MULTIVARIATE ANALYSES WITH fmri DATA

Transcription

1 MULTIVARIATE ANALYSES WITH fmri DATA Sudhir Shankar Raman Translational Neuromodeling Unit (TNU) Institute for Biomedical Engineering University of Zurich & ETH Zurich

2 Motivation Modelling Concepts Learning From Data Multivariate Bayes in SPM Generative Embedding

3 Motivation Local activations Univariate approach 1 2 significant not significant

4 Univariate to Multivariate 1 2 not significant not significant 1 2

5 Motivation Modelling Terminology Learning from data Multivariate Bayes in SPM Generative Embedding

6 Steps for analysis Feature Extraction Classification Clustering Modelling Regression Inference Cross validation Performance Prediction Model Selection

7 Feature Space Features F 1 F 2... F P S Data Points S S N Discrete Continuous

8 Feature Space Examples Raw data F 1 F 2... F P S 1 S 2. Data Point or Feature Vector. High dimensionality S N Class/Cluster distributions Interpretation Voxel activity Model parameters GLM regression coefficients DCM connection parameters

9 Model Selection - Generalizability Model Fit Model Complexity Bishop (2006), Pitt & Miyung (2002), TICS

10 Modelling goals Prediction Y h X Predictive Density

11 Modelling goals Model Selection Sparse Coding Distributed Coding Model Evidence

12 Motivation Modelling Concepts Learning From Data Multivariate Bayes in SPM Generative Embedding

13 Learning from Data Supervised Learning Unsupervised Learning Reinforcement Learning Semi-supervised Learning

14 Supervised Learning Independent variables X Function - f Continuous dependent variable Y Categorical

15 Classification X Function - f Y Generative classifier Discriminative classifier Kernel Methods Support Vector Machines φ Kernel Function K x i, x j = φ x i. φ x j Kernel methods for pattern analysis, Taylor, Cristianini, 2004

16 Other popular classifiers Gaussian Processes C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, Deep Belief networks G.E. Hinton, S. Osindero, and Y. Teh, A fast learning algorithm for deep belief nets, Neural Computation, vol 18, 2006

17 K-fold Cross Validation Model Selection Performance evaluation 1 Balanced Accuracy F1 Score Training data Test data Accuracy 87% 2 75% 3 89%

18 Performance Single Subject Binomial Test p = P X k H 0 = 1 B k n, π 0 Brodersen et al. 2013, NeuroImage k=30

19 Performance Multiple Subjects Random effects Fixed effects Brodersen et al. 2013, NeuroImage

20 Using classification for fmri data Whole brain Searchlight classifier Mourao-Miranda et al. (2005) NeuroImage, Marquand et al. (2010) NeuroImage Kriegeskorte et al. (2006) PNAS Pattern localization Word Category Food Building People Pereira et al. (2009) NeuroImage, Mitchell et al. (2004) Machine Learning

21 Confounds GLM vs MVPA Todd et al. 2013, NeuroImage

22 Practicals Classification using SVM Bishop (2006) PRML

23 Unsupervised Learning Building a representation of data Dimensionality Reduction Clustering Time series K-means Mixture models

24 Clustering using K-means Cost function Algorithm 1. Initialize 2. Estimate assignments 3. Estimate cluster centroids 4. Repeat 2,3 until convergence Bishop PRML (2006)

25 Clustering Mixture of Gaussians Bishop PRML (2006)

26 Interpretation Cluster parameters Cluster 1 Cluster 2 Internal Criterion Model Evidence External Criterion - Purity Inferred Labels Subjects External Labels

27 Practicals Clustering K-Means Finite Gaussian mixture model Bishop (2006) PRML

28 Motivation Modelling Learning from Data Multivariate Bayes in SPM Generative Embedding

29 Encoding Vs Decoding Models

30 Encoding Vs Decoding Friston et al NeuroImage

31 Coding hypotheses Sparse vectors Spatial vectors Smooth vectors Distributed vectors Singular vectors of data UUV T = RY T Support vectors U = RY T

32 Coding hypotheses Friston et al NeuroImage

33 VB Inference Friston et al NeuroImage

34 Bayesian decoding of motion Attention to motion dataset - Büchel & Friston 1999 Cerebral Cortex Experimental factors: 1. Photic 2. Motion 3. Attention Friston et al NeuroImage

35 Multivariate Bayes in SPM

36 Results Friston et al NeuroImage

37 Results

38 Laminar activity related to novelty and episodic encoding Maas et al Nature Communications

39 Demo Bayesian decoding of motion in SPM

40 Motivation Modelling Principles Learning from Data Multivariate Bayes in SPM Generative Embedding

41 Voxel activity Subject 1 Subject 2. Dynamic causal model (DCM) High dimensionality Unusual cluster distributions Lack of interpretation Connectivity Subject 1 Subject 2. Subject N Classification Clustering Subject N Group 1 Group 2

42 Generative Embedding - Classification Brodersen et al. plos computation biology 2011.

43 DCM - Speech processing Brodersen et al. plos computation biology 2011.

44 Working memory - fmri 41 Schizophrenia patients (DSM IV,ICD 10), 42 controls Visual numeric n-back working memory task ms ms Deserno, Lorenz et al The Journal of Neuroscience 32 (1). Society for Neuroscience:

45 Model based clustering Brodersen et al 2014 Neuroimage

46 Results Healthy vs Schizophrenic Brodersen et al 2014 Neuroimage

47 Results Schizophrenia patients Brodersen et al 2014 Neuroimage

48 Unified model for identifying subgroups Raman et al A hierarchical model for integrating unsupervised generative embedding and empirical Bayes.Submitted

49 Summary Modelling Principles Learning from Data Multivariate Bayes in SPM Generative Embedding

50 Thank you