Carmin.tv

Mathematics
and Interactions

Please leave your feedback in order for us to improve your experience !
Not Only Scalar Curvature Seminar
58 videos

Not Only Scalar Curvature Seminar

Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday
8 videos

Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
2 videos

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models

Lean for the curious mathematician / Lean pour mathématiciens
4 videos

Lean for the curious mathematician / Lean pour mathématiciens

All the collections
CIMPA
CIRM
IHES
IHP
LMR
SMF
All the institutions
Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Collection Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Organizer(s) Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Date(s) 15/06/2020 - 19/06/2020
linked URL https://www.cirm-math.com/cirm-virtual-event-2146.html
00:00:00 / 00:00:00
16 25

De-biasing arbitrary convex regularizers and asymptotic normality

By Pierre C. Bellec

A new Central Limit Theorem (CLT) is developed for random variables of the form ξ=z⊤f(z)−divf(z) where z∼N(0,In). The normal approximation is proved to hold when the squared norm of f(z) dominates the squared Frobenius norm of ∇f(z) in expectation. Applications of this CLT are given for the asymptotic normality of de-biased estimators in linear regression with correlated design and convex penalty in the regime p/n→γ∈(0,∞). For the estimation of linear functions ⟨a,β⟩ of the unknown coefficient vector β, this analysis leads to asymptotic normality of the de-biased estimate for most normalized directions a0, where "most" is quantified in a precise sense. This asymptotic normality holds for any coercive convex penalty if γ<1 and for any strongly convex penalty if γ≥1. In particular the penalty needs not be separable or permutation invariant.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19640503
  • Cite this video Bellec, Pierre C. (05/06/2020). De-biasing arbitrary convex regularizers and asymptotic normality. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19640503
  • URL https://dx.doi.org/10.24350/CIRM.V.19640503

Domain(s)

Bibliography

  • BELLEC, Pierre C. et ZHANG, Cun-Hui. Second order Poincar\'e inequalities and de-biasing arbitrary convex regularizers when $ p/n\to\gamma$. arXiv preprint arXiv:1912.11943, 2019. - https://arxiv.org/abs/1912.11943
  • BELLEC, Pierre C. et ZHANG, Cun-Hui. De-biasing the lasso with degrees-of-freedom adjustment. arXiv preprint arXiv:1902.08885, 2019. - https://arxiv.org/abs/1902.08885

Document(s)

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Copyright Carmin.tv 2024
By browsing our website, you accept the use of cookies to improve your experience. Find out more about our privacy policy.
Approve
Give feedback