**Il Memming Park**

Wednesday 10th July 2013

**Time: 4pm**

** **

Basement Seminar Room

Alexandra House, 17 Queen Square, London, WC1N 3AR

**Universal binary models of population spiking for distribution and entropy estimation**

Entropy estimators and probabilistic models for binary spike patterns are key tools for studying the neural code and variability. Neural responses have characteristic statistical structure that generic entropy estimators fail to exploit, and popular binary distribution models such as the Ising model have rigid assumptions and are computationally intractable for large populations. To overcome these limitations, we propose a family of "universal" models for binary spike patterns, where universality refers to the ability to model arbitrary distributions over all possible binary patterns. We construct universal binary models using a Dirichlet process centered on a well-behaved parametric base measure over the binary words, which naturally combines the flexibility of a histogram and the parsimony of a parametric model. For distribution estimation, we derive computationally efficient inference methods using Bernoulli and cascaded logistic base measures, which scale tractably to large populations. We also establish a condition for the equivalence between the cascaded logistic and the Ising model, making cascaded logistic a reasonable choice for base measure in a universal binary model. For entropy estimation, we devise a compact representation of the data and two simple priors that allow for computationally efficient Bayesian least squares estimator for large populations. We demonstrate the flexibility and performance of those estimators on simulated and real neural recordings.