Hierarchical Bayesian inference in the visual cortex

The paper titled Hierarchical Bayesian inference in the visual cortex by Tai Sing Lee and David Mumford is already a classic. This was one of the first papers that really got me into thinking of brain from a Hierarchical Bayesian perspective. I had read several papers on the Bayesian aspect of the neocortex by the time this paper came up in the journal club at the Redwood Neuroscience Institute. But many of those papers left me unsatisfied because they were explaining isolated phenomena from a Bayesian perspective. I was left wondering whether the Bayesian method was just another fancy way to fit the data or whether it had any real explanatory power. This paper from Lee and Mumford brought many things together for me.  The paper is very easy to read and I highly recommend it for those who have serious interest in understanding the brain.
It is a fairly high level paper — the ┬ámodels in the paper are not concrete enough to be implemented or validated. That doesn’t diminish the importance of this paper though. However, because of its high-level, all-encompassing nature, I sometimes have a tough time answering questions like “How does your model differ from the model Lee and Mumford presented?”. It is tough to differ from the models in this paper. You can only add details (very important ones) that are mostly consistent with this paper.
One of the important omissions in this paper is that it doesn’t grapple with the question of invariant representations, which is an important property of the visual cortex. The word “invariance” appears only once in this paper. One of my early papers tried to bring the idea of invariant representations into this framework.
Hierarchical Bayesian inference in the visual cortex
Tai Sing Lee and David Mumford

Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spa- tiotemporal filters that extract local features from a visual scene. The extracted information is then chan- neled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas.

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