Using a linear dynamic system to measure functional connectivity from M/EEG.

Objective.Measures of functional connectivity (FC) can elucidate which cortical regions work together in order to complete a variety of behavioral tasks. This study's primary objective was to expand a previously published model of measuring FC to include multiple subjects and several regions of interest. While FC has been more extensively investigated in vision and other sensorimotor tasks, it is not as well understood in audition. The secondary objective of this study was to investigate how auditory regions are functionally connected to other cortical regions when attention is directed to different distinct auditory stimuli.Approach.This study implements a linear dynamic system (LDS) to measure the structured time-lagged dependence across several cortical regions in order to estimate their FC during a dual-stream auditory attention task.Results.The model's output shows consistent functionally connected regions across different listening conditions, indicative of an auditory attention network that engages regardless of endogenous switching of attention or different auditory cues being attended.Significance.The LDS implemented in this study implements a multivariate autoregression to infer FC across cortical regions during an auditory attention task. This study shows how a first-order autoregressive function can reliably measure functional connectivity from M/EEG data. Additionally, the study shows how auditory regions engage with the supramodal attention network outlined in the visual attention literature.

Statistical Deconvolution for Inference of Infection Time Series.

Accurate measurement of daily infection incidence is crucial to epidemic response. However, delays in symptom onset, testing, and reporting obscure the dynamics of transmission, necessitating methods to remove the effects of stochastic delays from observed data. Existing estimators can be sensitive to model misspecification and censored observations; many analysts have instead used methods that exhibit strong bias. We develop an estimator with a regularization scheme to cope with stochastic delays, which we term the robust incidence deconvolution estimator. We compare the method to existing estimators in a simulation study, measuring accuracy in a variety of experimental conditions. We then use the method to study COVID-19 records in the United States, highlighting its stability in the face of misspecification and right censoring. To implement the robust incidence deconvolution estimator, we release incidental, a ready-to-use R implementation of our estimator that can aid ongoing efforts to monitor the COVID-19 pandemic.

Neural Granger Causality.

While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of nonlinear methods by applying structured multilayer perceptrons (MLPs) or recurrent neural networks (RNNs) combined with sparsity-inducing penalties on the weights. By encouraging specific sets of weights to be zero-in particular, through the use of convex group-lasso penalties-we can extract the Granger causal structure. To further contrast with traditional approaches, our framework naturally enables us to efficiently capture long-range dependencies between series either via our RNNs or through an automatic lag selection in the MLP. We show that our neural Granger causality methods outperform state-of-the-art nonlinear Granger causality methods on the DREAM3 challenge data. This data consists of nonlinear gene expression and regulation time courses with only a limited number of time points. The successes we show in this challenging dataset provide a powerful example of how deep learning can be useful in cases that go beyond prediction on large datasets. We likewise illustrate our methods in detecting nonlinear interactions in a human motion capture dataset.

It's complicated: characterizing the time-varying relationship between cell phone mobility and COVID-19 spread in the US.

Restricting in-person interactions is an important technique for limiting the spread of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). Although early research found strong associations between cell phone mobility and infection spread during the initial outbreaks in the United States, it is unclear whether this relationship persists across locations and time. We propose an interpretable statistical model to identify spatiotemporal variation in the association between mobility and infection rates. Using 1 year of US county-level data, we found that sharp drops in mobility often coincided with declining infection rates in the most populous counties in spring 2020. However, the association varied considerably in other locations and across time. Our findings are sensitive to model flexibility, as more restrictive models average over local effects and mask much of the spatiotemporal variation. We conclude that mobility does not appear to be a reliable leading indicator of infection rates, which may have important policy implications.

Statistical model-based approaches for functional connectivity analysis of neuroimaging data.

We present recent literature on model-based approaches to estimating functional connectivity from neuroimaging data. In contrast to the typical focus on a particular scientific question, we reframe a wider literature in terms of the underlying statistical model used. We distinguish between directed versus undirected and static versus time-varying connectivity. There are numerous advantages to a model-based approach, including easily specified inductive bias, handling limited data scenarios, and building complex models from simpler building blocks.

A Survey of Non-Exchangeable Priors for Bayesian Nonparametric Models.

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern, there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.

Quantitative patterns of stylistic influence in the evolution of literature.

Literature is a form of expression whose temporal structure, both in content and style, provides a historical record of the evolution of culture. In this work we take on a quantitative analysis of literary style and conduct the first large-scale temporal stylometric study of literature by using the vast holdings in the Project Gutenberg Digital Library corpus. We find temporal stylistic localization among authors through the analysis of the similarity structure in feature vectors derived from content-free word usage, nonhomogeneous decay rates of stylistic influence, and an accelerating rate of decay of influence among modern authors. Within a given time period we also find evidence for stylistic coherence with a given literary topic, such that writers in different fields adopt different literary styles. This study gives quantitative support to the notion of a literary "style of a time" with a strong trend toward increasingly contemporaneous stylistic influence.

Nonparametric sparsification of complex multiscale networks.

Many real-world networks tend to be very dense. Particular examples of interest arise in the construction of networks that represent pairwise similarities between objects. In these cases, the networks under consideration are weighted, generally with positive weights between any two nodes. Visualization and analysis of such networks, especially when the number of nodes is large, can pose significant challenges which are often met by reducing the edge set. Any effective "sparsification" must retain and reflect the important structure in the network. A common method is to simply apply a hard threshold, keeping only those edges whose weight exceeds some predetermined value. A more principled approach is to extract the multiscale "backbone" of a network by retaining statistically significant edges through hypothesis testing on a specific null model, or by appropriately transforming the original weight matrix before applying some sort of threshold. Unfortunately, approaches such as these can fail to capture multiscale structure in which there can be small but locally statistically significant similarity between nodes. In this paper, we introduce a new method for backbone extraction that does not rely on any particular null model, but instead uses the empirical distribution of similarity weight to determine and then retain statistically significant edges. We show that our method adapts to the heterogeneity of local edge weight distributions in several paradigmatic real world networks, and in doing so retains their multiscale structure with relatively insignificant additional computational costs. We anticipate that this simple approach will be of great use in the analysis of massive, highly connected weighted networks.