Probabilistic Label Relation Graphs with Ising Models

We consider classification problems in which the label space has structure. A common example is hierarchical label spaces, corresponding to the case where one label subsumes another (e.g., animal subsumes dog). But labels can also be mutually exclusive (e.g., dog vs cat) or unrelated (e.g., furry, carnivore). In our prior work, we introduced the notion of a HEX graph, which is a way of encoding hierarchy and exclusion relations between labels into a conditional random field (CRF). We combined the CRF with a deep neural network (DNN), resulting in state of the art results when applied to visual object classification problems where the training labels were drawn from different levels of the ImageNet hierarchy (e.g., an image might be labeled with the basic level category ``dog'', rather than the more specific label ``husky''). In this paper, we extend the HEX model to allow for soft or probabilistic relations between labels, which is useful when there is uncertainty about the relationship between two labels (e.g., a penguin is ``sort of'' a subclass of birds, but not to the same degree as a robin or sparrow). We call our new model pHEX, for probabilistic HEX. We show that the pHEX graph can be converted to an Ising model, which allows us to use existing off-the-shelf inference methods (in contrast to the HEX method, which needed specialized inference algorithms). Experimental results show significant improvements in a number of large-scale object classification tasks.