  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.
