asymptotic variance via approximate message passing

    David Donoho and Andrea Montanari. High dimensional robust m-estimation: Asymptotic variance via approximate message passing. Probability Theory and Related Fields, 166: 0 935--969, 2016

    work page 2016

  21. [21]

    On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators

    Noureddine El Karoui. On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators. Probability Theory and Related Fields, 170: 0 95--175, 2018

    work page 2018

  22. [22]

    On robust regression with high-dimensional predictors

    Noureddine El Karoui, Daniel Bean, Peter J Bickel, Chuang Lim, and Bin Yu. On robust regression with high-dimensional predictors. Proceedings of the National Academy of Sciences, 110 0 (36): 0 14557--14562, 2013

    work page 2013

  23. [23]

    Ipad: stable interpretable forecasting with knockoffs inference

    Yingying Fan, Jinchi Lv, Mahrad Sharifvaghefi, and Yoshimasa Uematsu. Ipad: stable interpretable forecasting with knockoffs inference. Journal of the American Statistical Association, 115 0 (532): 0 1822--1834, 2020

    work page 2020

  24. [24]

    Approximate message passing algorithms for rotationally invariant matrices

    Zhou Fan. Approximate message passing algorithms for rotationally invariant matrices. The Annals of Statistics, 50 0 (1): 0 197--224, 2022

    work page 2022

  25. [25]

    One-at-a-time knockoffs: controlled false discovery rate with higher power

    Charlie K Guan, Zhimei Ren, and Daniel W Apley. One-at-a-time knockoffs: controlled false discovery rate with higher power. arXiv preprint arXiv:2502.18750, 2025

    work page arXiv 2025

  26. [26]

    Universality of regularized regression estimators in high dimensions

    Qiyang Han and Yandi Shen. Universality of regularized regression estimators in high dimensions. The Annals of Statistics, 51 0 (4): 0 1799--1823, 2023

    work page 2023

  27. [27]

    The Elements of Statistical Learning: Data Mining, Inference, and Prediction

    Trevor Hastie, Robert Tibshirani, Jerome H Friedman, and Jerome H Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, 2 edition, 2009

    work page 2009

  28. [28]

    Controlling the false discoveries in lasso

    Hanwen Huang. Controlling the false discoveries in lasso. Biometrics, 73 0 (4): 0 1102--1110, 2017

    work page 2017

  29. [29]

    A flexible framework for hypothesis testing in high dimensions

    Adel Javanmard and Jason D Lee. A flexible framework for hypothesis testing in high dimensions. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82 0 (3): 0 685--718, 2020

    work page 2020

  30. [30]

    Confidence intervals and hypothesis testing for high-dimensional regression

    Adel Javanmard and Andrea Montanari. Confidence intervals and hypothesis testing for high-dimensional regression. The Journal of Machine Learning Research, 15 0 (1): 0 2869--2909, 2014 a

    work page 2014

  31. [31]

    Hypothesis testing in high-dimensional regression under the gaussian random design model: Asymptotic theory

    Adel Javanmard and Andrea Montanari. Hypothesis testing in high-dimensional regression under the gaussian random design model: Asymptotic theory. IEEE Transactions on Information Theory, 60 0 (10): 0 6522--6554, 2014 b

    work page 2014

  32. [32]

    Debiasing the lasso: Optimal sample size for gaussian designs

    Adel Javanmard and Andrea Montanari. Debiasing the lasso: Optimal sample size for gaussian designs. The Annals of Statistics, 46 0 (6A): 0 2593--2622, 2018

    work page 2018

  33. [33]

    Power of knockoff: The impact of ranking algorithm, augmented design, and symmetric statistic

    Zheng Tracy Ke, Jun S Liu, and Yucong Ma. Power of knockoff: The impact of ranking algorithm, augmented design, and symmetric statistic. Journal of Machine Learning Research, 25 0 (3): 0 1--67, 2024

    work page 2024

  34. [34]

    Black-box tests for algorithmic stability

    Byol Kim and Rina Foygel Barber. Black-box tests for algorithmic stability. Information and Inference: A Journal of the IMA, 12 0 (4): 0 2690--2719, 2023

    work page 2023

  35. [35]

    Bounding the smallest singular value of a random matrix without concentration

    Vladimir Koltchinskii and Shahar Mendelson. Bounding the smallest singular value of a random matrix without concentration. International Mathematics Research Notices, 2015 0 (23): 0 12991--13008, 2015

    work page 2015

  36. [36]

    Asymptotics for high dimensional regression m-estimates: fixed design results

    Lihua Lei, Peter J Bickel, and Noureddine El Karoui. Asymptotics for high dimensional regression m-estimates: fixed design results. Probability Theory and Related Fields, 172: 0 983--1079, 2018

    work page 2018

  37. [37]

    A non-asymptotic distributional theory of approximate message passing for sparse and robust regression

    Gen Li and Yuting Wei. A non-asymptotic distributional theory of approximate message passing for sparse and robust regression. arXiv preprint arXiv:2401.03923, 2024

    work page arXiv 2024

  38. [38]

    Causal and Selective Inference in Complex Statistical Models

    Shuangning Li. Causal and Selective Inference in Complex Statistical Models. Department of Statistics, Stanford University, 2022

    work page 2022

  39. [39]

    Spectrum-aware adjustment: A new debiasing framework with applications to principal components regression

    Yufan Li and Pragya Sur. Spectrum-aware adjustment: A new debiasing framework with applications to principal components regression. arXiv preprint arXiv:2309.07810, 2023

    work page arXiv 2023

  40. [40]

    Random linear estimation with rotationally-invariant designs: Asymptotics at high temperature

    Yufan Li, Zhou Fan, Subhabrata Sen, and Yihong Wu. Random linear estimation with rotationally-invariant designs: Asymptotics at high temperature. IEEE Transactions on Information Theory, 2023

    work page 2023

  41. [41]

    From soft-minoration to information-constrained optimal transport and spiked tensor models

    Jingbo Liu. From soft-minoration to information-constrained optimal transport and spiked tensor models. In 2023 IEEE International Symposium on Information Theory (ISIT), pages 666--671. IEEE, 2023

    work page 2023

  42. [42]

    Power analysis of knockoff filters for correlated designs

    Jingbo Liu and Philippe Rigollet. Power analysis of knockoff filters for correlated designs. Advances in Neural Information Processing Systems, 32, 2019

    work page 2019

  43. [43]

    Second-order converses via reverse hypercontractivity

    Jingbo Liu, Ramon Van Handel, and Sergio Verd \'u . Second-order converses via reverse hypercontractivity. Mathematical Statistics and Learning, 2 0 (2): 0 103--163, 2020

    work page 2020

  44. [44]

    Fast and powerful conditional randomization testing via distillation

    Molei Liu, Eugene Katsevich, Lucas Janson, and Aaditya Ramdas. Fast and powerful conditional randomization testing via distillation. Biometrika, 109 0 (2): 0 277--293, 2022

    work page 2022

  45. [45]

    Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion

    Cong Ma, Kaizheng Wang, Yuejie Chi, and Yuxin Chen. Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion. In International Conference on Machine Learning, pages 3345--3354. PMLR, 2018

    work page 2018

  46. [46]

    The distribution of the lasso: Uniform control over sparse balls and adaptive parameter tuning

    L \'e o Miolane and Andrea Montanari. The distribution of the lasso: Uniform control over sparse balls and adaptive parameter tuning. The Annals of Statistics, 49 0 (4): 0 2313--2335, 2021

    work page 2021

  47. [47]

    Universality of empirical risk minimization

    Andrea Montanari and Basil N Saeed. Universality of empirical risk minimization. In Conference on Learning Theory, pages 4310--4312. PMLR, 2022

    work page 2022

  48. [48]

    Vector approximate message passing for the generalized linear model

    Philip Schniter, Sundeep Rangan, and Alyson K Fletcher. Vector approximate message passing for the generalized linear model. In 2016 50th Asilomar conference on signals, systems and computers, pages 1525--1529, 2016

    work page 2016

  49. [49]

    The holdout randomization test for feature selection in black box models

    Wesley Tansey, Victor Veitch, Haoran Zhang, Raul Rabadan, and David M Blei. The holdout randomization test for feature selection in black box models. Journal of Computational and Graphical Statistics, 31 0 (1): 0 151--162, 2022

    work page 2022

  50. [50]

    Regularized linear regression: A precise analysis of the estimation error

    Christos Thrampoulidis, Samet Oymak, and Babak Hassibi. Regularized linear regression: A precise analysis of the estimation error. In Conference on Learning Theory, pages 1683--1709. PMLR, 2015

    work page 2015

  51. [51]

    On asymptotically optimal confidence regions and tests for high-dimensional models

    Sara van de Geer, Peter B \"u hlmann, Yaacov Ritov, and Ruben Dezeure. On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics, 42 0 (3): 0 1166--1202, 2014

    work page 2014

  52. [52]

    Probability in high dimension

    Ramon Van Handel. Probability in high dimension. Lecture Notes (Princeton University), 2014

    work page 2014

  53. [53]

    Estimation in rotationally invariant generalized linear models via approximate message passing

    Ramji Venkataramanan, Kevin K \"o gler, and Marco Mondelli. Estimation in rotationally invariant generalized linear models via approximate message passing. In International Conference on Machine Learning, pages 22120--22144. PMLR, 2022

    work page 2022

  54. [54]

    High-dimensional probability, 2009

    Roman Vershynin. High-dimensional probability, 2009

    work page 2009

  55. [55]

    High-dimensional probability: An introduction with applications in data science, volume 47

    Roman Vershynin. High-dimensional probability: An introduction with applications in data science, volume 47. Cambridge university press, 2018

    work page 2018

  56. [56]

    A Power and Prediction Analysis for Knockoffs with Lasso Statistics

    Asaf Weinstein, Rina Barber, and Emmanuel Candes. A power and prediction analysis for knockoffs with lasso statistics. arXiv preprint arXiv:1712.06465, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  57. [57]

    Controlling false discovery rate using gaussian mirrors

    Xin Xing, Zhigen Zhao, and Jun S Liu. Controlling false discovery rate using gaussian mirrors. Journal of the American Statistical Association, 118 0 (541): 0 222--241, 2023

    work page 2023

  58. [58]

    Confidence intervals for low dimensional parameters in high dimensional linear models

    Cun-Hui Zhang and Stephanie S Zhang. Confidence intervals for low dimensional parameters in high dimensional linear models. Journal of the Royal Statistical Society Series B: Statistical Methodology, 76 0 (1): 0 217--242, 2014

    work page 2014

  59. [59]

    Approximate message passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization

    Xinyi Zhong, Tianhao Wang, and Zhou Fan. Approximate message passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization. arXiv preprint arXiv:2110.02318, 2021

    work page arXiv 2021

  60. [60]

    Post-selection inference via algorithmic stability

    Tijana Zrnic and Michael I Jordan. Post-selection inference via algorithmic stability. The Annals of Statistics, 51 0 (4): 0 1666--1691, 2023

    work page 2023