Stochastic Analysis of Neural Spike Count Dependencies [Elektronische Ressource] / Arno Onken. Betreuer: Klaus Obermayer

Arno Onken

Sujets

• Naturwissenschaften

Informations

• Publié par: technische_universitat_berlin
• Publié le: 01 janvier 2011
• Nombre de lectures: 13
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Technische Universitat Berlin¨
Stochastic Analysis
of Neural Spike Count Dependencies
vorgelegt von
Diplom-Informatiker
Arno Onken
aus Aurich
Von der Fakultat IV - Elektrotechnik und Informatik¨
der Technischen Universitat Berlin¨
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
Dr. rer. nat.
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Klaus-Robert Mu¨ller
Berichter: Prof. Dr. Klaus Obermayer
Berichter: Prof. Dr. Valentin Dragoi
Tag der wissenschaftlichen Aussprache: 17.08.2011
Berlin 2011
D 83
berlini
1Acknowledgments
First of all, I would like to express my greatest gratitude to Prof. Klaus Obermayer
for supervising my Ph.D. research. In his group and in the Bernstein Center for
Computational Neuroscience Berlin he has established a profoundly animating sci-
entificenvironment. Thediscussionswehadwerealwayssharpandtothepoint. Yet
I had great freedom in choosing my research topics and pursuing my own ideas. He
provided unconfined opportunities for traveling to conferences where he gave me the
opportunity to get in touch with important researchers from the field. I also like to
thanktheothermembersofmyBCCNPh.D.committee: FelixWichmann,Manfred
Opper and Laurenz Wiskott. During our meetings we had critical discussions and
they gave some very constructive comments.
Furthermore, I would like to express special thanks to my collaborators Valentin
Dragoi, Matthias Munk and Maneesh Sahani. Every one of them gave me the
opportunity to visit their outstanding labs, impressed me with their hospitality and
allowed me to satisfy my curiosity. At meetings and conferences we had quite a
number of fruitful discussions.
IamdeeplyindebtedtoSteffenGru¨new¨alderwhohelpedmeinsomanywaysthat
they are too numerous to list here. During my first two years he not only provided
me with a background in scientific working, but also brought me on the right track.
Most notable is the NIPS 2008 conference for which we had underestimated our
success chances quite a bit. Even after he moved to John Taylor’s lab he did not
stop supporting me.
Next, I would like to thank Robert Martin who introduced me to the BCCN
and was very encouraging. He spent time on proof reading early manuscripts and
highlighted means to improve my talks. Special thanks go to the coordinators of
the BCCN Ph.D. program: Daniela Pelz and Vanessa Casagrande. They did a great
job and helped clarifying whenever a formal requirement was unclear. I also want
to thank Benjamin Staude for some very influential advices early on in my studies.
I would like to thank my roommate Johannes Mohr for all those countless fruitful
discussions.
Moreover, I would like to thank the students who worked under my supervision:
MahmoudMabrouk,DuncanBlythe,Andr´eGroßardtandSachaSokoloski. Working
with them was fun and inspiring.
Finally,IliketothankmycolleaguesintheNeuralInformationProcessinggroup
for useful input during the breaks: Felix Franke, Yun Shen, Nicolas Neubauer,
Michal Natora, Wendelin Bohmer, Klaus Wimmer, Marcel Stimberg, Konstantin¨
Mergenthaler, Josef Ladenbauer, Philipp Meier, Michael Sibila, Deepak Srinivasan,
Johannes Jain, Stephan Schmitt, Kamil Adiloglu, Rong Guo, Aki Naito, Susanne
Sch¨onknecht, Philipp Kallerhoff, Sambu Seo and Robert Anni´es.
1This thesis was supported by BMBF grants 01GQ0410 and 01GQ1001B.iiiii
Abstract
The question of how populations of neurons process information is not fully under-
stood yet. With the advent of new experimental techniques, however, it becomes
possible to measure a great number of neurons simultaneously. As a result, models
of co-variation of neurons are becoming increasingly important. In this thesis new
methods are introduced for analyzing the importance of stochastic dependencies for
neural coding. The methods are verified on artificial data and applied to data that
wererecordedfromanimals. Itisdemonstratedthatthenovelfeaturesofthemodels
can be material for investigating the neural code.
First, a novel framework for modeling multivariate spike counts is introduced.
Theframeworkisbasedoncopulas,whichmakeitpossibletocouplearbitrarysingle
neurondistributionsandplaceawiderangeofdependencystructuresatthedisposal.
Methods for parameter inference and for estimation of information measures are
provided. Moreover, a relation between network architectures and copula properties
isestablished. Thecopula-basedmodelsarethenappliedtodatathatwererecorded
from the prefrontal cortex of macaque monkey during a visual working memory
task. We demonstrate that copula-based models are better suited for the data than
common standard models and we identify possible underlying network structures of
the recorded neurons.
We then extend the copula approach by introducing a copula family that can be
used to model strong higher-order correlations. The family is constructed as a mix-
ture family with copula components of different order. In order to demonstrate the
usefulness of the model we construct a network of leaky integrate-and-fire neurons.
The network is connected in such a way that higher-ordercorrelationsare present in
theresultingspikecounts. Thenewcopulafamilyisthencomparedtoothercopulas
andtotheIsingmodel. Weshow,thatcomparedtotheothermodelsthenewcopula
family provides a better fit to the artificial data.
In athirdstudy, we investigatethesufficiencyof thelinearcorrelationcoefficient
for describing the dependencies of spike counts generated from a small network of
leaky integrate-and-fire neurons. It is shown that estimated entropies can deviate
by more than 25% of the true entropy if the model relies on the linear correlation
coefficient only. We therefore propose a copula-based goodness-of-fit test which
makes it easy to check whether a given copula-based model is appropriate for the
data at hand. The test is then verified on several artificial data sets.
Finally, we study the importance of higher-order correlations of spike counts for
information-theoreticmeasures. Forthatpurposeweintroduceagoodness-of-fittest
that has a second-order maximum entropy distribution as a reference distribution.
The test quantifies the fit in terms of a selectable divergence measure such as the
mutual information difference and is applicable even when the number of available
data samples is very small. We verify the method on artificial data and apply it
to data that were recorded from the primary visual cortex of an anesthetized cat
duringanadaptationexperiment. Wecanshowthathigher-ordercorrelationshavea
significantconditiondependentimpactontheentropyandonthemutualinformation
of the recorded spike counts.ivContents
1 Introduction to the Thesis 1
1.1 Neural Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Types of Neural Codes . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Variability and Noise in Neural Systems . . . . . . . . . . . . 4
1.1.3 Noise Correlations . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Analysis of Neural Codes . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Model Based Approaches . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Information Quantification . . . . . . . . . . . . . . . . . . . 13
1.2.3 Decoding Framework . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Addressed Questions and Outline . . . . . . . . . . . . . . . . . . . . 19
2 Copula-based Analysis of Neural Responses 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Copula Framework for Spike Count Analysis . . . . . . . . . . . . . 24
2.2.1 Copula Models of Multivariate Distributions . . . . . . . . . 24
2.2.2 Multivariate Spike Count Distributions Based on Copulas . . 25
2.2.3 The Flashlight Transformation and Mixtures of Copulas . . . 27
2.2.4 Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.5 Estimation of the Mutual Information . . . . . . . . . . . . . 30
2.2.6 Simplified Framework for Bivariate Models . . . . . . . . . . 31
2.3 Proof of Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.1 Reliability of Model Estimation . . . . . . . . . . . . . . . . . 32
2.3.2 Application to Artificial Network Data . . . . . . . . . . . . . 33
2.3.3 Application to Multi-tetrode Data . . . . . . . . . . . . . . . 35
2.3.4 Appropriateness of the Model . . . . . . . . . . . . . . . . . . 40
2.3.5 Information Analysis . . . . . . . . . . . . . . . . . . . . . . . 41
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Frank Higher-order Copula Family 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.1 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.2 Applied Copula Families . . . . . . . . . . . . . . . . . . . . . 50
3.2.3 Frank Higher-order Copula Family . . . . . . . . . . . . . . . 51vi Contents
3.2.4 Estimation of the Entropy . . . . . . . . . . . . . . . . . . . . 52
3.3 Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 The Cost of Ignoring Short-term Non-stationarity . . . . . . 53
3.3.2 Modeling Higher-order Correlations . . . . . . . . . . . . . . 54
3.4 Discussion . . . . . . .