Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naïve estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.

PIPPET: A Bayesian framework for generalized entrainment to stochastic rhythms

When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a “beat”), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. Here we propose that the problem of rhythm tracking is most naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. We formalize this problem as a case of inferring a distribution on a hidden state from point process data in continuous time: either Phase Inference from Point Process Event Timing (PIPPET) or Phase And Tempo Inference (PATIPPET). This approach to rhythm tracking generalizes to non-isochronous and multi-voice rhythms. We demonstrate that these inference problems can be approximately solved using a variational Bayesian method that generalizes the Kalman-Bucy filter to point-process data. These solutions reproduce multiple characteristics of overt and covert human rhythm tracking, including period-dependent phase corrections, illusory contraction of unexpectedly empty intervals, and failure to track excessively syncopated rhythms, and could could be plausibly approximated in the brain. PIPPET can serve as the basis for models of performance on a wide range of timing and entrainment tasks and opens the door to even richer predictive processing and active inference models of rhythmic timing.

Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch–Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.