Generation of surrogate event sequences via joint distribution of successive inter-event intervals

Abstract

The study of many dynamical systems relies on the analysis of experimentally-recorded sequences of events for which information is encoded in the sequence of interevent intervals. A correct interpretation of the results of the application of analytical techniques to these sequences requires the assessment of statistical significance. In most cases, the corresponding null-hypothesis distribution is unknown, thus forbidding an evaluation of the significance. An alternative solution, which is efficient in the case of continuous signals, is provided by the generation of surrogate data that share statistical and spectral properties with the original dataset. However, in the case of event sequences, the available algorithms for the generation of surrogate data can become cumbersome and computationally demanding. In this work, we present a new method for the generation of surrogate event sequences that relies on the joint distribution of successive interevent intervals. Our method, which was tested on both synthetic and experimental sequences, performs equally well or even better than conventional methods in terms of interevent interval distribution and autocorrelation while abating the computational time by at least one order of magnitude.

The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges

“…Surrogate testing is a crucial tool to ensure the reliability of the results (Schreiber and Schmitz, 2000). Nevertheless, although extensions and new development of surrogate techniques can help to avoid misinterpretations about the strength of an interaction (Andrzejak et al, 2003;Lancaster et al, 2018;Ricci et al, 2019), causal relationships are notoriously difficult to identify (Mayr, 1961;Laland et al, 2011). Although some approaches have been proposed to test the significance of directionality indices (Thiel et al, 2006;Romano et al, 2009;Faes et al, 2010;Jelfs and Chan, 2017), we still lack reliable surrogate techniques for directionality indices as well as for techniques to detect and characterize coupling functions.…”

Comparing surrogates to evaluate precisely timed higher-order spike correlations

“…Methods such as spike train randomization (within single trials; Grün et al, 2003), spike exchange (across neurons or trials; Harrison et al, 2007;Smith and Kohn, 2008), ISI shuffling (within and across trials; Ikegaya et al, 2004;Masuda and Aihara, 2003;Nádasdy et al, 1999;Rivlin-Etzion et al, 2006), spike shuffling across neurons (within-trial; Ikegaya et al, 2004;Nádasdy et al, 1999) do not fulfill our requirements (Grün, 2009). Other methods are designed to preserve the auto-correlation of a spike train, with the assumption of stationarity and the Markov property of a process (Ricci et al, 2019;Perinelli et al, 2020). Some studies have already shown evidence of problems arising from the application of uniform dithering, such as the non-preservation of the ISI distribution (Louis et al, 2010a), in particular in the case of the Poisson process (Platkiewicz et al, 2017), but not in the context of multiple parallel spike trains, or in the context of binarization.…”

“…Due to the results of these studies, we have concentrated on surrogate techniques that preserve the firing rate profile of the original neurons, but methods such as spike train randomization (within single trials, [26]), spike exchange (across neurons or trials, [59,62]), ISI shuffling (within and across trials, [63][64][65][66]), spike shuffling across neurons (within-trial, [63,65]) do not fulfill our requirements [4]. Other methods are designed to preserve the auto-correlation of a spike train, with the assumption of stationarity and Markovianity of a process [67,68]. Some studies also already evidenced problems arising from the application of uniform dithering, such as the non-preservation of the ISI distribution [35], in particular in the case of the Poisson process [69], but not in the context of multiple parallel spike trains, or in the context of binarization.…”

A measure of concurrent neural firing activity based on mutual information

“…The statistical significance of the synchrony values computed in simulated and experimental data was assessed, in the context of statistical hypothesis testing, computing the CFI MI index for the analyzed pair of spike trains and over a set of surrogate pairs generated under the null hypothesis of uncorrelated trains. Surrogate spike trains were generated using a recently proposed method specifically designed for point processes, denoted as JOint DIstribution of successive inter-event intervals (JODI) (Ricci et al, 2019). The JODI algorithm generates, in a reliable and computationally efficient way, surrogate data retaining the same amplitude distribution and approximating the auto-correlation of the original inter-event intervals, while destroying any coupling.…”

“…The software implementation of the proposed approach, including the algorithms for binary state representation of the spiking activity (Mijatović et al, 2018), computation of CFI MI index, and assessment of its statistical significance based on surrogate data analysis (Ricci et al, 2019), are collected in the CFI MI MAT-LAB toolbox, which can be freely downloaded from https://github.com/mijatovicg/CFI-MI.…”