SNN Machine learning

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

http://www.promedas.nl/live

• 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 problemsNo solution for large problems

Approximate inference

Optimal control theory

ft

tf duygtytutyC ))(),(())(())(),((

Minimization of cost function:

error cost at the end

cost to reach the target

)())(),(( tdttutyfdtdy

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 controlslinear superposition of solutionsqualitative 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

small noise large noise

Control signal

Trajectory

Modelling neural networks with activity dependent synapses

Dynamic synapses

Recurrent connectivity and Dynamic synapsesAssociative memorydynamical 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 post-synaptic 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

Sanchez-vives, McCormick 2000

(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.

Phenomenological model: Tsodyks y Markram (1997)

j

jtotal Ay=I

][

thjjth

totalii

m

V(t)VΘ(t)sthresholdV

)(IF neuronRI+V=dt

dVτ

π),F(f=f inout

jjjj

jjfac

jj

jjjin

jj

jjjrec

jjj

U)u(U; FxD

(t)(t)] s -u U [τ

(t)u -

dt(t)du

tytxtz

(t)(t)s(t)F Dτ(t)y

-dt

(t)dy

(t)(t)s(t)F Dτ

(t)y(t)x

dt(t)dx

1

1

);()(1)(

1

Attractor neural networks

outin

totali

thi

ijjjij

ii

f,fm(s)IhVθ

GFD

Vs

)(

]2σ[=11Prob 1 (t)h T)=(t+s ii

activity neural of patterns ,

rule Learning

)(

Pξ

=)ξ(

θsFD=θh=h

μ

ijj

jjijiii

synapses

neurons 2N

N

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

200;27.0,5.0,05.0

facrec

U

2rec

mmy 1

3000;2.0 NU

Storage capacity

Sensitivity to external stimuli: hi+dim

Stim

ulus

gro

ws

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

• 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

• An MEG experiment have been designed to get insight into error related fields in a BCI context.

• The protocol has been carefully chosen to avoid lateralization due to movement in the screen.

• The protocol is intended to provide us with data containing error related fields and minimal extra input.

Classification methods with best results till now...

• 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• 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:

– 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:

Functional connectivity : Gaussian graphical models

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.

Time domain.Provides a symmetric independence matrix.Does not capture time evolution.Assumes normally distributed residuals.

Gomez, Ramsey


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.


•The Gaussian model reveals clusters of correlated activity and significant differences between stimulus and response states related with motor areas.


With Granger causality we are able to identify a set of source electrodes (red dots) which drive another subset of target electrodes.

Sources are similar in both conditions, although targets differ for stimulus and response conditions.

Bayesian Variable Selection: causal modeling or prediction?

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:

15 26 108 213 3200.00

0.05

0.10

0.15

Prediction with smaller and larger SNP modelsUpper limit for prediction (heritability) approx. 0.25, <10 SNPs statistically significant

Average number of fitted SNPs

Pre

dict

ion

R2

Janss, Franke, Buitelaar

Some extensions / research topics 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

y1 y2 y3 y4 y5

Pathway 1 Pathway 2

x1 x2 x3 x4 x5 x6 x7 x8 x9 … x500000

u1 u2 u3

Interactionsselected within

pathways

EV latentvectors

x1 x2 x3 x4 x5 x6 x7 x8 x9 … x500000

y1 y2 y3

fMRI dataper voxel

Janss, Franke, Buitelaar

PROMEDAS

• 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

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 bomenPromedas 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

• 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

SNN Machine learning

Documents

Transcript of SNN Machine learning