DOCSLIB.ORG

Optimizing Data for Modeling Neuronal Responses

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

TECHNOLOGY REPORT published: 10 January 2019 doi: 10.3389/fnins.2018.00986 Optimizing Data for Modeling Neuronal Responses Peter Zeidman 1*†, Samira M. Kazan 1†, Nick Todd 2, Nikolaus Weiskopf 1,3, Karl J. Friston 1 and Martina F. Callaghan 1 1 Wellcome Centre for Human Neuroimaging, UCL Institute of Neurology, University College London, London, United Kingdom, 2 Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, United States, 3 Department of Neurophysics, Max Planck Institute for Human Cognition and Brain Sciences, Leipzig, Germany In this technical note, we address an unresolved challenge in neuroimaging statistics: how to determine which of several datasets is the best for inferring neuronal responses. Comparisons of this kind are important for experimenters when choosing an imaging protocol—and for developers of new acquisition methods. However, the hypothesis that one dataset is better than another cannot be tested using conventional statistics (based on likelihood ratios), as these require the data to be the same under each hypothesis. Edited by: Here we present Bayesian data comparison (BDC), a principled framework for evaluating Daniel Baumgarten, UMIT–Private Universität für the quality of functional imaging data, in terms of the precision with which neuronal Gesundheitswissenschaften, connectivity parameters can be estimated and competing models can be disambiguated. Medizinische Informatik und Technik, For each of several candidate datasets, neuronal responses are modeled using Bayesian Austria (probabilistic) forward models, such as General Linear Models (GLMs) or Dynamic Casual Reviewed by: Alberto Sorrentino, Models (DCMs). Next, the parameters from subject-specific models are summarized at Università di Genova, Italy the group level using a Bayesian GLM. A series of measures, which we introduce here, Dimitris Pinotsis, City University of London, are then used to evaluate each dataset in terms of the precision of (group-level) parameter United Kingdom estimates and the ability of the data to distinguish similar models. To exemplify the *Correspondence: approach, we compared four datasets that were acquired in a study evaluating multiband Peter Zeidman fMRI acquisition schemes, and we used simulations to establish the face validity of the [email protected] comparison measures. To enable people to reproduce these analyses using their own † These authors have contributed data and experimental paradigms, we provide general-purpose Matlab code via the SPM equally to this work software. Specialty section: Keywords: dynamic causal modeling, DCM, fMRI, PEB, multiband This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience INTRODUCTION Received: 29 June 2018 Hypothesis testing involves comparing the evidence for different models or hypotheses, given some Accepted: 10 December 2018 measured data. The key quantity of interest is the likelihood ratio—the probability of observing the Published: 10 January 2019 data under one model relative to another—written p y m1 / p(y|m2) for models m1 and m2 and Citation: dataset y. Likelihood ratios are ubiquitous in statistics, forming the basis of the F-test and the Bayes Zeidman P, Kazan SM, Todd N, factor in classical and Bayesian statistics, respectively. They are the most powerful test for any given Weiskopf N, Friston KJ and level of significance by the Neyman-Pearson lemma (Neyman and Pearson, 1933). However, the Callaghan MF (2019) Optimizing Data for Modeling Neuronal Responses. likelihood ratio test assumes that there is only one dataset y–and so cannot be used to compare Front. Neurosci. 12:986. different datasets. Therefore, an unresolved problem, especially pertinent to neuroimaging, is how doi: 10.3389/fnins.2018.00986 to test the hypothesis that one dataset is better than another for making inferences. Frontiers in Neuroscience | www.frontiersin.org 1 January 2019 | Volume 12 | Article 986 Zeidman et al. Optimizing Data With DCM Neuronal activity and circuitry cannot generally be observed acceleration factor. Multiband is an approach for rapid directly, but rather are inferred from measured timeseries. In the acquisition of fMRI data, in which multiple slices are acquired case of fMRI, the data are mediated by neuro-vascular coupling, simultaneously and subsequently unfolded using coil sensitivity the BOLD response and noise. To estimate the underlying information (Larkman et al., 2001; Xu et al., 2013). The rapid neuronal responses, models are specified which formalize the sampling enables sources of physiological noise to be separated experimenter’s understanding of how the data were generated. from sources of experimental variance more efficiently, however, Hypotheses are then tested by making inferences about model a penalty for this increased temporal resolution is a reduction parameters, or by comparing the evidence under different of the signal-to-noise ratio (SNR) of each image. A detailed models. For example, an F-test can be performed on the General analysis of these data is published separately (Todd et al., Linear Model (GLM) using classical statistics, or Bayesian Model 2017). We do not seek to draw any novel conclusions about Comparison can be used to select between probabilistic models. multiband acceleration from this specific dataset, but rather we From the experimenter’s perspective, the best dataset provides use it to illustrate a generic approach for comparing datasets. the most precise estimates of neuronal responses (enabling Additionally, we conducted simulations to establish the face efficient inference about parameters) and provides the greatest validity of the outcome measures, using estimated effect sizes and discrimination among competing models (enabling efficient SNR levels from the empirical multiband data. inference about models). The methodology we introduce here offers several novel Here, we introduce Bayesian data comparison (BDC)—a set contributions. First, it provides a sensitive comparison of of information measures for evaluating a dataset’s ability to data by evaluating their ability to reduce uncertainty about support inferences about both parameters and models. While neuronal parameters, and to discriminate among competing they are generic and can be used with any sort of probabilistic models. Second, our procedure identifies the best dataset for models, we illustrate their application using Dynamic Causal hypothesis testing at the group level, reflecting the objectives Modeling (DCM) for fMRI (Friston et al., 2003) because it of most cognitive neuroscience studies. Unlike a classical GLM offers several advantages. Compared to the GLM, DCM provides analysis—where only the maximum likelihood estimates from a richer characterization of neuroimaging data, through the each subject are taken to the group level—the (parametric use of biophysical models, based on differential equations that empirical) Bayesian methods used here take into account the separate neuronal and hemodynamic parameters. This means uncertainty of the parameters (the full covariance matrix), when one can evaluate which dataset is best for estimating neuronal modeling at the group level. Additionally, this methodology parameters specifically. These models also include connections provides the necessary tools to evaluate which imaging protocolis among regions, making DCM the usual approach for inferring optimal for effective connectivity analyses, although we anticipate effective (directed) connectivity from fMRI data. many questions about data quality will not necessarily relate to By using the same methodology to select among datasets as connectivity. We provide a single Matlab function for conducting experimenters use to select between connectivity models, feature all the analyses described in this paper, which is available in selection and hypothesis testing can be brought into alignment the SPM (http://www.fil.ion.ucl.ac.uk/spm/) software package for connectivity studies. Moreover, a particularly useful feature (spm_dcm_bdc.m). This function can be used to evaluate any of DCM for comparing datasets is that it employs Bayesian type of imaging protocol, in terms of the precision with which statistics. The posterior probability over neuronal parameters model parameters are estimated and the complexity of the forms a multivariate normal distribution, providing expected generative models that can be disambiguated. values for each parameter, as well as their covariance. The precision (inverse covariance) quantifies the confidence we place METHODS in the parameter estimates, given the data. After establishing that an experimental effect exists, for example by conducting an initial We begin by briefly reprising the theory behind DCM and GLM analysis or by reference to previous studies, the precision introducing the set of outcome measures used to evaluate data of the parameters can be used to compare datasets. DCM also quality. We then illustrate the analysis pipeline in the context enables experimenters to distinguish among models, in terms of an exemplar fMRI dataset and evaluate the measures using | of which model maximizes the log model evidence ln p(y m). simulations. We cannot use this quantity to compare different datasets, but we can ask which of several datasets provides the most Dynamic Causal Modeling efficient discrimination among models. For these reasons, we DCM is a framework for evaluating generative models of time used Bayesian methods as the basis for comparing datasets, both
Recommended publications
  • Plos Computational Biology 2018

    Plos Computational Biology 2018

    RESEARCH ARTICLE Bayesian comparison of explicit and implicit causal inference strategies in multisensory heading perception Luigi Acerbi1☯¤*, Kalpana Dokka2☯, Dora E. Angelaki2, Wei Ji Ma1,3 1 Center for Neural Science, New York University, New York, NY, United States of America, 2 Department of Neuroscience, Baylor College of Medicine, Houston, TX, United States of America, 3 Department of Psychology, New York University, New York, NY, United States of America a1111111111 ☯ These authors contributed equally to this work. a1111111111 ¤ Current address: DeÂpartement des neurosciences fondamentales, Universite de Genève, Genève, a1111111111 Switzerland a1111111111 * [email protected], [email protected] a1111111111 Abstract The precision of multisensory perception improves when cues arising from the same cause OPEN ACCESS are integrated, such as visual and vestibular heading cues for an observer moving through a Citation: Acerbi L, Dokka K, Angelaki DE, Ma WJ stationary environment. In order to determine how the cues should be processed, the brain (2018) Bayesian comparison of explicit and implicit must infer the causal relationship underlying the multisensory cues. In heading perception, causal inference strategies in multisensory heading perception. PLoS Comput Biol 14(7): e1006110. however, it is unclear whether observers follow the Bayesian strategy, a simpler non-Bayes- https://doi.org/10.1371/journal.pcbi.1006110 ian heuristic, or even perform causal inference at all. We developed an efficient and robust Editor: Samuel J. Gershman, Harvard University, computational framework to perform Bayesian model comparison of causal inference strate- UNITED STATES gies, which incorporates a number of alternative assumptions about the observers. With this Received: July 26, 2017 framework, we investigated whether human observers' performance in an explicit cause attribution and an implicit heading discrimination task can be modeled as a causal inference Accepted: March 28, 2018 process.

  • Bayesian Model Reduction

    Bayesian model reduction Karl Friston, Thomas Parr and Peter Zeidman The Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, UK. Correspondence: Peter Zeidman The Wellcome Centre for Human Neuroimaging Institute of Neurology 12 Queen Square, London, UK WC1N 3AR [email protected] Summary This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning. Keywords: Bayesian methods, empirical Bayes, model comparison, neurobiology, structure learning 1. Introduction Over the past years, Bayesian model comparison and structure learning have become key issues in the neurosciences (Collins and Frank, 2013, Friston et al., 2017a, Salakhutdinov et al., 2013, Tenenbaum et al., 2011, Tervo et al., 2016, Zorzi et al., 2013); particularly, in optimizing models of neuroimaging time series (Friston et al., 2015, Woolrich et al., 2009) and as a fundamental problem that our brains have to solve (Friston et al., 2017a, Schmidhuber, 1991, Schmidhuber, 2010).
  • A Tutorial on Group Effective Connectivity Analysis, Part 2: Second Level Analysis with PEB

    A Tutorial on Group Effective Connectivity Analysis, Part 2: Second Level Analysis with PEB

    A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB Peter Zeidman*1, Amirhossein Jafarian1, Mohamed L. Seghier2, Vladimir Litvak1, Hayriye Cagnan3, Cathy J. Price1, Karl J. Friston1 1 Wellcome Centre for Human Neuroimaging 12 Queen Square London WC1N 3AR 2 Cognitive Neuroimaging Unit, ECAE, Abu Dhabi, UAE 3 Nuffield Department of Clinical Neurosciences Level 6 West Wing John Radcliffe Hospital Oxford OX3 9DU * Corresponding author Conflicts of interest: None Abstract This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject’s neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper.
  • Second Level Analysis with PEB

    Second Level Analysis with PEB

    NeuroImage 200 (2019) 12–25 Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/neuroimage A guide to group effective connectivity analysis, part 2: Second level analysis with PEB Peter Zeidman a,*, Amirhossein Jafarian a, Mohamed L. Seghier b, Vladimir Litvak a, Hayriye Cagnan c, Cathy J. Price a, Karl J. Friston a a Wellcome Centre for Human Neuroimaging, 12 Queen Square, London, WC1N 3AR, UK b Cognitive Neuroimaging Unit, ECAE, Abu Dhabi, United Arab Emirates c Nuffield Department of Clinical Neurosciences, Level 6, West Wing, John Radcliffe Hospital, Oxford, OX3 9DU, UK ABSTRACT This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i.e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors.