A Kernel-Expanded Stochastic Neural Network
This addresses fundamental training and uncertainty problems in machine learning for researchers and practitioners, though it appears incremental as it builds on existing methods like SVR and latent variable models.
The paper tackles the issues of local minima and uncertainty assessment in deep neural networks by proposing the kernel-expanded stochastic neural network (K-StoNet), which incorporates support vector regression and reformulates the network as a latent variable model, resulting in theoretical guarantees for global convergence and easier uncertainty quantification.
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.