  The Ising Model has recently received much attention for the statistical
description of neural spike train data. In this paper, we propose and
demonstrate its use for building decoders capable of predicting, on a
millisecond timescale, the stimulus represented by a pattern of neural
activity. After fitting to a training dataset, the Ising decoder can be applied
"online" for instantaneous decoding of test data. While such models can be fit
exactly using Boltzmann learning, this approach rapidly becomes computationally
intractable as neural ensemble size increases. We show that several approaches,
including the Thouless-Anderson-Palmer (TAP) mean field approach from
statistical physics, and the recently developed Minimum Probability Flow
Learning (MPFL) algorithm, can be used for rapid inference of model parameters
in large-scale neural ensembles. Use of the Ising model for decoding, unlike
other problems such as functional connectivity estimation, requires estimation
of the partition function. As this involves summation over all possible
responses, this step can be limiting. Mean field approaches avoid this problem
by providing an analytical expression for the partition function. We
demonstrate these decoding techniques by applying them to simulated neural
ensemble responses from a mouse visual cortex model, finding an improvement in
decoder performance for a model with heterogeneous as opposed to homogeneous
neural tuning and response properties. Our results demonstrate the practicality
of using the Ising model to read out, or decode, spatial patterns of activity
comprised of many hundreds of neurons.
