Detecting Multiple Change Points Using Adaptive Regression Splines With Application to Neural Recordings.

Hazem Toutounji,Daniel Durstewitz

doi:10.3389/fninf.2018.00067

Abstract

Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such change points in time series statistics have been developed over the years, in addition to test criteria to evaluate their significance. Issues to consider when developing change point analysis methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many changes as contained in potentially high-dimensional time series. Here, a general method called Paired Adaptive Regressors for Cumulative Sum is developed for detecting multiple change points in the mean of multivariate time series. The method's advantages over alternative approaches are demonstrated through a series of simulation experiments. This is followed by a real data application to neural recordings from rat medial prefrontal cortex during learning. Finally, the method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is discussed, along with potential drawbacks and suggestions to remedy them.

Highlights

Stationary data are the exception rather than the rule in many areas of science (Paillard, 1998; Elsner et al, 2004; Shah et al, 2007; Aston and Kirch, 2012; Stock and Watson, 2014; Fan et al, 2015; Latimer et al, 2015; Gärtner et al, 2017)
A single change points (CPs) was identified by using the cumulative sum (CUSUM) method and estimating the PARCS1 model, both followed by bootstrap significance testing with B = 10,000 permutations, nominal significance level α = 0.05, and blocks of size k = 1
We showed that PARCS substantially reduces center bias in estimating CPs compared to the most basic specification of the CUSUM method, and presented conditions under which it compares to or outperforms the maximum-likelihood CUSUM statistic

Summary

Introduction

Stationary data are the exception rather than the rule in many areas of science (Paillard, 1998; Elsner et al, 2004; Shah et al, 2007; Aston and Kirch, 2012; Stock and Watson, 2014; Fan et al, 2015; Latimer et al, 2015; Gärtner et al, 2017). Time series statistics often change, sometimes abruptly, due to transitions in the underlying system dynamics, adaptive processes or external factors In neuroscience, both behavioral time series (Smith et al, 2004; Durstewitz et al, 2010; Powell and Redish, 2016) and their neural correlates (Roitman and Shadlen, 2002; Durstewitz et al, 2010; Gärtner et al, 2017) exhibit strongly nonstationary features which relate to important cognitive processes such as learning (Smith et al, 2004; Durstewitz et al, 2010; Powell and Redish, 2016) and perceptual decision making (Roitman and Shadlen, 2002; Latimer et al, 2015; Hanks and Summerfield, 2017). They are of wide interest to both statistical data analysis and the study of dynamical systems, and are commonly referred to as change points (CPs; Chen and Gupta, 2012)

Methods

Results

Conclusion