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#### How to infer distributions in the brain from subsampled observations

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##### Citation

Levina, A., & Priesemann, V. (2017). *How to infer distributions
in the brain from subsampled observations*. Poster presented at Bernstein Conference 2017, Göttingen, Germany.

Cite as: https://hdl.handle.net/21.11116/0000-0003-1F94-4

##### Abstract

nferring the dynamics of a system from observations is a challenge, even if one can

observe all system units or components. The same task becomes even more challenging

if one can sample only a small fraction of the units at a time. As the prominent

example, spiking activity in the brain can be accessed only for a very small fraction

of all neurons in parallel. These limitations do not affect our ability to infer single

neuron properties, but it influences our understanding of the global network dynamics

or connectivity. Subsampling can hamper inferring whether a system shows scale-free

topology or scale-free dynamics (criticality) [1,2]. Criticality is a dynamical state that

maximizes information processing capacity in models, and therefore is a favorable

candidate state for brain function. Experimental approaches to test for criticality extract

spatio-temporal clusters of spiking activity, called avalanches, and test whether they

followed power laws. These avalanches can propagate over the entire system, thus

observations are strongly affected by subsampling. Therefore, we developed a formal

ansatz to infer avalanche distributions in the full system from subsampling using both

analytical approximation and numerical results.

In the mathematical model subsampling from exponential (or, more generally, negative

binomial distribution) does not change the class of distribution, but only its parameters.

In contrast, power law distributions, do not manifest as power laws under subsampling

[3]. We study changes in distributions to derive “subsampling scaling” that allows to

extrapolate the results from subsampling to a full system:

P

(

s

) =

p

sub

P

sub

(

s/p

sub

)

,

where

P

(

s

)

is an original distribution,

P

sub

– distribution in the subsampled system,

p

sub

probability to observe any particular event. In the model of critical avalanches

subsampling scaling collapses distributions for all number of sampled units (Figure 1. B).

However, for subcritical settings no distribution collapse is observed (Figure 1. D). With

the help of this novel discovery we studied dissociated cortical cultures. We artificially

subsampled recordings by considering only fraction of all electrodes. We observed that

in the first days subsampling scaling does not collapse distributions well, whereas mature

( from day 21) allow for a good collapse, indicating development toward criticality

(Figure 1. C, E) [4].

observe all system units or components. The same task becomes even more challenging

if one can sample only a small fraction of the units at a time. As the prominent

example, spiking activity in the brain can be accessed only for a very small fraction

of all neurons in parallel. These limitations do not affect our ability to infer single

neuron properties, but it influences our understanding of the global network dynamics

or connectivity. Subsampling can hamper inferring whether a system shows scale-free

topology or scale-free dynamics (criticality) [1,2]. Criticality is a dynamical state that

maximizes information processing capacity in models, and therefore is a favorable

candidate state for brain function. Experimental approaches to test for criticality extract

spatio-temporal clusters of spiking activity, called avalanches, and test whether they

followed power laws. These avalanches can propagate over the entire system, thus

observations are strongly affected by subsampling. Therefore, we developed a formal

ansatz to infer avalanche distributions in the full system from subsampling using both

analytical approximation and numerical results.

In the mathematical model subsampling from exponential (or, more generally, negative

binomial distribution) does not change the class of distribution, but only its parameters.

In contrast, power law distributions, do not manifest as power laws under subsampling

[3]. We study changes in distributions to derive “subsampling scaling” that allows to

extrapolate the results from subsampling to a full system:

P

(

s

) =

p

sub

P

sub

(

s/p

sub

)

,

where

P

(

s

)

is an original distribution,

P

sub

– distribution in the subsampled system,

p

sub

probability to observe any particular event. In the model of critical avalanches

subsampling scaling collapses distributions for all number of sampled units (Figure 1. B).

However, for subcritical settings no distribution collapse is observed (Figure 1. D). With

the help of this novel discovery we studied dissociated cortical cultures. We artificially

subsampled recordings by considering only fraction of all electrodes. We observed that

in the first days subsampling scaling does not collapse distributions well, whereas mature

( from day 21) allow for a good collapse, indicating development toward criticality

(Figure 1. C, E) [4].