The problem of perfect predictors in statistical spike train models

TL;DR

This paper examines the challenge of perfect predictors in GLMs for spike train data, proposing multiple approaches like regularization and Bayesian methods, with practical applications to neural data.

Contribution

It introduces and compares various methods to handle perfect predictors in spike train models, guiding method selection based on specific analysis needs.

Findings

Regularization improves parameter estimation in perfect predictor scenarios.

Bayesian estimation offers a robust alternative to maximum likelihood.

Different methods have distinct advantages depending on the data and goals.

Abstract

Generalized Linear Models (GLMs) have been used extensively in statistical models of spike train data. However, the maximum likelihood estimates of the model parameters and their uncertainty, can be challenging to compute in situations where response and non-response can be separated by a single predictor or a linear combination of multiple predictors. Such situations are likely to arise in many neural systems due to properties such as refractoriness and incomplete sampling of the signals that influence spiking. In this paper, we describe multiple classes of approaches to address this problem: using an optimization algorithm with a fixed iteration limit, computing the maximum likelihood solution in the limit, Bayesian estimation, regularization, change of basis, and modifying the search parameters. We demonstrate a specific application of each of these methods to spiking data from rat somatosensory cortex and discuss the advantages and disadvantages of each. We also provide an example of a roadmap for selecting a method based on the problem's particular analysis issues and scientific goals.