Network Information and Connected Correlations - Dr. Christian B ...

guineanhillΤεχνίτη Νοημοσύνη και Ρομποτική

20 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

87 εμφανίσεις

Visuelle Kodierung

Christian B. Mendl

Unabhängige Nachwuchsgruppe „Visuelle Kodierung“

am Max
-
Planck
-
Institut für Neurobiologie

unter Tim Gollisch

Ziele der Arbeitsgruppe


Untersuchung der Sehreizverarbeitung und
‐Kodierung in der Retina (Augennetzhaut)


Grundlagenforschung für zukünftige Netzhaut
-
Implantate


Retina experimentell gut zugängliches
Nervenzellsystem; Modell für neuronale
Kodierung

Schematischer Aufbau der Retina

Säugetier
-
Retina (
schematisch
):
es

gibt

sechs

Klassen

von
Neuronen

in
der

Säugetier
-
Retina:
Stäbchen

(1),
Zapfen

(2),
Horizontalzellen

(3),
Bipolarzellen

(4),
Amakrinzellen

(5) und
retinale

Ganglionzellen

(6).

Heinz
Wässle
,
Parallel
Processing in
the

Mammalian

Retina

Nature Reviews
Neuroscience
,
Vol

5,
October

2004

Experimentelles
Messprinzip

Spike
-
Triggered

Average

(STA)

Chichilnisky
, E. J.
A simple
white noise analysis of
neuronal light responses
.

Computation in Neural
Systems, 2001, 12, 199

213

Spike
-
Triggered

Average

(
cont
.)

Chichilnisky
, E. J.
A
simple white noise
analysis of neuronal
light responses
.

Computation in
Neural Systems, 2001,
12, 199

213

Spike
-
Triggered

Average

(
cont
.)

Chichilnisky
, E. J.
A
simple white noise
analysis of neuronal
light responses
.

Computation in
Neural Systems, 2001,
12, 199

213

Pairwise

Correlations


Significant
i
nteractions between
neurons in the
vertebrate retina


Exponential increase in number of
possible collective states


Simplifying hypotheses required to
effectively capture network statistics


Ising model taking into account
pairwise

interactions only gives
quantitatively good results

Elad

Schneidman
,
Michael J. Berry II,
Ronen Segev and
William Bialek.
Weak
pairwise

correlations
imply strongly
correlated network
states in a neural
population.
Nature,
2006
doi:10.1038/nature04
701

Analysis Setup

Simultaneous responses of
40 retinal ganglion cells in
the salamander to a natural
movie clip. Each dot

represents the time of an
action potential.

Failure of the Independent
Approximation

Distribution of synchronous events
after shuffling each cell’s spike train to
eliminate all correlations, compared to
the Poisson distribution

Occurrence rate predicted if all cells were independent

Probability distribution of
synchronous spiking events
approximates an exponential

Ising

Model for
Pairwise

Interactions

Elad

Schneidman
, Susanne Still,
Michael J.
Berry and William
Bialek
.
Network
Information and
Connected
Correlations
.

Phys.
Rev
.
Lett
.,
December

2003.

Interaction strength
J
ij

plotted against the
correlation coefficient
C
ij

Maximum entropy
principle used for
parameter fitting

Pairwise

Interactions Approximation

is Quantitatively Sufficient

Maximum entropy model
taking into account all
pairwise

correlations

Fraction of full network correlation (measured by the multi
-
information I
N
) in 10
-
cell groups that is captured by the
maximum entropy model of second order, I
(2)
/I
N

Independent model

Interactions and Local Fields in
Networks of Different Size

a)
Density map of effective
interaction fields
experienced by a single cell
versus its own bias or local
field

b)
Mean interactions
J
ij

and
local fields h
i

describing
groups of N cells

c)
Pairwise

interaction in a
network of 10 cells
J
ij
(10)
plotted against the
interaction values of the
same pair in a
subnetwork

containing only 5 cells
J
ij
(5)

Extrapolation to Larger Networks

a)
Average independent cell entropy S
1

and network multi
-
information I
n

(true entropy equals S
N
=S
1
-
I
N
)

b)
Information that N cells provide about the activity of cell N+1

c)
Examples of ‘check cells’: the probability of spiking is an almost perfectly
linear encoding of the number of spikes generated by the other cells

Conclusions

(
Pairwise

Interactions)


Summary: pairwise interactions
sufficient to explain network
statistics


Critical annotation: correlations
due to stimuli not taken into
account


Results confirmed by a very
similar paper by
Shlens

et.al.
avoiding external stimulation;
moreover, interactions limited
to adjacent cells

Jonathon
Shlens

et.al.
The
Structure of Multi
-
Neuron
Firing Patterns in
Primate
Retina.
The Journal of
Neuroscience, 2006,
26(32)