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In structured classification problems, there is a direct conflict between expressive models and efficient inference: while graphical models such as Markov random fields or factor graphs can represent arbitrary dependences among instance labels, the cost of inference via belief propagation in these models grows rapidly as the graph structure becomes more complicated. One important source of complexity in belief propagation is the need to marginalize large factors to compute messages. This operation takes time exponential in the number of variables in the factor, and can limit the expressiveness of the models we can use. In this paper, we study a new class of potential functions, which we call decomposable k-way potentials, and provide efficient algorithms for computing messages from these potentials during belief propagation. We believe these new potentials provide a good balance between expressive power and efficient inference in practical structured classification problems. We discuss three instances of decomposable potentials: the associative Markov network potential, the nested junction tree, and a new type of potential which we call the voting potential. We use these potentials to classify images of protein subcellular location patterns in groups of cells. Classifying subcellular location patterns can help us answer many important questions in computational biology, including questions about how various treatments affect the synthesis and behavior of proteins and networks of proteins within a cell. Our new representation and algorithm lead to substantial improvements in both inference speed and classification accuracy.

Graphical Models for Structured Classification, with an Application to Interpreting Images of Protein Subcellular Location Patterns