Gaussian averages of interpolated bodies and applications to approximate reconstruction

Y. Gordon; A. E. Litvak; S. Mendelson; A. Pajor

doi:10.1016/j.jat.2007.04.007

Gaussian averages of interpolated bodies and applications to approximate reconstruction

Y. Gordon, A. E. Litvak^*, S. Mendelson, A. Pajor

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of B_pⁿ with ρ B_qⁿ for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of B_{p ∞}ⁿ with ρ B₂ⁿ for 0 < p ≤ 1 and ρ > 0. We present an application of this result to a statistical problem known as the approximate reconstruction problem.

Original language	English
Pages (from-to)	59-73
Number of pages	15
Journal	Journal of Approximation Theory
Volume	149
Issue number	1
DOIs	https://doi.org/10.1016/j.jat.2007.04.007
Publication status	Published - Nov 2007

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10.1016/j.jat.2007.04.007

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title = "Gaussian averages of interpolated bodies and applications to approximate reconstruction",

abstract = "We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bpn with ρ Bqn for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of Bp ∞n with ρ B2n for 0 < p ≤ 1 and ρ > 0. We present an application of this result to a statistical problem known as the approximate reconstruction problem.",

keywords = "{"}Low M-estimate{"}, Approximate reconstruction, Diameter of a section, Gaussian averages, Gaussian process, Gelfand widths, Interpolation, Learning theory",

author = "Y. Gordon and Litvak, {A. E.} and S. Mendelson and A. Pajor",

year = "2007",

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doi = "10.1016/j.jat.2007.04.007",

language = "English",

volume = "149",

pages = "59--73",

journal = "Journal of Approximation Theory",

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T1 - Gaussian averages of interpolated bodies and applications to approximate reconstruction

AU - Gordon, Y.

AU - Litvak, A. E.

AU - Mendelson, S.

AU - Pajor, A.

PY - 2007/11

Y1 - 2007/11

N2 - We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bpn with ρ Bqn for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of Bp ∞n with ρ B2n for 0 < p ≤ 1 and ρ > 0. We present an application of this result to a statistical problem known as the approximate reconstruction problem.

AB - We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bpn with ρ Bqn for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of Bp ∞n with ρ B2n for 0 < p ≤ 1 and ρ > 0. We present an application of this result to a statistical problem known as the approximate reconstruction problem.

KW - "Low M-estimate"

KW - Approximate reconstruction

KW - Diameter of a section

KW - Gaussian averages

KW - Gaussian process

KW - Gelfand widths

KW - Interpolation

KW - Learning theory

UR - http://www.scopus.com/inward/record.url?scp=35648994961&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2007.04.007

DO - 10.1016/j.jat.2007.04.007

M3 - Article

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VL - 149

SP - 59

EP - 73

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 1

ER -

Gaussian averages of interpolated bodies and applications to approximate reconstruction

Abstract

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