Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data

TL;DR

This paper introduces an adaptive group Lasso neural network approach for high-dimensional, time-dependent data, effectively identifying key variables and improving function approximation in dynamical systems.

Contribution

It develops a novel adaptive group Lasso deep neural network model with a proximal algorithm for efficient optimization, tailored for functions depending on few variables.

Findings

Outperforms recent state-of-the-art methods in empirical tests.

Effectively identifies active variables in high-dimensional data.

Achieves loss decay through the proposed optimization procedure.

Abstract

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.