Maximum Entropy Models from Phase Harmonic Covariances - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Maximum Entropy Models from Phase Harmonic Covariances

Résumé

We define maximum entropy models of non-Gaussian stationary random vectors from covariances of non-linear representations. These representations are calculated by multiplying the phase of Fourier or wavelet coefficients with harmonic integers, which amounts to compute a windowed Fourier transform along their phase. Rectifiers in neural networks compute such phase windowing. The covariance of these harmonic coefficients capture dependencies of Fourier and wavelet coefficients across frequencies, by canceling their random phase. We introduce maximum entropy models conditioned by such covariances over a graph of local interactions. These models are approximated by transporting an initial maximum entropy measure with a gradient descent. The precision of wavelet phase harmonic models is numerically evaluated over turbulent flows and other non-Gaussian stationary processes.
Fichier principal
Vignette du fichier
PhaseStat49.pdf (2.16 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02982280 , version 1 (28-10-2020)
hal-02982280 , version 2 (29-01-2021)

Identifiants

  • HAL Id : hal-02982280 , version 1

Citer

Sixin Zhang, Stéphane Mallat. Maximum Entropy Models from Phase Harmonic Covariances. 2020. ⟨hal-02982280v1⟩
53 Consultations
71 Téléchargements

Partager

Gmail Facebook X LinkedIn More