Universal models for binary spike patterns using centered Dirichlet processesIl Memming Park, Evan Archer, Kenneth Latimer, & Jonathan W. Pillow 
Advances in Neural Information Processing Systems 26,
24632471. (2013)
Probabilistic models for binary spike patterns provide a powerful tool for understanding the statistical dependencies in largescale neural recordings. Maximum entropy (or "maxent") models, which seek to explain dependencies in terms of loworder interactions between neurons, have enjoyed remarkable success in modeling such patterns, particularly for small groups of neurons. However, these models are computationally intractable for large populations, and loworder maxent models have been shown to be inadequate for some datasets. 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 2^m binary patterns. We construct universal models using a Dirichlet process centered on a wellbehaved parametric base measure, which naturally combines the flexibility of a histogram and the parsimony of a parametric model. 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 equivalence between the cascaded logistic and the 2ndorder maxent or "Ising" model, making cascaded logistic a reasonable choice for base measure in a universal model. We illustrate the performance of these models using neural data. 
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