Recognition in Hierarchical Models
Peter Dayan
In F Cucker & M Shub, editors,
Foundations of Computational Mathematics. Berlin, Germany:
Springer.
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 different types of exact, sampling-based and
approximate recognition models in the light of computational and
cortical constraints.
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