SNN Machine learning
Bert Kappen,
Luc Janss, Wim Wiegerinck, Vicenc Gomez,
Alberto Llera, Mohammad Azar,
Bart van den Broek, 2 vacancies
Ender Akay, Willem Burgers
Activities
• Approximate inference
– Graphical models
– Analytical methods
– Sampling method
• Control theory
– Approximate inference
– Reinforcement learning
– Interaction modeling
• Neuroscience
– Adaptive BCI
– ECoG
– Neural networks
• Bioinformatics
– Genetic linkage analysis
– Genome-wide association studies
– Missing person identification
• Smart Research
– Wine portal
– Petro-physical expert system
– Credit card fraud detection
• Promedas
– www.promedas.nl/live
– UMCU
– Promedu
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Approximate inference
Control theory
Neural networks
ABCI
ECoG
GWAS
Promedas
Graphical models
What are probabilities given evidence:
Intractable for large number of variables: 2n for binary variables
Junction tree method
Complexity reduction: 2n ! 2k (n=8, k=3)
State of the art for intermediate size problems
No solution for large problems
Approximate inference
Optimal control theory
dy
 f ( y (t ), u (t ))dt   (t )
dt
Minimization of cost function:t
f
C ( y (t ), u (t ))   ( y (t f ))   g ( y ( ), u ( ))d
t
error cost at
the end
cost to reach the
target
Optimal solution hard to compute
Optimal control theory
Optimal control as a sum over trajectories, Kappen PRL 2005
Linear Bellman equation:
efficient computation of optimal controls
linear superposition of solutions
qualitative different results for high and low noise
Efficient computation
Theodorou, Schaal, USC 2009
linear superposition of solutions
Da Silva, Popovic, MIT 2009
Qualitative different results for high and low
noise
• Delayed Choice
– Optimal control predicts when
to act
– More noise means more delay
Results
Trajectory
Control
signal
small noise
large noise
Modelling neural networks with activity
dependent synapses
Dynamic synapses
Recurrent connectivity and Dynamic synapses
Associative memory
dynamical memories
Storage capacity
Sensitivity to external stimuli.
Relation to up-down states and powerlaws
Discussion
Marro, Torres, Mejias
a) Electrophysiological preparation in
pyramidal neurons (layer 5) for a
pairing experiment.
b) Pairing: several current pulses
(during 200 ms) in the pre and postsynaptic neuron (4-8 action
potentials, AP) are injected 30 times
each 20 s.
c) Before: the response to stimuli is
variable and noisy.
d) After: optimal response to the first
current pulse and there is a decrease
of response to the next pulses.
e) The effect of “pairing” is robust
and Hebbian.
Markram and Tsodyks, nature 1996: Dynamic synapses
(a) Intracellular recording in the primary visual cortex of a
halothane-anesthetized cat reveals a rhythmic sequence of
depolarized and hyperpolarized membrane potentials. (b)
Expansion of three of the depolarizing sequences for
clarity. (c) Autocorrelogram of the intracellular recording
reveals a marked periodicity of about one cycle per three
seconds. (d) Simultaneous intracellular and extracellular
recordings of the slow oscillation in ferret visual cortical
slices maintained in vitro. Note the marked synchrony
between the two recordings. The intracellular recording is
from a layer 5 intrinsically bursting neuron. The trigger
level for the window discriminator of the extracellular
multi-unit recording is indicated. (e) The depolarized state
at three different membrane potentials. (f)
Autocorrelogram of the intracellular recording in (d) shows
a marked periodicity of approximately once per 4 seconds.
Sanchez-vives, McCormick 2000
Phenomenological model: Tsodyks y Markram (1997)
dx j(t)
dt
dy j(t)
dt

1  x j(t)  y j(t)
τ rec
 -
y j(t)
τ in
 D j(t)F j(t)s j(t)
 D j(t)F j(t)s j(t)
z (t )  1  x(t )  y (t );
du j(t)
u j(t)
  U [ 1 -u j(t)] s j(t)
dt
τ fac
D j  x j ; Fj  U  ( 1  U)u j
I total =  Ay j
j
dVi
= Vi + RI total (IF neuron)
dt
Vth threshold  s j(t)  Θ[V j(t)  Vth ]
τm
f out = F(f in ,π)
Attractor neural networks
si  Vi

ij ( ) D j F j  Gij
N neurons
θi  Vth
N 2 synapses
hi  I total
m(s)  f in , f out
Probsi(t+1 )=1 = σ[ 2T
1

hi(t)]
hi = hi  θi =  ij ( ) D j F j s j  θi
j

(ξ ) = Learning rule
ξ μ , P patterns of neural activity
Associative memory with “static synapses” (Dj=1, Fj=1)
Hopfield network
Time
Oscillations occur for P>1 and more realistic neuron models
(Pantic et al, Neural Comp. 2002)
Phase portrait
Storage capacity
y  m1  m
U  0.05, 0.5, 0.7
 rec  2;  fac  200
U  0.2; N  3000
 rec  2
Stimulus grows
Sensitivity to external stimuli: hi+dim
Discussion
 Synapses show a high variability with a diverse origin: the stochastic opening of the
vesicles, variations in the Glutamate concentration through synapses or the spatial
heterogeneity of the synaptic response in the dendrite tree (Franks et al. 2003).
 Due to synapse dynamics, the neural activity loses stability which increases the
sensitivity to changing external stimuli: the concept of dynamical memories
 Synaptic depression reduces memory capacity
 Synaptic facilitation improves short time memories
Adaptive BCI
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A BCI device is called adaptive if it is able to
change during performance in order to
improve it.
Proposed approach: Use Error Related
Potentials to provide the device with
feedback about its own performance.
Llera, Gomez, van Gerven, Jensen
General idea
• Are Error Related Potentials possible to
classify at the single trial level?
Experimental design
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An MEG experiment have been designed to get insight
into error related fields in a BCI context.
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The protocol has been carefully chosen to avoid
lateralization due to movement in the screen.
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The protocol is intended to provide us with data
containing error related fields and minimal extra input.
Classification methods with best
results till now...
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Transformation to 28 frequencies in range 3-30 Hz.
Normalization.
273 channels
6 time steps of 100 ms
150 trials per subject
Linear Support Vector Machine
Illustration on toy data
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One dimensional feature space.
Two Gaussian distributions, one for each class.
Learning boundary using delta rule each time that we detect an error potential.
Since Error Potentials classification is not 100%, we can have two undesirable effects:
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Not learn when we should (prob2).
Learn when we should not (prob1).
Assume that probability of errors is the same for both classes.
ECoG connectivity patterns during a motor
response task
•We have computed the brain connectivity patterns associated to a simple motor
response task from ECoG data recordings:
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Functional connectivity : Gaussian graphical models
Time domain.
Provides a symmetric independence matrix.
Does not capture time evolution.
Assumes normally distributed residuals.
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Effective connectivity : Direct Transfer Function (DFT), Granger causality.
Frequency domain.
Provides a non-symmetric causal matrix.
Does capture time evolution.
Assumes a good fit of the MVAR model.
Gomez, Ramsey
ECoG connectivity patterns during a motor
response task
104 electrodes (101 after preprocessing).
 Implanted on the left hemisphere.
 Two days, 40 trials per condition per day.
 Sampling Rate 512 Hz: 1792 samples per trial.
 22 bits, bandpass filter 0.15 – 134.4 Hz).
 Inter-electrode distance : 1 cm.
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ECoG connectivity patterns during a motor
response task
•The Gaussian model reveals clusters of correlated activity and
significant differences between stimulus and response states
related with motor areas.
ECoG connectivity patterns during a motor
response task
With Granger causality we are able to identify a set of source electrodes (red
dots) which drive another subset of target electrodes.
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Sources are similar in both conditions, although targets differ for stimulus and
response conditions.
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Bayesian Variable Selection: causal
modeling or prediction?
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Stochastic search multiple-regression building (using Gibbs
sampling algorithm based on George & McCulloch 1995).
Efficient in large p problems (500K predictors)
Extended in a hierarchical model to estimate shrinkage
parameter from the data, which we have shown to avoid overfit.
Model averaging using half-certain associations was shown to
improve prediction substantially:
Prediction with smaller and larger SNP models
Upper limit for prediction (heritability) approx. 0.25, <10 SNPs statistically significant
Prediction R2
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0.15
0.10
0.05
0.00
15
26
108
213
320
Average number of fitted SNPs
Janss, Franke, Buitelaar
Some extensions / research topics
Pathway 2
Pathway 1
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Use of prior information to help
(constrain) finding interactions
between predictors
Multi-phenotype modelling and
prediction using an embedded
Eigenvector decomposition in a
Bayesian hierarchical model.
Multi-layered variable selection
to model genetic effects on
brain fMRI, which models
cognitive tasks and psychiatric
disorders
x1 x2 x3 x4 x5 x6 x7 x8 x9 … x500000
y
Interactions
selected within
pathways
x1 x2 x3 x4 x5 x6 x7 x8 x9 … x500000
u 1 u2 u3
EV latent
vectors
y1 y2 y3 y4 y5
x1 x2 x3 x4 x5 x6 x7 x8 x9 … x500000
fMRI data
per voxel
y1 y2 y3
Janss, Franke, Buitelaar
PROMEDAS
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PRObabilistic
Medical
Diagnostic
Advisory System
Waarom?
• Toenemende complexiteit van diagnostiek
• Falen in medisch handelen
– 98000 patiënten in de VS sterven per jaar als gevolg van falend
medisch handelen
– Foute diagnose is frequent (8- 40 %)
• Toenemende kosten gezondheidszorg
• Beschikbaarheid van elektronische data
•Input:
•patiëntgegevens,
klachten, symptomen,
labgegevens
•Output:
•Diagnoses, suggesties
voor vervolgonderzoek
•Gebruikers:
•Huisartsen
•Opleiding
•Management
•Medisch specialisten
Grafische modellen
Grafische modellen
Exponentiele complexiteit
10
1 sec
20
20.000 sec
30
15 year
40
300.000 year
50
1010 year
Bomen zijn netwerken zonder lussen
De berekening is zeer snel voor bomen
Promedas graaf benaderen als boom
Message passing
• Exact op bomen
• Goed op netwerken met weinig lussen
• Wordt slechter met
– aantal lussen
– verbindingssterkte
Medische inhoud
• Interne geneeskunde voor specialisten
– 4000 diagnoses, 4000 symptomen, 60000 relaties
– informele klinische evaluatie
• 50 test patients
– score of correct diagnoses in top 3
• 6 % all in the top 3
• 26 % two in the top 3
• 54 % one in the top 3
• 14 % not correct
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Sinds oktober 2008 geintegreerd in UMCU. Ongeveer 1200 sessies per maand.
Toekomst plannen
• Promedas wordt gecommercialiseerd door een nieuw bedrijf Promedas
BV.
• Mogelijke markten:
– Web applicatie of cd-rom
– Geïntegreerd in een ziekenhuis informatiesysteem
– Telemedicine
– ….
Projectteam
• Algoritmes & software
– SNN, Radboud Universiteit Nijmegen
• Medische inhoud
– UMC Utrecht
www.promedas.nl
Onderwijs N & S voor deze richting
• Bachelor
– Neural networks and
information theory
– Neurofysica
• Master
– Machine Learning
– Computational
Neuroscience
– SNN Colloquia