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 layer wisely 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.

中文翻译：

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深度最大边缘判别投影


本文提出了一种统一的贝叶斯最大边缘判别投影框架，该框架能够联合学习判别特征空间和最大边缘分类器以及潜在表示和观察之间的不同关系。我们假设潜在表示遵循正态分布，其足够的统计量是观测值的函数。该功能可以通过浅层或深层结构灵活实现。浅层结构包括线性、非线性基于核的函数，甚至卷积投影，可以进一步明智地进行层训练以构建多层卷积特征学习模型。为了利用深度神经网络的优势，特别是其高表达能力和高效的参数学习，我们将贝叶斯建模和流行的神经网络（例如多层感知器和卷积神经网络）结合起来，构建端到端的贝叶斯深度神经网络所提出的框架下的判别投影，退化为现有的单层结构的浅线性或卷积投影。此外，通过随机梯度马尔可夫链蒙特卡罗，导出了针对不同函数实现的有效可扩展推理，以处理大规模数据。最后，我们通过真实世界数据的实验证明了所提出模型的有效性和效率，包括四个图像基准（MNIST、CIFAR-10、STL-10和SVHN）和一个测量的雷达高分辨率距离剖面数据集，对参数和计算复杂度进行了详细分析。