Hierarchical compositional feature learning
This work addresses the challenge of unsupervised feature learning in binary images, offering a novel inference method that simplifies tasks like classification and inpainting, though it is incremental in its approach to generative models.
The authors tackled the problem of unsupervised discovery and disentanglement of hierarchical building blocks in binary images using a hierarchical compositional network (HCN), achieving this through max-product message passing for inference and learning without requiring EM.
We introduce the hierarchical compositional network (HCN), a directed generative model able to discover and disentangle, without supervision, the building blocks of a set of binary images. The building blocks are binary features defined hierarchically as a composition of some of the features in the layer immediately below, arranged in a particular manner. At a high level, HCN is similar to a sigmoid belief network with pooling. Inference and learning in HCN are very challenging and existing variational approximations do not work satisfactorily. A main contribution of this work is to show that both can be addressed using max-product message passing (MPMP) with a particular schedule (no EM required). Also, using MPMP as an inference engine for HCN makes new tasks simple: adding supervision information, classifying images, or performing inpainting all correspond to clamping some variables of the model to their known values and running MPMP on the rest. When used for classification, fast inference with HCN has exactly the same functional form as a convolutional neural network (CNN) with linear activations and binary weights. However, HCN's features are qualitatively very different.