model-based classification kay henning brodersen · 2020. 5. 17. · evidence for sparse coding vs....
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Model-based classification through generative embedding
Kay Henning Brodersen
Machine Learning and Pattern Recognition Group Department of Computer Science, ETH Zurich
Computational Neuroeconomics Group Department of Economics, University of Zurich
http://people.inf.ethz.ch/bkay/
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Computational science and psychiatry
Spectrum diseases
diverse genetic basis
strong gene-environment interactions
variability in treatment response and outcome
Consequences
multiple pathophysiological mechanisms
even when symptoms are similar, causes may differ across patients
need to infer pathophysiological mechanisms in individual patients!
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Model-based inference on individual pathophysiology
model-based
diagnostic tests
application to brain activity data from individual patients
model of neuronal (patho)physiology
spectrum disease
type 2
type 3
type 1
diagnostic classification
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Conventional vs. model-based classification
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L.H
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24
,4)
mm
L.MGB → L.MGB Voxel (-42,-26,10) mm
Voxel (-56,-20,10) mm R.HG → L.HG
controls patients
Conventional classification Model-based classification
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Colleagues & collaborators
Joachim M Buhmann ETH Zurich
Klaas Enno Stephan University of Zurich · University College London
Kate Lomakina University of Zurich · ETH Zurich
Alexander Leff University College London
Cheng Soon Ong ETH Zurich
Thomas Schofield University College London
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Model-based classification
Can we exploit the rich discriminative information encoded in individual patterns of connection strengths?
Data representations in classification analyses
Structure-based classification
• mild traumatic brain injury • Alzheimer’s disease • autistic spectrum disorder • frontotemporal
dementia • mild cognitive
impairment • schizophrenia • aphasia
Activation-based classification
• depression • schizophrenia • mild cognitive
impairment
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Prediction versus inference
The goal of prediction is to find a highly accurate encoding or decoding function.
The goal of inference is to decide between competing hypotheses about mechanisms or representations in the brain.
predicting a cognitive state using a
brain-machine interface
predicting a subject-specific
diagnostic status
comparing a model that links distributed neuronal
activity to a cognitive state with a model that does not
weighing the evidence for sparse
coding vs. dense coding
powerful discriminative algorithms for classification
mechanistically interpretable generative models of brain function
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Model-based classification through generative embedding
Brodersen, Haiss, Ong, Jung, Tittgemeyer, Buhmann, Weber, Stephan (2011) NeuroImage Brodersen, Schofield, Leff, Ong, Lomakina, Buhmann, Stephan (2011) PLoS Comp Biol
step 2 — kernel construction
step 1 — model inversion
measurements from an individual
subject
subject-specific inverted generative model
subject representation in the generative score space
A → B
A → C
B → B
B → C
A
C B
step 3 — classification
separating hyperplane to discriminate between groups
A
C B
jointly discriminative connection strengths
step 4 — interpretation
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(1) L.MGB -> L.MGB
(14)
R.H
G -
> L
.HG
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activity 𝑧1(𝑡)
Choosing a generative model: DCM for fMRI
intrinsic connectivity
direct inputs
modulation of connectivity
neural state equation
CuzBuAz j
j )( )(
u
zC
z
z
uB
z
zA
j
j
)(
haemodynamic forward model
𝑥 = 𝑔(𝑧, 𝜃ℎ)
observed BOLD signal
neuronal states
t
driving input 𝑢1(𝑡)
modulatory input 𝑢2(𝑡)
t
activity 𝑧2(𝑡)
activity 𝑧3(𝑡)
signal 𝑥1(𝑡)
signal 𝑥2(𝑡)
signal 𝑥3(𝑡)
Jansen & Rit (1995) Biological Cybernetics Friston, Harrison & Penny (2003) NeuroImage
Stephan & Friston (2007), Handbook of Brain Connectivity
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Choosing a generative model: DCM for LFP/EEG
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Excitatory spiny cells in granular layers
Exogenous input u
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Intrinsic
connections5
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Excitatory spiny cells in granular layers
Excitatory pyramidal cells in agranular layers
Inhibitory cells in agranular layers
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Synaptic ‘alpha’ kernelSynaptic ‘alpha’ kernel
Sigmoid functionSigmoid function
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Extrinsic
Connections:
Forward
Backward
Lateral
Moran et al. 2009 NeuroImage
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Training and testing a model-based classifier
n
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Training a kernel-based discriminant classifier:
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Using the model to make predictions:
Linear SVM
In the case of generative embedding:
𝑘 𝑥𝑖 , 𝑥𝑗 = 𝑥𝑖𝑇𝑥𝑗
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1 ROI definition and n model inversions
unbiased estimate
Repeat n times: 1 ROI definition and n model inversions
unbiased estimate
1 ROI definition and n model inversions
slightly optimistic estimate: voxel selection for training set and test set based on test data
Repeat n times: 1 ROI definition and 1 model inversion
slightly optimistic estimate: voxel selection for training set based on test data and test labels
Repeat n times: 1 ROI definition and n model inversions
unbiased estimate
1 ROI definition and n model inversions
highly optimistic estimate: voxel selection for training set and test set based on test data and test labels
Specifying and inverting the model – how?
F
D
E C
B
A
Definition of ROIs
Are regions of interest defined anatomically or functionally?
anatomically functionally
Functional contrasts
Are the functional contrasts defined across all subjects or between groups?
across subjects
between groups
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Model We model the likelihood functions for 𝑘+ positive and 𝑘− negative correct predictions as:
𝑝 𝑘+ 𝜋+, 𝑛+ = Bin 𝑘+ 𝜋+, 𝑛+ 𝑝 𝑘− 𝜋−, 𝑛− = Bin(𝑘−|𝜋−, 𝑛−)
The class-specific accuracies 𝜋+ and 𝜋− can be modelled as latent random variables with conjugate Beta priors:
𝑝 𝜋+ 𝛼+, 𝛽+ = Beta 𝜋+ 𝛼+, 𝛽+
𝑝 𝜋− 𝛼−, 𝛽− = Beta 𝜋− 𝛼−, 𝛽−
This prior is uninformative when using the hyperparameters 𝛼+ = 𝛽+ = 𝛼− = 𝛽− = 1. The balanced
accuracy is given by 𝜙 ≔1
2𝜋+ + 𝜋− .
Full Bayesian approach to performance evaluation
Beta(𝜋+|1,1)
Beta(𝜋+|7,3)
Brodersen, Chumbley, Mathys, Daunizeau, Ong, Buhmann & Stephan (in preparation)
𝑘+ 𝑘−
𝜋+ 𝜋−
𝛼+, 𝛽+ 𝛼−, 𝛽−
𝜋 + 𝜋 −
~
𝜙 =𝜋 + + 𝜋 −
2
Inference Inverting the model yields the posterior balanced classification accuracy,
𝑝 𝜙 𝑘+, 𝑘−, 𝑛+, 𝑛−, 𝛼+, 𝛽+, 𝛼−, 𝛽−
= Beta 2 𝜙 − 𝑧 𝛼𝑛+, 𝛽𝑛
+ Beta 2𝑧 𝛼𝑛−, 𝛽𝑛
− 𝑑𝑧1
0.
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Summary of the analysis
pre-processing
estimation of group contrasts based on all subjects except subject j selection of voxels for regions of interest
unsupservised DCM inversion for each subject
training the SVM on all subjects except subject j testing the SVM on subject j
performance evaluation
1 2 3
repeat for each subject
A
C B
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Example: diagnosis of moderate aphasia
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Regions of interest
x = –56 mm y = –20 mm z = 8 mm
L R
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Neuronal model
Schofield, Penny, Stephan, Crinion, Thompson, Price & Leff (under review) Brodersen, Schofield, Leff, Ong, Lomakina, Buhmann & Stephan (2011) PLoS Comp Biol
L.MGB
L.PT
L.HG (A1)
R.MGB
R.PT
R.HG (A1)
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Univariate analysis
range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x)
range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x) range(d1$x, d2$x)
L.MGB → L.MGB L.MGB → L.HG L.MGB → L.PT L.HG → L.HG *** L.HG → L.PT *** L.HG → R.HG L.PT → L.MGB L.PT → L.HG
L.PT → L.PT L.PT → R.PT R.MGB → R.MGB R.MGB → R.HG R.MGB → R.PT *** R.HG → L.HG *** R.HG → R.HG R.HG → R.PT
R.PT → L.PT R.PT → R.MGB R.PT → R.HG R.PT → R.PT input to L.MGB input to R.MGB patients controls
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Connectional fingerprints
patients controls
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FPR (1 - specificity)T
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PP
V (
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Classification performance
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anatomical contrast searchlight PCA means correlations eigenvariates correlations eigenvariates z-correlations gen.embed., original model gen.embed., feedforward gen.embed., left hemisphere gen.embed., right hemisphere
activation- based
correlation- based
model- based
a c s p m e z o f l r
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Biologically implausible models perform poorly
A B
L.MGB
L.PT
L.HG (A1)
R.MGB
R.PT
R.HG (A1)
C
L.MGB
L.PT
L.HG (A1)
R.MGB
R.PT
R.HG (A1)
auditory stimuli auditory stimuli auditory stimuli
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Discriminative features in model space
L.MGB
L.PT
L.HG (A1)
R.MGB
R.PT
R.HG (A1)
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Discriminative features in model space
L.MGB
L.PT
L.HG (A1)
R.MGB
R.PT
R.HG (A1)
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Illustration of the generative score space
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L.H
G
Vo
xe
l (6
4,-
24
,4)
mm
L.MGB → L.MGB Voxel (-42,-26,10) mm
Voxel (-56,-20,10) mm R.HG → L.HG
controls patients
Voxel-based input space Generative score space
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❶ Strong classification performance
Generative embedding exploits the rich discriminative information encoded in ‘hidden’ quantities, such as coupling parameters. It may therefore outperform conventional schemes.
❷ Creation of a low-dimensional, interpretable feature space
The approach replaces high-dimensional fMRI data by a low-dimensional subject-specific fingerprint, where each dimension has a specific biological interpretation.
❸ Domains of application
Generative embedding can be used both for trial-by-trial decoding (EEG, MEG, or LFP data) and for subject-by-subject classification analyses (fMRI data).
Summary