Modeling and Analysis of Neural Spike Trains

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Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes

Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use direct or nonlinear transform of standard MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.Comment: Conference on Uncertainty in Artificial Intelligence 202

On the role of theory and modeling in neuroscience

In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community

Statistical Identification of Synchronous Spiking

In some parts of the nervous system, especially in the periphery, spike timing in response to a stimulus, or in production of muscle activity, is highly precise and reproducible. Elsewhere, neural spike trains may exhibit substantial variability when examined across repeated trials. There are many sources of the apparent variability in spike trains, ranging from subtle changes in experimental conditions to features of neural computation that are basic objects of scientific interest. When variation is large enough to cause potential confusion about apparent timing patterns, careful statistical analysis can be critically important. In this chapter we discuss statistical methods for analysis and interpretation of synchrony, by which we mean the approximate temporal alignment of spikes across two or more spike trains. Other kinds of timing patterns are also of interest [2, 57, 74, 69, 23], but synchrony plays a prominent role in the literature, and the principles that arise from consideration of synchrony can be applied in other contexts as well. The methods we describe all follow the general strategy of handling imperfect reproducibility by formalizing scientific questions in terms of statistical models, where relevant aspects of variation are described using probability. We aim not only to provide a succinct overview of useful techniques, but also to emphasize the importance of taking this fundamental first step, of connecting models with questions, which is sometimes overlooked by non-statisticians. More specifically, we emphasize that (i) detection of synchrony presumes a model of spiking without synchrony, in statistical jargon this is a null hypothesis, and (ii) quantification of the amount of synchrony requires a richer model of spiking that explicitly allows for synchrony, and in particular, permits statistical estimation of synchrony</p