Universal models for binary spike patterns using centered Dirichlet processes

Probabilistic models for binary spike patterns provide a powerful tool for understanding the statistical dependencies in large-scale neural recordings. Maximum entropy (or "maxent'') models, which seek to explain dependencies in terms of low-order 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 low-order 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 well-behaved 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 cascade-logistic base measures, which scale tractably to large populations. We also establish a condition for equivalence between the cascade-logistic and the 2nd-order maxent or "Ising'' model, making cascade-logistic a reasonable choice for base measure in a universal model. We illustrate the performance of these models using neural data.