Computational models for imaging analyses Zurich SPM Course February 6, 2015 Christoph Mathys

What the brain is about What do our imaging methods measure? Brain activity. But when does the brain become active? When predictions (or their precision) have to be adjusted. So where do the brain’s predictions come from? From a model. Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 2

What does this mean for neuroimaging? If brain activity reflects model updating, we need to understand what model is updated in what way to make sense of brain activity. Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 3

The Bayesian brain and predictive coding Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 4 Hermann von Helmholtz

Advantages of model-based imaging Model-based imaging permits us to infer the computational (predictive) mechanisms underlying neuronal activity. to localize such mechanisms. to compare different models. Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 5

How to build a model Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 6 Sensory inputHidden states Prediction Inference based on prediction errors Fundamental ingredients:

Example of a simple learning model Rescorla-Wagner learning: Page 7 Previous value (prediction) Learning rate New input Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph Mathys

From perception to action Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 8 Sensory input True hidden states Inferred hidden states Action WorldAgent Generative process Inversion of perceptual generative model Decision model

From perception to action Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 9 Sensory input True hidden states Inferred hidden states Action WorldAgent

Example of a simple decision model Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 10

All the necessary ingredients Perceptual model (updates based on prediction errors) Value function (inferred state -> action value) Decision model (value -> action probability) Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 11

Reinforcement learning example (O’Doherty et al., 2003) Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 12 O’Doherty et al. (2003), Gläscher et al. (2010)

Reinforcement learning example Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 13 O’Doherty et al. (2003) Significant effects of prediction error with fixed learning rate

Bayesian models for the Bayesian brain Page 14Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph Mathys Sensory input True hidden states Inferred hidden states Action WorldAgent

State of the world Model Log-volatility x 3 of tendency Gaussian random walk with constant step size ϑ p(x 3 (k) ) ~ N(x 3 (k-1), ϑ ) Tendency x 2 towards category “1” Gaussian random walk with step size exp(κx 3 +ω) p(x 2 (k) ) ~ N(x 2 (k-1), exp(κx 3 +ω)) Stimulus category x 1 (“0” or “1”) Sigmoid trans- formation of x 2 p(x 1 =1) = s(x 2 ) p(x 1 =0) = 1-s(x 2 ) The hierarchical Gaussian filter (HGF): a computationally tractable model for individual learning under uncertainty Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph MathysPage 15

HGF: variational inversion and update equations Page 16 Prediction error Precisions determine learning rate Feb 6, 2015Model-based imaging, Zurich SPM Course, Christoph Mathys

Example: Iglesias et al. (2013) Feb 6, 2015Page 17Model-based imaging, Zurich SPM Course, Christoph Mathys Model comparison:

HGF: adaptive learning rate Feb 6, 2015Page 18 Simulation: Model-based imaging, Zurich SPM Course, Christoph Mathys

Individual model-based regressors Feb 6, 2015Page 19Model-based imaging, Zurich SPM Course, Christoph Mathys

Example: Iglesias et al. (2013) Feb 6, 2015Page 20Model-based imaging, Zurich SPM Course, Christoph Mathys

Example: Iglesias et al. (2013) Feb 6, 2015Page 21Model-based imaging, Zurich SPM Course, Christoph Mathys

Example: Iglesias et al. (2013) Feb 6, 2015Page 22Model-based imaging, Zurich SPM Course, Christoph Mathys

Example: Iglesias et al. (2013) Feb 6, 2015Page 23Model-based imaging, Zurich SPM Course, Christoph Mathys

How to estimate and compare models: the HGF Toolbox Feb 6, 2015Page 24Model-based imaging, Zurich SPM Course, Christoph Mathys Available at Start with README and tutorial there Modular, extensible Matlab-based

How it’s done in SPM Feb 6, 2015Page 25Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 26Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 27Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 28Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 29Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 30Model-based imaging, Zurich SPM Course, Christoph Mathys

How it’s done in SPM Feb 6, 2015Page 31Model-based imaging, Zurich SPM Course, Christoph Mathys

Take home Feb 6, 2015Page 32Model-based imaging, Zurich SPM Course, Christoph Mathys The brain is an organ whose job is prediction. To make its predictions, it needs a model. Model-based imaging infers the model at work in the brain. It enables inference on mechanisms, localization of mechanisms, and model comparison. Sensory input True hidden states Inferred hidden states Action WorldAgent

Thank you Feb 6, 2015Page 33Model-based imaging, Zurich SPM Course, Christoph Mathys