Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn Neural Networks
This work addresses the challenge of probing and learning neural networks more effectively for researchers and practitioners in machine learning, though it appears incremental as it builds on existing generative and discriminative modeling concepts.
The authors tackled the problem of understanding and improving neural networks by proposing the HOPE framework, which models hidden layers as a hybrid of orthogonal projection and mixture models, and demonstrated significant performance gains over state-of-the-art methods on tasks like MNIST and TIMIT.
In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative modeling framework. The HOPE model itself can be learned unsupervised from unlabelled data based on the maximum likelihood estimation as well as discriminatively from labelled data. More interestingly, we have shown the proposed HOPE models are closely related to neural networks (NNs) in a sense that each hidden layer can be reformulated as a HOPE model. As a result, the HOPE framework can be used as a novel tool to probe why and how NNs work, more importantly, to learn NNs in either supervised or unsupervised ways. In this work, we have investigated the HOPE framework to learn NNs for several standard tasks, including image recognition on MNIST and speech recognition on TIMIT. Experimental results have shown that the HOPE framework yields significant performance gains over the current state-of-the-art methods in various types of NN learning problems, including unsupervised feature learning, supervised or semi-supervised learning.