LAUSR

In this paper, a unified Bayesian max-margin discriminant projection framework is proposed, which is able to jointly learn the discriminant feature space and the max-margin classifier with different relationships between the latent representations and observations. We assume that the latent representation follows a normal distribution whose sufficient statistics are functions of the observations. The function can be flexibly realized through either shallow or deep structures. The shallow structure includes linear, nonlinear kernel-based functions, and even the convolutional projection, which can be further trained layerwisely to build a multilayered convolutional feature learning model. To take the advantage of the deep neural networks, especially their highly expressive ability and efficient parameter learning, we integrate Bayesian modeling and the popular neural networks, for example, mltilayer perceptron and convolutional neural network, to build an end-to-end Bayesian deep discriminant projection under the proposed framework, which degenerated into the existing shallow linear or convolutional projection with the single-layer structure. Moreover, efficient scalable inferences for the realizations with different functions are derived to handle large-scale data via a stochastic gradient Markov chain Monte Carlo. Finally, we demonstrate the effectiveness and efficiency of the proposed models by the experiments on real-world data, including four image benchmarks (MNIST, CIFAR-10, STL-10, and SVHN) and one measured radar high-resolution range profile dataset, with the detailed analysis about the parameters and computational complexity.