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A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression.

ABSTRACT: 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.

SUBMITTER: Nicolaou N

PROVIDER: S-EPMC4905976 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BACKGROUND:'Non-parametric directionality' (NPD) is a novel method for estimation of directed functional connectivity (dFC) in neural data. The method has previously been verified in its ability to recover causal interactions in simulated spiking networks in Halliday et al. (2015). METHODS:This work presents a validation of NPD in continuous neural recordings (e.g. local field potentials). Specifically, we use autoregressive models to simulate time delayed correlations between neural signals. We then test for the accurate recovery of networks in the face of several confounds typically encountered in empirical data. We examine the effects of NPD under varying: a) signal-to-noise ratios, b) asymmetries in signal strength, c) instantaneous mixing, d) common drive, e) data length, and f) parallel/convergent signal routing. We also apply NPD to data from a patient who underwent simultaneous magnetoencephalography and deep brain recording. RESULTS:We demonstrate that NPD can accurately recover directed functional connectivity from simulations with known patterns of connectivity. The performance of the NPD measure is compared with non-parametric estimators of Granger causality (NPG), a well-established methodology for model-free estimation of dFC. A series of simulations investigating synthetically imposed confounds demonstrate that NPD provides estimates of connectivity that are equivalent to NPG, albeit with an increased sensitivity to data length. However, we provide evidence that: i) NPD is less sensitive than NPG to degradation by noise; ii) NPD is more robust to the generation of false positive identification of connectivity resulting from SNR asymmetries; iii) NPD is more robust to corruption via moderate amounts of instantaneous signal mixing. CONCLUSIONS:The results in this paper highlight that to be practically applied to neural data, connectivity metrics should not only be accurate in their recovery of causal networks but also resistant to the confounding effects often encountered in experimental recordings of multimodal data. Taken together, these findings position NPD at the state-of-the-art with respect to the estimation of directed functional connectivity in neuroimaging.

Project description:Full quantification of Positron Emission Tomography (PET) requires an arterial input function (AIF) for measurement of certain targets, or using particular radiotracers, or for the quantification of specific outcome measures. The AIF represents the measurement of radiotracer concentrations in the arterial blood plasma over the course of the PET examination. Measurement of the AIF is prone to error as it is a composite measure created from the combination of multiple measurements of different samples with different equipment, each of which can be sources of measurement error. Moreover, its measurement requires a high degree of temporal granularity for early time points, which necessitates a compromise between quality and quantity of recorded samples. For these reasons, it is often desirable to fit models to this data in order to improve its quality before using it for quantification of radiotracer binding in the tissue. The raw observations of radioactivity in arterial blood and plasma samples are derived from radioactive decay, which is measured as a number of recorded counts. Count data have several specific properties, including the fact that they cannot be negative as well as a particular mean-variance relationship. Poisson regression is the most principled modelling strategy for working with count data, as it both incorporates and exploits these properties. However, no previous studies to our knowledge have taken this approach, despite the advantages of greater efficiency and accuracy which result from using the appropriate distributional assumptions. Here, we implement a Poisson regression modelling approach for the AIF as proof-of-concept of its application. We applied both parametric and non-parametric models for the input function curve. We show that a negative binomial distribution is a more appropriate error distribution for handling overdispersion. Furthermore, we extend this approach to a hierarchical non-parametric model which is shown to be highly resilient to missing data. We thus demonstrate that Poisson regression is both feasible and effective when applied to AIF data, and propose that this is a promising strategy for modelling blood count data for PET in future.

Project description:ObjectivesThe COVID-19 pandemic (caused by SARS-CoV-2) has introduced significant challenges for accurate prediction of population morbidity and mortality by traditional variable-based methods of estimation. Challenges to modelling include inadequate viral physiology comprehension and fluctuating definitions of positivity between national-to-international data. This paper proposes that accurate forecasting of COVID-19 caseload may be best preformed non-parametrically, by vector autoregression (VAR) of verifiable data regionally.MethodsA non-linear VAR model across 7 major demographically representative New York City (NYC) metropolitan region counties was constructed using verifiable daily COVID-19 caseload data March 12-July 23, 2020. Through association of observed case trends with a series of (county-specific) data-driven dynamic interdependencies (lagged values), a systematically non-assumptive approximation of VAR representation for COVID-19 patterns to-date and prospective upcoming trends was produced.ResultsModified VAR regression of NYC area COVID-19 caseload trends proves highly significant modelling capacity of observed patterns in longitudinal disease incidence (county R2 range: 0.9221-0.9751, all p < 0.001). Predictively, VAR regression of daily caseload results at a county-wide level demonstrates considerable short-term forecasting fidelity (p < 0.001 at one-step ahead) with concurrent capacity for longer-term (tested 11-week period) inferences of consistent, reasonable upcoming patterns from latest (model data update) disease epidemiology.ConclusionsIn contrast to macroscopic variable-assumption projections, regionally-founded VAR modelling may substantially improve projection of short-term community disease burden, reduce potential for biostatistical error, as well as better model epidemiological effects resultant from intervention. Predictive VAR extrapolation of existing public health data at an interdependent regional scale may improve accuracy of current pandemic burden prognoses.

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A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression.

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