<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Nicholas Richardson</style></author><author><style face="normal" font="default" size="100%">Lam Si Tung Ho</style></author><author><style face="normal" font="default" size="100%">Giang Tran</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data</style></title><secondary-title><style face="normal" font="default" size="100%">Sampling Theory, Signal Processing, and Data Analysis</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2108.10825</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In this paper, we propose an adaptive group Lasso deep neural network for high-dimensional function approximation where input data are generated from a dynamical system and the target function depends on few active variables or few linear combinations of variables. We approximate the target function by a deep neural network and enforce an adaptive group Lasso constraint to the weights of a suitable hidden layer in order to represent the constraint on the target function. We utilize the proximal algorithm to optimize the penalized loss function. Using the non-negative property of the Bregman distance, we prove that the proposed optimization procedure achieves loss decay. Our empirical studies show that the proposed method outperforms recent state-of-the-art methods including the sparse dictionary matrix method, neural networks with or without group Lasso penalty.</style></abstract></record></records></xml>