title: A hierarchical model for integrating unsupervised generative embedding and empirical Bayes.
abstract: Generative models of neuroimaging data, such as dynamic causal models (DCMs), are commonly used for inferring effective connectivity from individual subject data. Recently introduced "generative embedding" approaches have used DCM-based connectivity parameters for supervised classification of individual patients or to find unknown subgroups in heterogeneous groups using unsupervised clustering methods.
  
  
  
  We present a novel framework which combines DCMs with finite mixture models into a single hierarchical model. This approach unifies the inference of connectivity parameters in individual subjects with inference on population structure, i.e. the existence of subgroups defined by model parameters, and allows for empirical Bayesian estimates of a subject's connectivity based on subgroup-specific prior distributions. We introduce a Markov chain Monte Carlo sampling method for inversion of this hierarchical generative model.
  
  
  
  This paper formally introduces the idea behind our novel concept and demonstrates the face validity of the model in application to both simulated data as well as an empirical fMRI dataset from healthy controls and patients with schizophrenia.
  
  
  
  The analysis of our empirical fMRI data demonstrates that our approach results in superior model evidence than the conventional non-hierarchical inversion of DCMs.
  
  
  
  In this paper, we have presented a novel unified framework to jointly infer the effective connectivity parameters in DCMs for multiple subjects and, at the same time, discover connectivity-defined cluster structure of the whole population, using a mixture model approach.
authors.affiliation: Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering, University of Zurich and ETH Zurich, Switzerland. Electronic address: ssudhir@ethz.ch.
authors.forename: Sudhir
authors.initials: S
authors.lastname: Raman
authors.affiliation: Department of Psychiatry and Psychotherapy, Charité Universitätsmedizin Berlin, Berlin, Germany; Max Planck Fellow Group "Cognitive and Affective Control of Behavioral Adaptation", Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany; Department of Neurology, Otto-von-Guericke University, Magdeburg, Germany.
authors.forename: Lorenz
authors.initials: L
authors.lastname: Deserno
authors.affiliation: Department of Psychiatry and Psychotherapy, Charité Universitätsmedizin Berlin, Berlin, Germany; Max Planck Fellow Group "Cognitive and Affective Control of Behavioral Adaptation", Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany.
authors.forename: Florian
authors.initials: F
authors.lastname: Schlagenhauf
authors.affiliation: Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering, University of Zurich and ETH Zurich, Switzerland; Wellcome Trust Centre for Neuroimaging, University College London, UK; Max Planck Institute for Metabolism Research, Cologne, Germany.
authors.forename: Klaas Enno
authors.initials: KE
authors.lastname: Stephan
mesh_terms: D000328:Adult; D001499:Bayes Theorem; D001921:Brain / Q000000981:diagnostic imaging / Q000503:physiopathology; D016000:Cluster Analysis; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008279:Magnetic Resonance Imaging / Q000379:methods; D008297:Male; D008390:Markov Chains; D008959:Models, Neurological; D015233:Models, Statistical; D009010:Monte Carlo Method; D059906:Neuroimaging / Q000379:methods*; D015203:Reproducibility of Results; D012559:Schizophrenia / Q000145:classification / Q000000981:diagnostic imaging / Q000503:physiopathology; D012984:Software; D000069558:Unsupervised Machine Learning
keywords: Clustering; DCM; Dynamic causal modelling; MCMC; Markov chain Monte Carlo sampling; Mixture model; Psychiatric spectrum diseases; Schizophrenia