Multistep Inference for Generalized Linear Spiking Models Curbs Runaway Excitation

Generalized linear models (GLMs) are useful tools to capture the characteristic features of spiking neurons; however, the long-term prediction of an autoregressive GLM inferred through maximum likelihood (ML) can be subject to runway self-excitation. We explain here that this runaway excitation is a consequence of the one-step-ahead ML inference used in estimating the parameters of the GLM. Alternatively, inference techniques that incorporate the likelihood of spiking multiple steps ahead in the future can alleviate this instability. We formulate a multi-step log-likelihood (MSLL) as an alternative objective for fitting spiking data. We maximize MSLL to infer an autoregressive GLM for individual spiking neurons recorded from the lateral intraparietal (LIP) area of monkeys during a perceptual decision-making task. While ML inference is shown to produce a GLM with poor fits of the neuron's interspike intervals and autocorrelation, in addition to its runaway excitation, MSLL fit models show a substantial improvement in interval statistics and stable spiking.