Recognition in Hierarchical Models

Various proposals have recently been made which cast cortical processing in terms of hierarchical statistical generative models (Mumford, 1994; Kawato, 1993; Hinton & Zemel, 1994; Zemel, 1994; Hinton et al , 1995; Dayan et al , 1995; Olshausen & Field, 1996; Rao & Ballard, 1995). In the case of vision, these claim that top-down connections in the cortical hierarchy capture essential aspects of how the activities of neurons in primary sensory areas are generated by the contents of visually observed scenes. The counterpart to a generative model is its statistical inverse, called a recognition model (Hinton & Zemel, 1994). This takes low-level activities and produces probability distributions over the entities in the world that could have led to them, expressed as activities of neurons in higher visual areas that model the image generation process. Even if a generative model is computationally tractable, its associated recognition model may not be. In this paper, we study various di erent types of exact, sampling-based and approximate recognition models in the light of computational and cortical constraints.