notesum.ai

Published at December 4

stat.ML

cs.LG

Released Date: December 4, 2024

Authors: Yuan Gao¹, Quanjun Lang¹, Fei Lu²

Aff.: ¹Not provided; ²University

Notations	Description
$R_{\phi}[\cdot],\quad v_{\phi}[\cdot]$	Operators $R_{\phi}[\cdot]:\mathbb{X}\to\mathbb{Y},\quad v_{\phi}[\cdot]:\mathbb{X}\to% \mathbb{Y}^{*}$
$\phi$	Function-valued parameter in operator, to be estimated from data
$\langle{f,v}\rangle,\,\quad\langle{\cdot,\cdot}\rangle_{H}$	Dual operation with $f\in\mathbb{Y},v\in\mathbb{Y}^{*}$ ; inner product in $H$
$\mathcal{E}(\cdot)$ $E_{\phi}(\cdot)$	$\mathbb{R}$ -valued loss function and energy function
$\mathcal{P}_{2}(\mathbb{R}^{d})$	The space of probability measures with finite second moments