The projected belief network (PBN) is a generative stochastic network with tractable likelihood function based on a feed-forward neural network (FFNN). The generative function operates by "backing up" through the FFNN. The PBN is two networks in one, a FFNN that operates in the forward direction, and a generative network that operates in the backward direction. Both networks co-exist based on the same parameter set, have their own cost functions, and can be separately or jointly trained. The PBN therefore has the potential to possess the best qualities of both discriminative and generative classifiers. To realize this potential, a separate PBN is trained on each class, maximizing the generative likelihood function for the given class, while minimizing the discriminative cost for the FFNN against "all other classes". This technique, called discriminative alignment (PBN-DA), aligns the contours of the likelihood function to the decision boundaries and attains vastly improved classification performance, rivaling that of state of the art discriminative networks. The method may be further improved using a hidden Markov model (HMM) as a component of the PBN, called PBN-DA-HMM. This paper provides a comprehensive treatment of PBN, PBN-DA, and PBN-DA-HMM. In addition, the results of two new classification experiments are provided. The first experiment uses air-acoustic events, and the second uses underwater acoustic data consisting of marine mammal calls. In both experiments, PBN-DA-HMM attains comparable or better performance as a state of the art CNN, and attain a factor of two error reduction when combined with the CNN.

翻译：投影信念网络（PBN）是一种基于前馈神经网络（FFNN）、具有可处理似然函数的生成式随机网络。其生成函数通过FFNN的“反向传播”机制运行。PBN实质上是“双网合一”：前向运作的FFNN与反向运作的生成网络共享同一参数集，各自拥有独立代价函数，可分别或联合训练。因此，PBN具有同时集成判别式与生成式分类器最佳特性的潜能。为实现这一潜能，针对每个类别分别训练独立的PBN，在最大化该类生成似然函数的同时，最小化FFNN针对“所有其他类别”的判别代价。这种称为判别对齐（PBN-DA）的技术，通过将似然函数等高线与决策边界对齐，显著提升了分类性能，达到与最先进判别网络相媲美的水平。进一步采用隐马尔可夫模型（HMM）作为PBN组件的方法（称为PBN-DA-HMM）可改进该技术。本文对PBN、PBN-DA及PBN-DA-HMM进行了系统性阐述，并提供了两项新分类实验的结果。第一项实验使用空气声学事件数据，第二项实验使用海洋哺乳动物叫声的水声数据。两项实验均表明：PBN-DA-HMM的性能可与最先进CNN相当甚至更优，且与CNN联合使用时误差可降低两倍。