DCM: Advanced topics. Klaas Enno Stephan. SPM Course Zurich 06 February 2015
|
|
- Ruby Hamilton
- 6 years ago
- Views:
Transcription
1 DCM: Advanced topics Klaas Enno Stephan SPM Course Zurich 06 February 205
2 Overview DCM a generative model Evolution of DCM for fmri Bayesian model selection (BMS) Translational Neuromodeling
3 Generative model p( y, m) p( m) p( y, m). enforces mechanistic thinking: how could the data have been caused? 2. generate synthetic data (observations) by sampling from the prior can model explain certain phenomena at all? 3. inference about model structure: formal approach to disambiguating mechanisms p(y m) 4. inference about parameters p( y) 5. basis for predictions about interventions control theory
4 Bayesian system identification u(t) Design experimental inputs Neural dynamics dx dt f ( x, u, ) Define likelihood model Observer function y g( x, ) p( y, m) N( g( ), ( )) p(, m) N(, ) Specify priors Inference on model structure Inference on parameters p( y p( m) y, m) p( y, m) p( ) d p( y, m) p(, m) p( y m) Invert model Make inferences
5 Variational Bayes (VB) Idea: find an approximation q(θ) to the true posterior p θ y. Often done by assuming a particular form for q and then optimizing its sufficient statistics (fixed form VB). true posterior p θ y divergence KL q p best proxy q θ hypothesis class
6 Variational Bayes ln p(y) = KL[q p divergence 0 (unknown) + F q, y neg. free energy (easy to evaluate for a given q) ln p y KL[q p ln p y F q, y KL[q p F q, y is a functional wrt. the approximate posterior q θ. F q, y Maximizing F q, y is equivalent to: minimizing KL[q p tightening F q, y as a lower bound to the log model evidence When F q, y is maximized, q θ is our best estimate of the posterior. initialization convergence
7 Alternative optimisation schemes Global optimisation schemes for DCM: MCMC Gaussian processes Papers submitted in SPM soon
8 Overview DCM a generative model Evolution of DCM for fmri Bayesian model selection (BMS) Translational Neuromodeling
9 The evolution of DCM in SPM DCM is not one specific model, but a framework for Bayesian inversion of dynamic system models The implementation in SPM has been evolving over time, e.g. improvements of numerical routines (e.g., optimisation scheme) change in priors to cover new variants (e.g., stochastic DCMs) changes of hemodynamic model To enable replication of your results, you should ideally state which SPM version (release number) you are using when publishing papers.
10 Factorial structure of model specification Three dimensions of model specification: bilinear vs. nonlinear single-state vs. two-state (per region) deterministic vs. stochastic
11 y activity x (t) y activity x 2 (t) y activity x 3 (t) neuronal states BOLD y λ x hemodynamic model modulatory input u 2 (t) integration driving input u (t) The classical DCM: a deterministic, one-state, bilinear model t t Neural state equation endogenous connectivity modulation of connectivity direct inputs x ( j) ( A u B ) x Cu j x A x ( j) B u x C u j x x
12 bilinear DCM modulation non-linear DCM driving input driving input modulation Two-dimensional Taylor series (around x 0 =0, u 0 =0): dx f f f f x f ( x, u ) f ( x0,0) x u ux dt x u x u x 2 Bilinear state equation: Nonlinear state equation: dx dt A m i u B i ( i) x Cu dx dt m n ( i) A uib x i j j D ( j) x Cu
13 u Neural population activity u x x x fmri signal change (%) 0 0 Nonlinear Dynamic Causal Model for fmri dx dt A m n ( i) uib i j x j D ( j) x Cu Stephan et al. 2008, NeuroImage
14 u input Single-state DCM x Intrinsic (within-region) coupling Extrinsic (between-region) coupling N NN N N ij ij ij x x x ub A Cu x x Two-state DCM E x I N E N I E II NN IE NN EE NN EE NN EE N II IE EE N EI EE ij ij ij ij x x x x x ub A Cu x x ) exp( I x I E x x Two-state DCM Marreiros et al. 2008, NeuroImage
15 Stochastic DCM dx dt v ( A u B ) x Cv u ( v) j ( j) ( x) all states are represented in generalised coordinates of motion j random state fluctuations w (x) account for endogenous fluctuations, have unknown precision and smoothness two hyperparameters fluctuations w (v) induce uncertainty about how inputs influence neuronal activity can be fitted to "resting state" data Estimates of hidden causes and states (Generalised filtering) inputs or causes - V hidden states - neuronal hidden states - hemodynamic predicted BOLD signal excitatory signal flow volume dhb observed predicted - Li et al. 20, NeuroImage time (seconds)
16 Spectral DCM deterministic model that generates predicted crossed spectra in a distributed neuronal network or graph finds the effective connectivity among hidden neuronal states that best explains the observed functional connectivity among hemodynamic responses advantage: replaces an optimisation problem wrt. stochastic differential equations with a deterministic approach from linear systems theory computationally very efficient disadvantages: assumes stationarity Friston et al. 204, NeuroImage
17 cross-spectra = inverse Fourier transform of crosscorrelation cross-correlation = generalized form of correlation (at zero lag, this is the conventional measure of functional connectivity) Friston et al. 204, NeuroImage
18 Overview DCM a generative model Evolution of DCM for fmri Bayesian model selection (BMS) Translational Neuromodeling
19 Model comparison and selection Given competing hypotheses on structure & functional mechanisms of a system, which model is the best? Which model represents the best balance between model fit and model complexity? For which model m does p(y m) become maximal? Pitt & Miyung (2002) TICS
20 p(y m) Bayesian model selection (BMS) Model evidence: Gharamani, 2004 p( y m) p( y, m) p( m) d accounts for both accuracy and complexity of the model y all possible datasets allows for inference about model structure Various approximations, e.g.: - negative free energy, AIC, BIC McKay 992, Neural Comput. Penny et al. 2004a, NeuroImage
21 Approximations to the model evidence in DCM Logarithm is a monotonic function Maximizing log model evidence = Maximizing model evidence Log model evidence = balance between fit and complexity log p( y m) accuracy ( m) complexity( m) log p( y, m) complexity( m) No. of parameters Akaike Information Criterion: Bayesian Information Criterion: AIC BIC log p( y, m) log p( y, m) p p 2 log N No. of data points Penny et al. 2004a, NeuroImage
22 The (negative) free energy approximation F Neg. free energy is a lower bound on log model evidence: log p( y m) F KL q, p y, m ln p y m KL[q p F q, y Like AIC/BIC, F is an accuracy/complexity tradeoff: F log p( y, m) KL q, p m accuracy complexity
23 The complexity term in F In contrast to AIC & BIC, the complexity term of the negative free energy F accounts for parameter interdependencies. KL q( ), p( m) 2 ln C 2 ln C y 2 T C y y The complexity term of F is higher the more independent the prior parameters ( effective DFs) the more dependent the posterior parameters the more the posterior mean deviates from the prior mean
24 Bayes factors To compare two models, we could just compare their log evidences. But: the log evidence is just some number not very intuitive! A more intuitive interpretation of model comparisons is made possible by Bayes factors: B 2 p( y p( y Kass & Raftery classification: Kass & Raftery 995, J. Am. Stat. Assoc. m m 2 ) ) positive value, [0;[ B 2 p(m y) Evidence to % weak 3 to % positive 20 to % strong 50 99% Very strong
25 Fixed effects BMS at group level Group Bayes factor (GBF) for...k subjects: GBF ij BF ij k ( k ) Average Bayes factor (ABF): ABF ij K k BF ( k ) ij Problems: - blind with regard to group heterogeneity - sensitive to outliers
26 Random effects BMS for heterogeneous groups Dirichlet parameters = occurrences of models in the population r ~ Dir( r; ) Dirichlet distribution of model probabilities r m y k ~ p( mk p) mk ~ p( mk p) mk ~ p( mk p) m ~ Mult( m;, r ~ p( y m ) y ~ p( y m ) y2 ~ p( y2 m2 ) y ~ p( y m ) ) Multinomial distribution of model labels m Measured data y Model inversion by Variational Bayes (VB) or MCMC Stephan et al. 2009a, NeuroImage Penny et al. 200, PLoS Comp. Biol.
27 m 2 LD LD LVF m MOG FG FG MOG MOG FG FG MOG LD RVF LD LVF LD LD LG LG LG LG RVF stim. LD LVF stim. RVF stim. LD RVF LVF stim. Subjects m 2 m Data: Stephan et al. 2003, Science Models: Stephan et al. 2007, J. Neurosci Log model evidence differences
28 5 p(r >0.5 y) = m 2 p r r 99.7% 2 m 3 p(r y) r % r r 84.3% Stephan et al. 2009a, NeuroImage
29 When does an EP signal deviation from chance? EPs express our confidence that the posterior probabilities of models are different under the hypothesis H that models differ in probability: r k /K does not account for possibility "null hypothesis" H 0 : r k =/K Bayesian omnibus risk (BOR) of wrongly accepting H over H 0 : protected EP: Bayesian model averaging over H 0 and H : Rigoux et al. 204, NeuroImage
30 Overfitting at the level of models #models risk of overfitting solutions: regularisation: definition of model space = setting p(m) family-level BMS Bayesian model averaging (BMA) posterior model probability: p m y p y m p( m) p y m p( m) m BMA: p m y p y, m p m y
31 FFX RFX 80 log GBF Summed log evidence (rel. to RBML) nonlinear linear CBM N CBM N (ε) RBM N RBM N (ε) CBM L CBM L (ε) RBM L RBM L (ε) m 2 Model space partitioning: comparing model families p(r >0.5 y) = m alpha p(r y) p r r % 0 CBM N CBM N (ε) RBM N RBM N (ε) CBM L CBM L (ε) RBM L RBM L (ε) 2.5 Model space partitioning alpha m m 2 * 4 k k 0.5 r2 26.5% r 73.5% r nonlinear models * 2 8 k k5 linear models Stephan et al. 2009, NeuroImage
32 Bayesian Model Averaging (BMA) abandons dependence of parameter inference on a single model and takes into account model uncertainty represents a particularly useful alternative when none of the models (or model subspaces) considered clearly outperforms all others when comparing groups for which the optimal model differs single-subject BMA: p m y p y, m p m y group-level BMA: p m n y.. N p y, m p m y n n.. N NB: p(m y..n ) can be obtained by either FFX or RFX BMS Penny et al. 200, PLoS Comput. Biol.
33 Schmidt et al. 203, JAMA Psychiatry
34 Schmidt et al. 203, JAMA Psychiatry
35 Prefrontal-parietal connectivity during working memory in schizophrenia 7 ARMS, 2 first-episode (3 non-treated), 20 controls Schmidt et al. 203, JAMA Psychiatry
36 definition of model space inference on model structure or inference on model parameters? inference on individual models or model space partition? inference on parameters of an optimal model or parameters of all models? optimal model structure assumed to be identical across subjects? comparison of model families using FFX or RFX BMS optimal model structure assumed to be identical across subjects? BMA yes no yes no FFX BMS RFX BMS FFX BMS RFX BMS FFX analysis of parameter estimates (e.g. BPA) RFX analysis of parameter estimates (e.g. t-test, ANOVA) Stephan et al. 200, NeuroImage
37 Overview DCM a generative model Evolution of DCM for fmri Bayesian model selection (BMS) Translational Neuromodeling
38 Model-based predictions for single patients model structure DA BMS parameter estimates generative embedding
39 Synaesthesia projectors experience color externally colocalized with a presented grapheme associators report an internally evoked association across all subjects: no evidence for either model but BMS results map precisely onto projectors (bottom-up mechanisms) and associators (top-down) van Leeuwen et al. 20, J. Neurosci.
40 Generative embedding (unsupervised): detecting patient subgroups Brodersen et al. 204, NeuroImage: Clinical
41 Generative embedding: DCM and variational Gaussian Mixture Models Supervised: SVM classification Unsupervised: GMM clustering 7% number of clusters number of clusters 42 controls vs. 4 schizophrenic patients fmri data from working memory task (Deserno et al. 202, J. Neurosci) Brodersen et al. (204) NeuroImage: Clinical
42 Detecting subgroups of patients in schizophrenia Optimal cluster solution three distinct subgroups (total N=4) subgroups differ (p < 0.05) wrt. negative symptoms on the positive and negative symptom scale (PANSS) Brodersen et al. (204) NeuroImage: Clinical
43 A hierarchical model for unifying unsupervised generative embedding and empirical Bayes Raman et al., submitted
44 Dissecting spectrum disorders Differential diagnosis model validation (longitudinal patient studies) BMS Generative embedding (unsupervised) Computational assays Generative models of behaviour & brain activity BMS Generative embedding (supervised) optimized experimental paradigms (simple, robust, patient-friendly) initial model validation (basic science studies) Stephan & Mathys 204, Curr. Opin. Neurobiol.
45 Methods papers: DCM for fmri and BMS part Brodersen KH, Schofield TM, Leff AP, Ong CS, Lomakina EI, Buhmann JM, Stephan KE (20) Generative embedding for model-based classification of fmri data. PLoS Computational Biology 7: e Brodersen KH, Deserno L, Schlagenhauf F, Lin Z, Penny WD, Buhmann JM, Stephan KE (204) Dissecting psychiatric spectrum disorders by generative embedding. NeuroImage: Clinical 4: 98- Daunizeau J, David, O, Stephan KE (20) Dynamic Causal Modelling: A critical review of the biophysical and statistical foundations. NeuroImage 58: Daunizeau J, Stephan KE, Friston KJ (202) Stochastic Dynamic Causal Modelling of fmri data: Should we care about neural noise? NeuroImage 62: Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. NeuroImage 9: Friston K, Stephan KE, Li B, Daunizeau J (200) Generalised filtering. Mathematical Problems in Engineering 200: Friston KJ, Li B, Daunizeau J, Stephan KE (20) Network discovery with DCM. NeuroImage 56: Friston K, Penny W (20) Post hoc Bayesian model selection. Neuroimage 56: Friston KJ, Kahan J, Biswal B, Razi A (204) A DCM for resting state fmri. Neuroimage 94: Kiebel SJ, Kloppel S, Weiskopf N, Friston KJ (2007) Dynamic causal modeling: a generative model of slice timing in fmri. NeuroImage 34: Li B, Daunizeau J, Stephan KE, Penny WD, Friston KJ (20). Stochastic DCM and generalised filtering. NeuroImage 58: Marreiros AC, Kiebel SJ, Friston KJ (2008) Dynamic causal modelling for fmri: a two-state model. NeuroImage 39: Penny WD, Stephan KE, Mechelli A, Friston KJ (2004a) Comparing dynamic causal models. NeuroImage 22:57-72.
46 Methods papers: DCM for fmri and BMS part 2 Penny WD, Stephan KE, Mechelli A, Friston KJ (2004b) Modelling functional integration: a comparison of structural equation and dynamic causal models. NeuroImage 23 Suppl :S Penny WD, Stephan KE, Daunizeau J, Joao M, Friston K, Schofield T, Leff AP (200) Comparing Families of Dynamic Causal Models. PLoS Computational Biology 6: e Penny WD (202) Comparing dynamic causal models using AIC, BIC and free energy. Neuroimage 59: Rigoux L, Stephan KE, Friston KJ, Daunizeau J (204). Bayesian model selection for group studies revisited. NeuroImage 84: Stephan KE, Harrison LM, Penny WD, Friston KJ (2004) Biophysical models of fmri responses. Curr Opin Neurobiol 4: Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38: Stephan KE, Harrison LM, Kiebel SJ, David O, Penny WD, Friston KJ (2007) Dynamic causal models of neural system dynamics: current state and future extensions. J Biosci 32: Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38: Stephan KE, Kasper L, Harrison LM, Daunizeau J, den Ouden HE, Breakspear M, Friston KJ (2008) Nonlinear dynamic causal models for fmri. NeuroImage 42: Stephan KE, Penny WD, Daunizeau J, Moran RJ, Friston KJ (2009a) Bayesian model selection for group studies. NeuroImage 46: Stephan KE, Tittgemeyer M, Knösche TR, Moran RJ, Friston KJ (2009b) Tractography-based priors for dynamic causal models. NeuroImage 47: Stephan KE, Penny WD, Moran RJ, den Ouden HEM, Daunizeau J, Friston KJ (200) Ten simple rules for Dynamic Causal Modelling. NeuroImage 49: Stephan KE, Mathys C (204). Computational approaches to psychiatry. Current Opinion in Neurobiology 25:
47 Thank you
Dynamic causal modeling for fmri
Dynamic causal modeling for fmri Methods and Models for fmri, HS 2015 Jakob Heinzle Structural, functional & effective connectivity Sporns 2007, Scholarpedia anatomical/structural connectivity - presence
More informationDCM for fmri Advanced topics. Klaas Enno Stephan
DCM for fmri Advanced topics Klaas Enno Stephan Overview DCM: basic concepts Evolution of DCM for fmri Bayesian model selection (BMS) Translational Neuromodeling Dynamic causal modeling (DCM) EEG, MEG
More informationDynamic Causal Modelling : Advanced Topics
Dynamic Causal Modelling : Advanced Topics Rosalyn Moran Virginia Tech Carilion Research Institute Department of Electrical & Computer Engineering, Virginia Tech Zurich SPM Course, Feb 19 th 2016 Overview
More informationEffective Connectivity & Dynamic Causal Modelling
Effective Connectivity & Dynamic Causal Modelling Hanneke den Ouden Donders Centre for Cognitive Neuroimaging Radboud University Nijmegen Advanced SPM course Zurich, Februari 13-14, 2014 Functional Specialisation
More informationWellcome Trust Centre for Neuroimaging, UCL, UK.
Bayesian Inference Will Penny Wellcome Trust Centre for Neuroimaging, UCL, UK. SPM Course, Virginia Tech, January 2012 What is Bayesian Inference? (From Daniel Wolpert) Bayesian segmentation and normalisation
More informationDynamic causal modeling for fmri
Dynamic causal modeling for fmri Methods and Models for fmri, HS 2016 Jakob Heinzle Structural, functional & effective connectivity Sporns 2007, Scholarpedia anatomical/structural connectivity - presence
More informationAnatomical Background of Dynamic Causal Modeling and Effective Connectivity Analyses
Anatomical Background of Dynamic Causal Modeling and Effective Connectivity Analyses Jakob Heinzle Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering University and ETH Zürich
More informationDynamic Causal Modelling for fmri
Dynamic Causal Modelling for fmri André Marreiros Friday 22 nd Oct. 2 SPM fmri course Wellcome Trust Centre for Neuroimaging London Overview Brain connectivity: types & definitions Anatomical connectivity
More informationBayesian inference J. Daunizeau
Bayesian inference J. Daunizeau Brain and Spine Institute, Paris, France Wellcome Trust Centre for Neuroimaging, London, UK Overview of the talk 1 Probabilistic modelling and representation of uncertainty
More informationWill Penny. SPM short course for M/EEG, London 2015
SPM short course for M/EEG, London 2015 Ten Simple Rules Stephan et al. Neuroimage, 2010 Model Structure The model evidence is given by integrating out the dependence on model parameters p(y m) = p(y,
More informationA prior distribution over model space p(m) (or hypothesis space ) can be updated to a posterior distribution after observing data y.
June 2nd 2011 A prior distribution over model space p(m) (or hypothesis space ) can be updated to a posterior distribution after observing data y. This is implemented using Bayes rule p(m y) = p(y m)p(m)
More informationDynamic Causal Modelling for EEG/MEG: principles J. Daunizeau
Dynamic Causal Modelling for EEG/MEG: principles J. Daunizeau Motivation, Brain and Behaviour group, ICM, Paris, France Overview 1 DCM: introduction 2 Dynamical systems theory 3 Neural states dynamics
More informationBayesian inference J. Daunizeau
Bayesian inference J. Daunizeau Brain and Spine Institute, Paris, France Wellcome Trust Centre for Neuroimaging, London, UK Overview of the talk 1 Probabilistic modelling and representation of uncertainty
More informationAn introduction to Bayesian inference and model comparison J. Daunizeau
An introduction to Bayesian inference and model comparison J. Daunizeau ICM, Paris, France TNU, Zurich, Switzerland Overview of the talk An introduction to probabilistic modelling Bayesian model comparison
More informationDynamic Causal Models
Dynamic Causal Models V1 SPC Will Penny V1 SPC V5 V5 Olivier David, Karl Friston, Lee Harrison, Andrea Mechelli, Klaas Stephan Wellcome Department of Imaging Neuroscience, ION, UCL, UK. Mathematics in
More informationStochastic Dynamic Causal Modelling for resting-state fmri
Stochastic Dynamic Causal Modelling for resting-state fmri Ged Ridgway, FIL, Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, London Overview Connectivity in the brain Introduction to
More informationBayesian inference. Justin Chumbley ETH and UZH. (Thanks to Jean Denizeau for slides)
Bayesian inference Justin Chumbley ETH and UZH (Thanks to Jean Denizeau for slides) Overview of the talk Introduction: Bayesian inference Bayesian model comparison Group-level Bayesian model selection
More informationWill Penny. SPM short course for M/EEG, London 2013
SPM short course for M/EEG, London 2013 Ten Simple Rules Stephan et al. Neuroimage, 2010 Model Structure Bayes rule for models A prior distribution over model space p(m) (or hypothesis space ) can be updated
More informationWill Penny. DCM short course, Paris 2012
DCM short course, Paris 2012 Ten Simple Rules Stephan et al. Neuroimage, 2010 Model Structure Bayes rule for models A prior distribution over model space p(m) (or hypothesis space ) can be updated to a
More informationDynamic Causal Modelling for EEG and MEG. Stefan Kiebel
Dynamic Causal Modelling for EEG and MEG Stefan Kiebel Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications Overview
More informationModels of effective connectivity & Dynamic Causal Modelling (DCM)
Models of effective connectivit & Dnamic Causal Modelling (DCM Presented b: Ariana Anderson Slides shared b: Karl Friston Functional Imaging Laborator (FIL Wellcome Trust Centre for Neuroimaging Universit
More informationDynamic Causal Modelling for evoked responses J. Daunizeau
Dynamic Causal Modelling for evoked responses J. Daunizeau Institute for Empirical Research in Economics, Zurich, Switzerland Brain and Spine Institute, Paris, France Overview 1 DCM: introduction 2 Neural
More informationDynamic Causal Modelling for EEG and MEG
Dynamic Causal Modelling for EEG and MEG Stefan Kiebel Ma Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic
More informationDynamic Modeling of Brain Activity
0a Dynamic Modeling of Brain Activity EIN IIN PC Thomas R. Knösche, Leipzig Generative Models for M/EEG 4a Generative Models for M/EEG states x (e.g. dipole strengths) parameters parameters (source positions,
More informationWill Penny. SPM for MEG/EEG, 15th May 2012
SPM for MEG/EEG, 15th May 2012 A prior distribution over model space p(m) (or hypothesis space ) can be updated to a posterior distribution after observing data y. This is implemented using Bayes rule
More informationModel Comparison. Course on Bayesian Inference, WTCN, UCL, February Model Comparison. Bayes rule for models. Linear Models. AIC and BIC.
Course on Bayesian Inference, WTCN, UCL, February 2013 A prior distribution over model space p(m) (or hypothesis space ) can be updated to a posterior distribution after observing data y. This is implemented
More informationOverview of SPM. Overview. Making the group inferences we want. Non-sphericity Beyond Ordinary Least Squares. Model estimation A word on power
Group Inference, Non-sphericity & Covariance Components in SPM Alexa Morcom Edinburgh SPM course, April 011 Centre for Cognitive & Neural Systems/ Department of Psychology University of Edinburgh Overview
More informationUnsupervised Learning
Unsupervised Learning Bayesian Model Comparison Zoubin Ghahramani zoubin@gatsby.ucl.ac.uk Gatsby Computational Neuroscience Unit, and MSc in Intelligent Systems, Dept Computer Science University College
More informationBayesian Inference Course, WTCN, UCL, March 2013
Bayesian Course, WTCN, UCL, March 2013 Shannon (1948) asked how much information is received when we observe a specific value of the variable x? If an unlikely event occurs then one would expect the information
More informationExperimental design of fmri studies
Experimental design of fmri studies Zurich SPM Course 2016 Sandra Iglesias Translational Neuromodeling Unit (TNU) Institute for Biomedical Engineering (IBT) University and ETH Zürich With many thanks for
More informationModels of effective connectivity & Dynamic Causal Modelling (DCM)
Models of effective connectivit & Dnamic Causal Modelling (DCM) Slides obtained from: Karl Friston Functional Imaging Laborator (FIL) Wellcome Trust Centre for Neuroimaging Universit College London Klaas
More informationThe General Linear Model (GLM)
he General Linear Model (GLM) Klaas Enno Stephan ranslational Neuromodeling Unit (NU) Institute for Biomedical Engineering University of Zurich & EH Zurich Wellcome rust Centre for Neuroimaging Institute
More informationDynamic causal models of neural system dynamics:current state and future extensions.
Dynamic causal models of neural system dynamics:current state and future extensions. Klaas Stephan, Lee Harrison, Stefan Kiebel, Olivier David, Will Penny, Karl Friston To cite this version: Klaas Stephan,
More informationExperimental design of fmri studies
Experimental design of fmri studies Sandra Iglesias Translational Neuromodeling Unit University of Zurich & ETH Zurich With many thanks for slides & images to: Klaas Enno Stephan, FIL Methods group, Christian
More informationGroup Analysis. Lexicon. Hierarchical models Mixed effect models Random effect (RFX) models Components of variance
Group Analysis J. Daunizeau Institute of Empirical Research in Economics, Zurich, Switzerland Brain and Spine Institute, Paris, France SPM Course Edinburgh, April 2011 Image time-series Spatial filter
More informationExperimental design of fmri studies
Experimental design of fmri studies Sandra Iglesias With many thanks for slides & images to: Klaas Enno Stephan, FIL Methods group, Christian Ruff SPM Course 2015 Overview of SPM Image time-series Kernel
More information9/12/17. Types of learning. Modeling data. Supervised learning: Classification. Supervised learning: Regression. Unsupervised learning: Clustering
Types of learning Modeling data Supervised: we know input and targets Goal is to learn a model that, given input data, accurately predicts target data Unsupervised: we know the input only and want to make
More informationPATTERN RECOGNITION AND MACHINE LEARNING
PATTERN RECOGNITION AND MACHINE LEARNING Chapter 1. Introduction Shuai Huang April 21, 2014 Outline 1 What is Machine Learning? 2 Curve Fitting 3 Probability Theory 4 Model Selection 5 The curse of dimensionality
More informationExperimental design of fmri studies & Resting-State fmri
Methods & Models for fmri Analysis 2016 Experimental design of fmri studies & Resting-State fmri Sandra Iglesias With many thanks for slides & images to: Klaas Enno Stephan, FIL Methods group, Christian
More informationLecture 6: Graphical Models: Learning
Lecture 6: Graphical Models: Learning 4F13: Machine Learning Zoubin Ghahramani and Carl Edward Rasmussen Department of Engineering, University of Cambridge February 3rd, 2010 Ghahramani & Rasmussen (CUED)
More informationBayesian modeling of learning and decision-making in uncertain environments
Bayesian modeling of learning and decision-making in uncertain environments Christoph Mathys Max Planck UCL Centre for Computational Psychiatry and Ageing Research, London, UK Wellcome Trust Centre for
More informationModelling temporal structure (in noise and signal)
Modelling temporal structure (in noise and signal) Mark Woolrich, Christian Beckmann*, Salima Makni & Steve Smith FMRIB, Oxford *Imperial/FMRIB temporal noise: modelling temporal autocorrelation temporal
More informationCausal modeling of fmri: temporal precedence and spatial exploration
Causal modeling of fmri: temporal precedence and spatial exploration Alard Roebroeck Maastricht Brain Imaging Center (MBIC) Faculty of Psychology & Neuroscience Maastricht University Intro: What is Brain
More informationModelling behavioural data
Modelling behavioural data Quentin Huys MA PhD MBBS MBPsS Translational Neuromodeling Unit, ETH Zürich Psychiatrische Universitätsklinik Zürich Outline An example task Why build models? What is a model
More informationComparing hemodynamic models with DCM
www.elsevier.com/locate/ynimg NeuroImage 38 (2007) 387 401 Comparing hemodynamic models with DCM Klaas Enno Stephan, a, Nikolaus Weiskopf, a Peter M. Drysdale, b,c Peter A. Robinson, b,c,d and Karl J.
More informationComparing Families of Dynamic Causal Models
Comparing Families of Dynamic Causal Models Will D. Penny 1 *, Klaas E. Stephan 1,2, Jean Daunizeau 1, Maria J. Rosa 1, Karl J. Friston 1, Thomas M. Schofield 1, Alex P. Leff 1 1 Wellcome Trust Centre
More informationExperimental design of fmri studies
Methods & Models for fmri Analysis 2017 Experimental design of fmri studies Sara Tomiello With many thanks for slides & images to: Sandra Iglesias, Klaas Enno Stephan, FIL Methods group, Christian Ruff
More informationMathematical Formulation of Our Example
Mathematical Formulation of Our Example We define two binary random variables: open and, where is light on or light off. Our question is: What is? Computer Vision 1 Combining Evidence Suppose our robot
More informationBayesian Inference. Chris Mathys Wellcome Trust Centre for Neuroimaging UCL. London SPM Course
Bayesian Inference Chris Mathys Wellcome Trust Centre for Neuroimaging UCL London SPM Course Thanks to Jean Daunizeau and Jérémie Mattout for previous versions of this talk A spectacular piece of information
More informationNeuroImage. Nonlinear dynamic causal models for fmri
NeuroImage 42 (2008) 649 662 Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/ynimg Nonlinear dynamic causal models for fmri Klaas Enno Stephan a,b,, Lars
More informationLecture 6: Model Checking and Selection
Lecture 6: Model Checking and Selection Melih Kandemir melih.kandemir@iwr.uni-heidelberg.de May 27, 2014 Model selection We often have multiple modeling choices that are equally sensible: M 1,, M T. Which
More informationPrinciples of DCM. Will Penny. 26th May Principles of DCM. Will Penny. Introduction. Differential Equations. Bayesian Estimation.
26th May 2011 Dynamic Causal Modelling Dynamic Causal Modelling is a framework studying large scale brain connectivity by fitting differential equation models to brain imaging data. DCMs differ in their
More informationCSC2535: Computation in Neural Networks Lecture 7: Variational Bayesian Learning & Model Selection
CSC2535: Computation in Neural Networks Lecture 7: Variational Bayesian Learning & Model Selection (non-examinable material) Matthew J. Beal February 27, 2004 www.variational-bayes.org Bayesian Model Selection
More informationBayesian Inference. Sudhir Shankar Raman Translational Neuromodeling Unit, UZH & ETH. The Reverend Thomas Bayes ( )
The Reverend Thomas Baes (1702-1761) Baesian Inference Sudhir Shankar Raman Translational Neuromodeling Unit, UZH & ETH With man thanks for some slides to: Klaas Enno Stephan & Ka H. Brodersen Wh do I
More informationThe General Linear Model (GLM)
The General Linear Model (GLM) Dr. Frederike Petzschner Translational Neuromodeling Unit (TNU) Institute for Biomedical Engineering, University of Zurich & ETH Zurich With many thanks for slides & images
More informationECE521 week 3: 23/26 January 2017
ECE521 week 3: 23/26 January 2017 Outline Probabilistic interpretation of linear regression - Maximum likelihood estimation (MLE) - Maximum a posteriori (MAP) estimation Bias-variance trade-off Linear
More informationMachine Learning Summer School
Machine Learning Summer School Lecture 3: Learning parameters and structure Zoubin Ghahramani zoubin@eng.cam.ac.uk http://learning.eng.cam.ac.uk/zoubin/ Department of Engineering University of Cambridge,
More informationarxiv: v1 [cs.sy] 13 Feb 2018
The role of noise modeling in the estimation of resting-state brain effective connectivity G. Prando M. Zorzi A. Bertoldo A. Chiuso Dept. of Information Engineering, University of Padova (e-mail: {prandogi,zorzimat,bertoldo,chiuso}@dei.unipd.it)
More informationMachine Learning! in just a few minutes. Jan Peters Gerhard Neumann
Machine Learning! in just a few minutes Jan Peters Gerhard Neumann 1 Purpose of this Lecture Foundations of machine learning tools for robotics We focus on regression methods and general principles Often
More informationVariational Scoring of Graphical Model Structures
Variational Scoring of Graphical Model Structures Matthew J. Beal Work with Zoubin Ghahramani & Carl Rasmussen, Toronto. 15th September 2003 Overview Bayesian model selection Approximations using Variational
More informationDynamic causal models of neural system dynamics. current state and future extensions
Dynamic causal models of neural system dynamics: current state and future etensions Klaas E. Stephan 1, Lee M. Harrison 1, Stefan J. Kiebel 1, Olivier David, Will D. Penny 1 & Karl J. Friston 1 1 Wellcome
More informationEmpirical Bayes for DCM: A Group Inversion Scheme
METHODS published: 27 November 2015 doi: 10.3389/fnsys.2015.00164 : A Group Inversion Scheme Karl Friston*, Peter Zeidman and Vladimir Litvak The Wellcome Trust Centre for Neuroimaging, University College
More informationCheng Soon Ong & Christian Walder. Canberra February June 2018
Cheng Soon Ong & Christian Walder Research Group and College of Engineering and Computer Science Canberra February June 2018 (Many figures from C. M. Bishop, "Pattern Recognition and ") 1of 254 Part V
More informationVariational Methods in Bayesian Deconvolution
PHYSTAT, SLAC, Stanford, California, September 8-, Variational Methods in Bayesian Deconvolution K. Zarb Adami Cavendish Laboratory, University of Cambridge, UK This paper gives an introduction to the
More informationMixed effects and Group Modeling for fmri data
Mixed effects and Group Modeling for fmri data Thomas Nichols, Ph.D. Department of Statistics Warwick Manufacturing Group University of Warwick Warwick fmri Reading Group May 19, 2010 1 Outline Mixed effects
More informationWill Penny. 21st April The Macroscopic Brain. Will Penny. Cortical Unit. Spectral Responses. Macroscopic Models. Steady-State Responses
The The 21st April 2011 Jansen and Rit (1995), building on the work of Lopes Da Sliva and others, developed a biologically inspired model of EEG activity. It was originally developed to explain alpha activity
More informationNon-Parametric Bayes
Non-Parametric Bayes Mark Schmidt UBC Machine Learning Reading Group January 2016 Current Hot Topics in Machine Learning Bayesian learning includes: Gaussian processes. Approximate inference. Bayesian
More informationContinuous Time Particle Filtering for fmri
Continuous Time Particle Filtering for fmri Lawrence Murray School of Informatics University of Edinburgh lawrence.murray@ed.ac.uk Amos Storkey School of Informatics University of Edinburgh a.storkey@ed.ac.uk
More informationMIXED EFFECTS MODELS FOR TIME SERIES
Outline MIXED EFFECTS MODELS FOR TIME SERIES Cristina Gorrostieta Hakmook Kang Hernando Ombao Brown University Biostatistics Section February 16, 2011 Outline OUTLINE OF TALK 1 SCIENTIFIC MOTIVATION 2
More informationM/EEG source analysis
Jérémie Mattout Lyon Neuroscience Research Center Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for
More informationGroup analysis. Jean Daunizeau Wellcome Trust Centre for Neuroimaging University College London. SPM Course Edinburgh, April 2010
Group analysis Jean Daunizeau Wellcome Trust Centre for Neuroimaging University College London SPM Course Edinburgh, April 2010 Image time-series Spatial filter Design matrix Statistical Parametric Map
More informationDynamic Data Modeling, Recognition, and Synthesis. Rui Zhao Thesis Defense Advisor: Professor Qiang Ji
Dynamic Data Modeling, Recognition, and Synthesis Rui Zhao Thesis Defense Advisor: Professor Qiang Ji Contents Introduction Related Work Dynamic Data Modeling & Analysis Temporal localization Insufficient
More informationStatistics 203: Introduction to Regression and Analysis of Variance Course review
Statistics 203: Introduction to Regression and Analysis of Variance Course review Jonathan Taylor - p. 1/?? Today Review / overview of what we learned. - p. 2/?? General themes in regression models Specifying
More informationModel Selection for Gaussian Processes
Institute for Adaptive and Neural Computation School of Informatics,, UK December 26 Outline GP basics Model selection: covariance functions and parameterizations Criteria for model selection Marginal
More informationCheng Soon Ong & Christian Walder. Canberra February June 2018
Cheng Soon Ong & Christian Walder Research Group and College of Engineering and Computer Science Canberra February June 218 Outlines Overview Introduction Linear Algebra Probability Linear Regression 1
More informationCS-E3210 Machine Learning: Basic Principles
CS-E3210 Machine Learning: Basic Principles Lecture 4: Regression II slides by Markus Heinonen Department of Computer Science Aalto University, School of Science Autumn (Period I) 2017 1 / 61 Today s introduction
More informationHGF Workshop. Christoph Mathys. Wellcome Trust Centre for Neuroimaging at UCL, Max Planck UCL Centre for Computational Psychiatry and Ageing Research
HGF Workshop Christoph Mathys Wellcome Trust Centre for Neuroimaging at UCL, Max Planck UCL Centre for Computational Psychiatry and Ageing Research Monash University, March 3, 2015 Systems theory places
More informationStatistical Inference
Statistical Inference J. Daunizeau Institute of Empirical Research in Economics, Zurich, Switzerland Brain and Spine Institute, Paris, France SPM Course Edinburgh, April 2011 Image time-series Spatial
More informationSemi-analytical approximations to statistical moments. of sigmoid and softmax mappings of normal variables
Semi-analytical approximations to statistical moments of sigmoid and softmax mappings of normal variables J. Daunizeau, Brain and Spine Institute, Paris, France ETH, Zurich, France Address for correspondence:
More informationInterpretable Latent Variable Models
Interpretable Latent Variable Models Fernando Perez-Cruz Bell Labs (Nokia) Department of Signal Theory and Communications, University Carlos III in Madrid 1 / 24 Outline 1 Introduction to Machine Learning
More informationClassification for High Dimensional Problems Using Bayesian Neural Networks and Dirichlet Diffusion Trees
Classification for High Dimensional Problems Using Bayesian Neural Networks and Dirichlet Diffusion Trees Rafdord M. Neal and Jianguo Zhang Presented by Jiwen Li Feb 2, 2006 Outline Bayesian view of feature
More informationMachine Learning Basics: Maximum Likelihood Estimation
Machine Learning Basics: Maximum Likelihood Estimation Sargur N. srihari@cedar.buffalo.edu This is part of lecture slides on Deep Learning: http://www.cedar.buffalo.edu/~srihari/cse676 1 Topics 1. Learning
More informationActive and Semi-supervised Kernel Classification
Active and Semi-supervised Kernel Classification Zoubin Ghahramani Gatsby Computational Neuroscience Unit University College London Work done in collaboration with Xiaojin Zhu (CMU), John Lafferty (CMU),
More informationComputer Vision Group Prof. Daniel Cremers. 3. Regression
Prof. Daniel Cremers 3. Regression Categories of Learning (Rep.) Learnin g Unsupervise d Learning Clustering, density estimation Supervised Learning learning from a training data set, inference on the
More informationThe General Linear Model. Guillaume Flandin Wellcome Trust Centre for Neuroimaging University College London
The General Linear Model Guillaume Flandin Wellcome Trust Centre for Neuroimaging University College London SPM Course Lausanne, April 2012 Image time-series Spatial filter Design matrix Statistical Parametric
More informationCOMP 551 Applied Machine Learning Lecture 20: Gaussian processes
COMP 55 Applied Machine Learning Lecture 2: Gaussian processes Instructor: Ryan Lowe (ryan.lowe@cs.mcgill.ca) Slides mostly by: (herke.vanhoof@mcgill.ca) Class web page: www.cs.mcgill.ca/~hvanho2/comp55
More informationAn Implementation of Dynamic Causal Modelling
An Implementation of Dynamic Causal Modelling Christian Himpe 24.01.2011 Overview Contents: 1 Intro 2 Model 3 Parameter Estimation 4 Examples Motivation Motivation: How are brain regions coupled? Motivation
More informationCS6220: DATA MINING TECHNIQUES
CS6220: DATA MINING TECHNIQUES Matrix Data: Prediction Instructor: Yizhou Sun yzsun@ccs.neu.edu September 14, 2014 Today s Schedule Course Project Introduction Linear Regression Model Decision Tree 2 Methods
More informationCS6220: DATA MINING TECHNIQUES
CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 2 Instructor: Yizhou Sun yzsun@ccs.neu.edu September 21, 2014 Methods to Learn Matrix Data Set Data Sequence Data Time Series Graph & Network
More informationCS6220: DATA MINING TECHNIQUES
CS6220: DATA MINING TECHNIQUES Matrix Data: Prediction Instructor: Yizhou Sun yzsun@ccs.neu.edu September 21, 2015 Announcements TA Monisha s office hour has changed to Thursdays 10-12pm, 462WVH (the same
More informationGentle Introduction to Infinite Gaussian Mixture Modeling
Gentle Introduction to Infinite Gaussian Mixture Modeling with an application in neuroscience By Frank Wood Rasmussen, NIPS 1999 Neuroscience Application: Spike Sorting Important in neuroscience and for
More informationIntroduction to Machine Learning. Introduction to ML - TAU 2016/7 1
Introduction to Machine Learning Introduction to ML - TAU 2016/7 1 Course Administration Lecturers: Amir Globerson (gamir@post.tau.ac.il) Yishay Mansour (Mansour@tau.ac.il) Teaching Assistance: Regev Schweiger
More informationA graph contains a set of nodes (vertices) connected by links (edges or arcs)
BOLTZMANN MACHINES Generative Models Graphical Models A graph contains a set of nodes (vertices) connected by links (edges or arcs) In a probabilistic graphical model, each node represents a random variable,
More informationStudy Notes on the Latent Dirichlet Allocation
Study Notes on the Latent Dirichlet Allocation Xugang Ye 1. Model Framework A word is an element of dictionary {1,,}. A document is represented by a sequence of words: =(,, ), {1,,}. A corpus is a collection
More informationBayesian Methods for Machine Learning
Bayesian Methods for Machine Learning CS 584: Big Data Analytics Material adapted from Radford Neal s tutorial (http://ftp.cs.utoronto.ca/pub/radford/bayes-tut.pdf), Zoubin Ghahramni (http://hunch.net/~coms-4771/zoubin_ghahramani_bayesian_learning.pdf),
More informationSRNDNA Model Fitting in RL Workshop
SRNDNA Model Fitting in RL Workshop yael@princeton.edu Topics: 1. trial-by-trial model fitting (morning; Yael) 2. model comparison (morning; Yael) 3. advanced topics (hierarchical fitting etc.) (afternoon;
More informationBayesian Learning in Undirected Graphical Models
Bayesian Learning in Undirected Graphical Models Zoubin Ghahramani Gatsby Computational Neuroscience Unit University College London, UK http://www.gatsby.ucl.ac.uk/ Work with: Iain Murray and Hyun-Chul
More informationOutline Introduction OLS Design of experiments Regression. Metamodeling. ME598/494 Lecture. Max Yi Ren
1 / 34 Metamodeling ME598/494 Lecture Max Yi Ren Department of Mechanical Engineering, Arizona State University March 1, 2015 2 / 34 1. preliminaries 1.1 motivation 1.2 ordinary least square 1.3 information
More informationICML Scalable Bayesian Inference on Point processes. with Gaussian Processes. Yves-Laurent Kom Samo & Stephen Roberts
ICML 2015 Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes Machine Learning Research Group and Oxford-Man Institute University of Oxford July 8, 2015 Point Processes
More informationProbabilistic Models in Theoretical Neuroscience
Probabilistic Models in Theoretical Neuroscience visible unit Boltzmann machine semi-restricted Boltzmann machine restricted Boltzmann machine hidden unit Neural models of probabilistic sampling: introduction
More information