  Probabilistic graphical models are traditionally known for their successes in
generative modeling. In this work, we advocate layered graphical models (LGMs)
for probabilistic discriminative learning. To this end, we design LGMs in close
analogy to neural networks (NNs), that is, they have deep hierarchical
structures and convolutional or local connections between layers. Equipped with
tensorized truncated variational inference, our LGMs can be efficiently trained
via backpropagation on mainstream deep learning frameworks such as PyTorch. To
deal with continuous valued inputs, we use a simple yet effective soft-clamping
strategy for efficient inference. Through extensive experiments on image
classification over MNIST and FashionMNIST datasets, we demonstrate that LGMs
are capable of achieving competitive results comparable to NNs of similar
architectures, while preserving transparent probabilistic modeling.

Machine Learning;Machine Learning