Identifying the directed connectivity that underlie networked activity between different cortical areas is critical for understanding the neural mechanisms behind sensory processing. Granger causality (GC) is widely used for this purpose in functional magnetic resonance imaging analysis, but there the temporal resolution is low, making it difficult to capture the millisecond-scale interactions underlying sensory processing. Magne- toencephalography (MEG) has millisecond resolution, but only provides low-dimensional sensor-level linear mixtures of neural sources, which makes GC inference challenging. Conventional methods proceed in two stages: First, cortical sources are estimated from MEG using a source localization technique, followed by GC inference among the estimated sources. However, the spatiotemporal biases in estimating sources propagate into the subsequent GC analysis stage, may result in both false alarms and missing true GC links. Here, we introduce the Network Localized Granger Causality (NLGC) inference paradigm, which models the source dynamics as latent sparse multivariate autoregressive processes and estimates their parameters directly from the MEG measurements, integrated with source localization, and employs the resulting parameter estimates to produce a precise statistical characterization of the detected GC links. We offer several theoretical and algorithmic innovations within NLGC and further examine its utility via comprehensive simulations and application to MEG data from an auditory task involving tone processing from both younger and older participants. Our simulation studies reveal that NLGC is markedly robust with respect to model mismatch, network size, and low signal-to-noise ratio, whereas the conventional two-stage methods result in high false alarms and mis-detections. We also demonstrate the advantages of NLGC in revealing the cortical network- level characterization of neural activity during tone processing and resting state by delineating task- and age-related connectivity changes.
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Data-Driven Performance Monitoring of Dynamical Systems Using Granger Causal Graphical Models
Data-driven analysis and monitoring of complex dynamical systems have been gaining popularity due to various reasons like ubiquitous sensing and advanced computation capabilities. A key rationale is that such systems inherently have high dimensionality and feature complex subsystem interactions due to which majority of the first-principle based methods become insufficient. We explore the family of a recently proposed probabilistic graphical modeling technique, called spatiotemporal pattern network (STPN) in order to capture the Granger causal relationships among observations in a dynamical system. We also show that this technique can be used for anomaly detection and root-cause analysis for real-life dynamical systems. In this context, we introduce the notion of Granger-STPN (G-STPN) inspired by the notion of Granger causality and introduce a new nonparametric technique to detect causality among dynamical systems observations. We experimentally validate our framework for detecting anomalies and analyzing root causes in a robotic arm platform and obtain superior results compared to when other causality metrics were used in previous frameworks.
more » « less- Award ID(s):
- 1845969
- NSF-PAR ID:
- 10491956
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Dynamic Systems, Measurement, and Control
- Volume:
- 142
- Issue:
- 8
- ISSN:
- 0022-0434
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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<italic>Abstract</italic> Cryptocurrencies and the underpinning blockchain technology have gained unprecedented public attention recently. In contrast to fiat currencies, transactions of cryptocurrencies, such as Bitcoin and Litecoin, are permanently recorded on distributed ledgers to be seen by the public. As a result, public availability of all cryptocurrency transactions allows us to create a complex network of financial interactions that can be used to study not only the blockchain graph, but also the relationship between various blockchain network features and cryptocurrency risk investment. We introduce a novel concept of chainlets, or blockchain motifs, to utilize this information. Chainlets allow us to evaluate the role of local topological structure of the blockchain on the joint Bitcoin and Litecoin price formation and dynamics. We investigate the predictive Granger causality of chainlets and identify certain types of chainlets that exhibit the highest predictive influence on cryptocurrency price and investment risk. More generally, while statistical aspects of blockchain data analytics remain virtually unexplored, the paper aims to highlight various emerging theoretical, methodological and applied research challenges of blockchain data analysis that will be of interest to the broad statistical community.
The Canadian Journal of Statistics 48: 561–581; 2020 © 2020 Statistical Society of Canada -
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.more » « less
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Abstract Background Immune responses need to be initiated rapidly, and maintained as needed, to prevent establishment and growth of infections. At the same time, resources need to be balanced with other physiological processes. On the level of transcription, studies have shown that this balancing act is reflected in tight control of the initiation kinetics and shutdown dynamics of specific immune genes.
Results To investigate genome-wide expression dynamics and trade-offs after infection at a high temporal resolution, we performed an RNA-seq time course on
D. melanogaster with 20 time points post Imd stimulation. A combination of methods, including spline fitting, cluster analysis, and Granger causality inference, allowed detailed dissection of expression profiles, lead-lag interactions, and functional annotation of genes through guilt-by-association. We identified Imd-responsive genes and co-expressed, less well characterized genes, with an immediate-early response and sustained up-regulation up to 5 days after stimulation. In contrast, stress response and Toll-responsive genes, among which were Bomanins, demonstrated early and transient responses. We further observed a strong trade-off with metabolic genes, which strikingly recovered to pre-infection levels before the immune response was fully resolved.Conclusions This high-dimensional dataset enabled the comprehensive study of immune response dynamics through the parallel application of multiple temporal data analysis methods. The well annotated data set should also serve as a useful resource for further investigation of the
D. melanogaster innate immune response, and for the development of methods for analysis of a post-stress transcriptional response time-series at whole-genome scale. -
Morrison, Abigail (Ed.)Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j ’s point process likelihood obtained considering or removing neuron i . CIF’s hyper-parameters are set on a per-neuron basis by minimizing Akaike’s information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4046673
