Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data
This addresses function approximation in high-dimensional dynamical systems for computational modeling applications, representing an incremental improvement over existing regularization methods.
The paper tackles high-dimensional function approximation where target functions depend on few variables or linear combinations, proposing an adaptive group Lasso deep neural network with a proximal optimization algorithm. Empirical results show it outperforms state-of-the-art methods including sparse dictionary matrix and other neural network approaches.
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.