Information processing with population codes

Pouget, A. Dayan, P. Zemel, R. (2000) Information processing with population codes. Nature Reviews Neuroscience 1: 125-132.

Place cells are a population code: Borst, Theunissen (1999). Visual features: orientation, color, direction of motion, depth and many other coded by population code: Usrey & Reid (1999), Zemel, Dayan, Pouget (1998). Motor commands in motor cortex: Tolhurst, Movshon Dean (1982). Leeches and crickets: Salinas & Abbott (1994).

Population codes are robust -- damage to single cell does not catastrophically harm information encoded. Other desirable properties: noise removal, short-term memory, nonlinear function.

Can decode population code with Bayesian maximization like models. Two types of maxima: Maximum a posterior (MAP) estimate: direction with highest probability (Maximize P(s|r)). Maximum likelihood (ML): maximize P(r|s). These are the same if the prior (P(s)) is flat -- i.e. no prior knowledge of s.

ML is optimal decoding method (Seung, Sompolinsky (1993), Deneve, Latham, Pouget (1999) [This will be a good one to do]), but requires substantial data to estimate tuning curves and noise distributions. Can use only preferred direction through 'voting' methods.

Estimation is like template matching MAP is cosine template match, ML template matches with template derived from tuning curve (this is why it is optimal). Neurons that have highest derivative have most influence over the decoding of the population code. Deneve et al 1999 shows how you can implement ML estimator in recurrent neural net.

A population code can form a basis set for all possible non-linear mappings. (basis like sin/cos is basis for fourier transform). Some unsupervised learning algorithms for learning the basis functions from data --  then the needed transformations can be formed from the basis functions. Olshausen & Field (1996), Bishop Svenson Williams (1998), Lewicki, Sejnowski (2000).

Basis function equivalence to population codes is why population codes are so computationally appealing. object recognition: Poggio & Edelman (1990). Object-centered representations: Salinas & Abbott (1997). sensorimotor transformations.

Two directions of motion will yield bimodal bump in population code if the directions are far apart, but only a single bump if motions are close together. ML would fail at decoding the two directions in this case.

Can reformulate population code to be representing a probability density function instead of a specific value. This could allow you to use the code to represent multiple motions by noting that the width of the distribution is wider, also allows for a form of Bayesian inference. However, there is no computational theory based on this idea like the basis function idea.