Gaussian Bounds for Noise Correlation of Functions
By Elchanan Mossel. Geometric and Functional Analysis, 2007
153 citations recorded by the source corpus.
In this paper we derive tight bounds on the expected value of products of low influence functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated probability spaces, on a generalization of an invariance principle recently obtained with O’Donnell and Oleszkiewicz for multilinear polynomials with low influences and bounded degree and on properties of multi-dimensional Gaussian distributions.
Subfields: Artificial Intelligence, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0c1384e60ac5184c4a6add660493b15d33982243
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Giovanni Peccati
- Ivan Nourdin
- Vitaly Feldman
- Prasad Raghavendra
- Yi Wu
- Joe Neeman
- Anindya De
- Gesine Reinert
In Finance
- Ivan Nourdin
- Giovanni Peccati
- Gesine Reinert
- Joe Neeman
- Anindya De
- Elchanan Mossel
- Prasad Raghavendra
- David Nualart
In Statistics and Probability
- Giovanni Peccati
- Ivan Nourdin
- Gesine Reinert
- Joe Neeman
- Anindya De
- Prasad Raghavendra
- Elchanan Mossel
- Vitaly Feldman
Citations in the corpus
- Decidability of Non-interactive Simulation of Joint Distributions (2016, unknown): “13”
- Agnostic Learning of Monomials by Halfspaces Is Hard (2009, background): “While invariance principles have been shown in various settings by [36], [11], [35], we restate a version of the principle well suited for our application.”
- A quantitative Arrow theorem (2009, background): “1 in [13] this can be done with η = C (1 − |ρ|)ǫ log(1/ǫ) .”
- Non interactive simulation of correlated distributions is decidable (2017, methodology): “Their argument uses quite general tools from Boolean function analysis such as the invariance principle [MOO10, Mos10] and regularity lemmas for low-degree polynomials [DSTW10, DDS14].”
- Invariance Principles for Homogeneous Sums: Universality of Gaussian Wiener Chaos (2009, methodology): “Our techniques combine an invariance principle by Mossel, O’Donnell and Oleszkiewicz with a refinement of some recent results by Nourdin and Peccati, about the approx- imation of laws of random variables belonging to a fixed (Gaussian) Wiener chaos.”