A Kernel-Expanded Stochastic Neural Network

TL;DR

The paper introduces K-StoNet, a novel neural network model that integrates support vector regression and kernel methods to overcome local minima issues and facilitate uncertainty quantification, with proven convergence guarantees.

Contribution

It presents a new kernel-expanded stochastic neural network model that reformulates training as convex problems and provides theoretical convergence guarantees.

Findings

K-StoNet converges to the global optimum asymptotically.

The model effectively quantifies prediction uncertainty.

Experimental results demonstrate improved training and prediction performance.

Abstract

The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we propose the so-called kernel-expanded stochastic neural network (K-StoNet) model, which incorporates support vector regression (SVR) as the first hidden layer and reformulates the neural network as a latent variable model. The former maps the input vector into an infinite dimensional feature space via a radial basis function (RBF) kernel, ensuring absence of local minima on its training loss surface. The latter breaks the high-dimensional nonconvex neural network training problem into a series of low-dimensional convex optimization problems, and enables its prediction uncertainty easily assessed. The K-StoNet can be easily trained using the imputation-regularized optimization (IRO) algorithm. Compared to traditional deep neural networks, K-StoNet possesses a theoretical guarantee to asymptotically converge to the global optimum and enables the prediction uncertainty easily assessed. The performances of the new model in training, prediction and uncertainty quantification are illustrated by simulated and real data examples.