Algorithms of causal inference for the analysis of effective connectivity among brain regions

Project, toolkit, and database of neuroinformatics ecosystem: A summary of previous studies on "Frontiers in Neuroinformatics"

In the field of neuroscience, the core of the cohort study project consists of collection, analysis, and sharing of multi-modal data. Recent years have witnessed a host of efficient and high-quality toolkits published and employed to improve the quality of multi-modal data in the cohort study. In turn, gleaning answers to relevant questions from such a conglomeration of studies is a time-consuming task for cohort researchers. As part of our efforts to tackle this problem, we propose a hierarchical neuroscience knowledge base that consists of projects/organizations, multi-modal databases, and toolkits, so as to facilitate researchers' answer searching process. We first classified studies conducted for the topic "Frontiers in Neuroinformatics" according to the multi-modal data life cycle, and from these studies, information objects as projects/organizations, multi-modal databases, and toolkits have been extracted. Then, we map these information objects into our proposed knowledge base framework. A Python-based query tool has also been developed in tandem for quicker access to the knowledge base, (accessible at https://github.com/Romantic-Pumpkin/PDT_fninf). Finally, based on the constructed knowledge base, we discussed some key research issues and underlying trends in different stages of the multi-modal data life cycle.

Structurally constrained effective brain connectivity

The relationship between structure and function is of interest in many research fields involving the study of complex biological processes. In neuroscience in particular, the fusion of structural and functional data can help to understand the underlying principles of the operational networks in the brain. To address this issue, this paper proposes a constrained autoregressive model leading to a representation of effective connectivity that can be used to better understand how the structure modulates the function. Or simply, it can be used to find novel biomarkers characterizing groups of subjects. In practice, an initial structural connectivity representation is re-weighted to explain the functional co-activations. This is obtained by minimizing the reconstruction error of an autoregressive model constrained by the structural connectivity prior. The model has been designed to also include indirect connections, allowing to split direct and indirect components in the functional connectivity, and it can be used with raw and deconvoluted BOLD signal. The derived representation of dependencies was compared to the well known dynamic causal model, giving results closer to known ground-truth. Further evaluation of the proposed effective network was performed on two typical tasks. In a first experiment the direct functional dependencies were tested on a community detection problem, where the brain was partitioned using the effective networks across multiple subjects. In a second experiment the model was validated in a case-control task, which aimed at differentiating healthy subjects from individuals with autism spectrum disorder. Results showed that using effective connectivity leads to clusters better describing the functional interactions in the community detection task, while maintaining the original structural organization, and obtaining a better discrimination in the case-control classification task.

A Complex Systems Perspective on Neuroimaging Studies of Behavior and Its Disorders

The study of complex systems deals with emergent behavior that arises as a result of nonlinear spatiotemporal interactions between a large number of components both within the system, as well as between the system and its environment. There is a strong case to be made that neural systems as well as their emergent behavior and disorders can be studied within the framework of complexity science. In particular, the field of neuroimaging has begun to apply both theoretical and experimental procedures originating in complexity science—usually in parallel with traditional methodologies. Here, we illustrate the basic properties that characterize complex systems and evaluate how they relate to what we have learned about brain structure and function from neuroimaging experiments. We then argue in favor of adopting a complex systems-based methodology in the study of neuroimaging, alongside appropriate experimental paradigms, and with minimal influences from noncomplex system approaches. Our exposition includes a review of the fundamental mathematical concepts, combined with practical examples and a compilation of results from the literature.

A Multiple-Trait Bayesian Variable Selection Regression Method for Integrating Phenotypic Causal Networks in Genome-Wide Association Studies

Bayesian regression methods that incorporate different mixture priors for marker effects are used in multi-trait genomic prediction. These methods can also be extended to genome-wide association studies (GWAS). In multiple-trait GWAS, incorporating the underlying causal structures among traits is essential for comprehensively understanding the relationship between genotypes and traits of interest. Therefore, we develop a GWAS methodology, SEM-Bayesian alphabet, which, by applying the structural equation model (SEM), can be used to incorporate causal structures into multi-trait Bayesian regression methods. SEM-Bayesian alphabet provides a more comprehensive understanding of the genotype-phenotype mapping than multi-trait GWAS by performing GWAS based on indirect, direct and overall marker effects. The superior performance of SEM-Bayesian alphabet was demonstrated by comparing its GWAS results with other similar multi-trait GWAS methods on real and simulated data. The software tool JWAS offers open-source routines to perform these analyses.

Causality in Cognitive Neuroscience: Concepts, Challenges, and Distributional Robustness

Whereas probabilistic models describe the dependence structure between observed variables, causal models go one step further: They predict, for example, how cognitive functions are affected by external interventions that perturb neuronal activity. In this review and perspective article, we introduce the concept of causality in the context of cognitive neuroscience and review existing methods for inferring causal relationships from data. Causal inference is an ambitious task that is particularly challenging in cognitive neuroscience. We discuss two difficulties in more detail: the scarcity of interventional data and the challenge of finding the right variables. We argue for distributional robustness as a guiding principle to tackle these problems. Robustness (or invariance) is a fundamental principle underlying causal methodology. A (correctly specified) causal model of a target variable generalizes across environments or subjects as long as these environments leave the causal mechanisms of the target intact. Consequently, if a candidate model does not generalize, then either it does not consist of the target variable's causes or the underlying variables do not represent the correct granularity of the problem. In this sense, assessing generalizability may be useful when defining relevant variables and can be used to partially compensate for the lack of interventional data.

Estimating the Memory Order of Electrocorticography Recordings

OBJECTIVE

This paper presents a data-driven method for estimating the memory order (the average length of the statistical dependence of a given sample on previous samples) of a recorded electrocorticography (ECoG) sequence.

METHODS

The proposed inference method is based on the relationship between the loss in predicting the next sample in a time-series and the dependence of this sample on the previous samples. Specifically, the memory order is estimated to be the number of past samples that minimize the least squares error (LSE) in predicting the next sample. To deal with the lack of an analytical model for ECoG recordings, the proposed method combines a collection of different predictors, thereby achieving LSE at least as low as the LSE achieved by each of the different predictors.

RESULTS

ECoG recordings from six patients with epilepsy were analyzed, and the empirical cumulative density functions (ECDFs) of the memory orders estimated from these recordings were generated, for rest as well as pre-ictal time intervals. For pre-ictal time intervals, the electrodes corresponding to the seizure-onset-zone were separately analyzed. The estimated ECDFs were different between patients and between different types of blocks. For all the analyzed patients, the estimated memory orders were on the order of tens of milliseconds (up to 100 ms).

SIGNIFICANCE

The proposed method facilitates the estimation of the causal associations between ECoG recordings, as these associations strongly depend on the recordings' memory. An improved estimation of causal associations can improve the performance of algorithms that use ECoG recordings to localize the epileptogenic zone. Such algorithms can aid doctors in their pre-surgical planning for the surgery of patients with epilepsy.

The Identity of Information: How Deterministic Dependencies Constrain Information Synergy and Redundancy

Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.

Multiscale Granger causality

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer across multiple time scales. We show that the multiscale processing of a vector autoregressive (AR) process introduces a moving average (MA) component, and describe how to represent the resulting ARMA process using state space (SS) models and to combine the SS model parameters for computing exact GC values at arbitrarily large time scales. We exploit the theoretical formulation to identify peculiar features of multiscale GC in basic AR processes, and demonstrate with numerical simulations the much larger estimation accuracy of the SS approach compared to pure AR modeling of filtered and downsampled data. The improved computational reliability is exploited to disclose meaningful multiscale patterns of information transfer between global temperature and carbon dioxide concentration time series, both in paleoclimate and in recent years.

A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula

We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open-source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541-1573, 2017. © 2016 Wiley Periodicals, Inc.

A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression

Causal prediction has become a popular tool for neuroscience applications, as it allows the study of relationships between different brain areas during rest, cognitive tasks or brain disorders. We propose a nonparametric approach for the estimation of nonlinear causal prediction for multivariate time series. In the proposed estimator, C NPMR , Autoregressive modeling is replaced by Nonparametric Multiplicative Regression (NPMR). NPMR quantifies interactions between a response variable (effect) and a set of predictor variables (cause); here, we modified NPMR for model prediction. We also demonstrate how a particular measure, the sensitivity Q, could be used to reveal the structure of the underlying causal relationships. We apply C NPMR on artificial data with known ground truth (5 datasets), as well as physiological data (2 datasets). C NPMR correctly identifies both linear and nonlinear causal connections that are present in the artificial data, as well as physiologically relevant connectivity in the real data, and does not seem to be affected by filtering. The Sensitivity measure also provides useful information about the latent connectivity.The proposed estimator addresses many of the limitations of linear Granger causality and other nonlinear causality estimators. C NPMR is compared with pairwise and conditional Granger causality (linear) and Kernel-Granger causality (nonlinear). The proposed estimator can be applied to pairwise or multivariate estimations without any modifications to the main method. Its nonpametric nature, its ability to capture nonlinear relationships and its robustness to filtering make it appealing for a number of applications.

An Information-Theoretic Framework to Map the Spatiotemporal Dynamics of the Scalp Electroencephalogram

We present the first application of the emerging framework of information dynamics to the characterization of the electroencephalography (EEG) activity. The framework provides entropy-based measures of information storage (self entropy, SE) and information transfer (joint transfer entropy (TE) and partial TE), which are applied here to detect complex dynamics of individual EEG sensors and causal interactions between different sensors. The measures are implemented according to a model-free and fully multivariate formulation of the framework, allowing the detection of nonlinear dynamics and direct links. Moreover, to deal with the issue of volume conduction, a compensation for instantaneous effects is introduced in the computation of joint and partial TE. The framework is applied to resting state EEG measured from healthy subjects in the eyes open (EO) and eyes closed (EC) conditions, evidencing condition-dependent patterns indicative of how information is distributed in the EEG sensor space. The SE was uniformly low during EO and significantly higher in the posterior areas during EC. The joint and partial TE were saturated by instantaneous effects, documenting how volume conduction blurs the detection of information flow in the EEG. However, the use of compensated TE measures led us to evidence meaningful patterns like the presence of local sinks of information flow and propagation motifs, and the emergence of prevalent front-to-back EEG propagation during EC. These findings support the feasibility of our information-theoretic approach to assess the spatiotemporal dynamics of the scalp EEG in different conditions.

Characterization of Cortical Networks and Corticocortical Functional Connectivity Mediating Arbitrary Visuomotor Mapping

Adaptive behaviors are built on the arbitrary linkage of sensory inputs to actions and goals. Although the sensorimotor and associative frontostriatal circuits are known to mediate arbitrary visuomotor mappings, the underlying corticocortico dynamics remain elusive. Here, we take a novel approach exploiting gamma-band neural activity to study the human cortical networks and corticocortical functional connectivity mediating arbitrary visuomotor mapping. Single-trial gamma-power time courses were estimated for all Brodmann areas by combing magnetoencephalographic and MRI data with spectral analysis and beam-forming techniques. Linear correlation and Granger causality analyses were performed to investigate functional connectivity between cortical regions. The performance of visuomotor associations was characterized by an increase in gamma-power and functional connectivity over the sensorimotor and frontoparietal network, in addition to medial prefrontal areas. The superior parietal area played a driving role in the network, exerting Granger causality on the dorsal premotor area. Premotor areas acted as relay from parietal to medial prefrontal cortices, which played a receiving role in the network. Link community analysis further revealed that visuomotor mappings reflect the coordination of multiple subnetworks with strong overlap over motor and frontoparietal areas. We put forward an associative account of the underlying cognitive processes and corticocortical functional connectivity. Overall, our approach and results provide novel perspectives toward a better understanding of how distributed brain activity coordinates adaptive behaviors.

SIGNIFICANCE STATEMENT

In everyday life, most of our behaviors are based on the arbitrary linkage of sensory information to actions and goals, such as stopping at a red traffic light. Despite their automaticity, such behaviors rely on the activity of a large brain network and elusive interareal functional connectivity. We take a novel approach exploiting noninvasive recordings of human brain activity to reveal the cortical networks and corticocortical functional connectivity mediating visuomotor mappings. Parietal areas were found to play a driving role in the network, whereas premotor areas acted as relays from parietal to medial prefrontal cortices, which played a receiving role. Overall, our approach and results provide novel perspectives toward a better understanding of how distributed brain activity coordinates adaptive behaviors.

Quantifying information transfer and mediation along causal pathways in complex systems

Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer aimed at decompositions of predictive information about a target variable, while excluding effects of common drivers and indirect influences. While common drivers clearly constitute a spurious causality, the aim of the present article is to develop measures quantifying different notions of the strength of information transfer along indirect causal paths, based on first reconstructing the multivariate causal network. Another class of novel measures quantifies to what extent different intermediate processes on causal paths contribute to an interaction mechanism to determine pathways of causal information transfer. The proposed framework complements predictive decomposition schemes by focusing more on the interaction mechanism between multiple processes. A rigorous mathematical framework allows for a clear information-theoretic interpretation that can also be related to the underlying dynamics as proven for certain classes of processes. Generally, however, estimates of information transfer remain hard to interpret for nonlinearly intertwined complex systems. But if experiments or mathematical models are not available, then measuring pathways of information transfer within the causal dependency structure allows at least for an abstraction of the dynamics. The measures are illustrated on a climatological example to disentangle pathways of atmospheric flow over Europe.

Multineuronal activity patterns identify selective synaptic connections under realistic experimental constraints

Structured multineuronal activity patterns within local neocortical circuitry are strongly linked to sensory input, motor output, and behavioral choice. These reliable patterns of pairwise lagged firing are the consequence of connectivity since they are not present in rate-matched but unconnected Poisson nulls. It is important to relate multineuronal patterns to their synaptic underpinnings, but it is unclear how effectively statistical dependencies in spiking between neurons identify causal synaptic connections. To assess the feasibility of mapping function onto structure we used a network model that showed a diversity of multineuronal activity patterns and replicated experimental constraints on data acquisition. Using an iterative Bayesian inference algorithm, we detected a select subset of monosynaptic connections substantially more precisely than correlation-based inference, a common alternative approach. We found that precise inference of synaptic connections improved with increasing numbers of diverse multineuronal activity patterns in contrast to increased observations of a single pattern. Surprisingly, neuronal spiking was most effective and precise at revealing causal synaptic connectivity when the lags considered by the iterative Bayesian algorithm encompassed the timescale of synaptic conductance and integration (∼10 ms), rather than synaptic transmission time (∼2 ms), highlighting the importance of synaptic integration in driving postsynaptic spiking. Last, strong synaptic connections were detected preferentially, underscoring their special importance in cortical computation. Even after simulating experimental constraints, top down approaches to cortical connectivity, from function to structure, identify synaptic connections underlying multineuronal activity. These select connections are closely tied to cortical processing.