CNS*2009 Workshop on

Methods of Information Theory in Computational Neuroscience

Wednesday and Thursday, July 22-23, 2009

Berlin, Germany

Overview

Methods originally developed in Information Theory have found wide applicability in computational neuroscience. Beyond these original methods there is a need to develop novel tools and approaches that are driven by problems arising in neuroscience.

A number of researchers in computational/systems neuroscience and in information/communication theory are investigating problems of information representation and processing. While the goals are often the same, these researchers bring different perspectives and points of view to a common set of neuroscience problems. Often they participate in different fora and their interaction is limited.

The goal of the workshop is to bring some of these researchers together to discuss challenges posed by neuroscience and to exchange ideas and present their latest work.

The workshop is targeted towards computational and systems neuroscientists with interest in methods of information theory as well as information/communication theorists with interest in neuroscience.

References

Baddeley, Hancock & Foldiak (eds), Information Theory and the Brain, Cambridge University Press, Cambridge, UK, 2000.

Borst & Theunissen, Information Theory and Neural Coding, Nature Neuroscience, 2, pp. 947 - 957, 1999. doi:10.1038/14731

D.H. Johnson, Dialogue Concerning Neural Coding and Information Theory, August 2003.

C.E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, 1948.

Organizers

Aurel A. Lazar, Department of Electrical Engineering, Columbia University and Alex G. Dimitrov, Center for Computational Biology, Montana State University.

Journal of Computational Neuroscience

Call for Papers

Special issue on Methods of Information Theory in Neuroscience Research

Alexander G. Dimitrov

Aurel A. Lazar

Jonathan D. Victor

Methods originally developed in Information Theory have found wide applicability in computational neuroscience. Beyond these original methods, novel tools and approaches have been developed that are driven by problems arising in neuroscience. A number of researchers in computational/systems neuroscience and in information/communication theory are investigating problems of information representation and processing.

The goal of the special issue of the Journal of Computational Neuroscience is to showcase the latest techniques, approaches and results in this area. The subject of the papers must fit the Aims & Scope of the journal, and must in particular not be purely methodological but also illustrate results that advance our understanding of brain function in a broad sense. The papers must contain new material, but we encourage the authors to also include review material to help the reader fully understand the context of the study. Papers that include experimental work are especially encouraged.

Submission is open to all as long as it fits the above criteria. The papers will go through the standard review process, with the same criteria as for normal articles submitted to the journal. They will be further reviewed for relevance to the special issue by the guest editors listed above. At submission, please indicate in comments that you wish to be considered for this issue.

Program Overview

Wednesday (9:00 AM - 5:30 PM), July 22, 2009

Morning Session (9:00 AM - 12:10 PM)
Neural Encoding and Processing
Chair: TBA

9:00 AM - 9:40 AM

Information Theoretic Analysis of Population Coding of Auditory Space

Nicholas A. Lesica, Department of Biology, Ludwig-Maximilians University, Munich.

With advances in electrophysiology and imaging, it is becoming increasingly common to study the joint responses of neuronal populations. Calculating mutual information directly from the experimental responses of large populations may not be possible, but the responses can be decoded and the mutual information between the actual and decoded stimulus can be measured (Rolls et al., J. Neurophysiol, 1998). This approach has many benefits, the most important of which is that the dimensionality of the 'response' space depends only on the number of distinct stimuli.

We used a decoding approach to investigate the coding of auditory space in gerbils and barn owls. We investigated the robustness of different measures of decoder performance: the number of decoding errors, the mutual information measured from the decoded responses (which is affected by both the number and the distribution of decoding errors), and the mutual information measured from the 'distances' between responses (which can be thought of as decoder confidence). Our results demonstrate the utility of information theoretic measures for the analysis of large populations with different strategies for coding auditory space.

9:40 AM - 10:20 AM

Information Theoretic Approaches to Predicting Optimal Neuronal Stimulus-Response Curves

Mark McDonnell, Institute for Telecommunications Research, University of South Australia, Adelaide.

Neuronal stimulus-response curves (also known as tuning curves) describe the response of a neural system (e.g. a single neuron or a population) as a function of a stimulus parameter. While usually defined simply as the mean response conditioned on the input stimulus, sometimes the importance of stimulus-dependent variance (and the underlying conditional distribution) is overlooked.

Here we present an approach to deriving optimal stimulus-response curves based on maximizing the mutual information between stimulus and response. We focus on curves that are sigmoidal, i.e. the mean response varies monotonically with increasing stimulus. The approach requires an assumed conditional distribution and stimulus dependent variance, with the mean conditional response as the only free variable. Both "Poisson-like" (mean equal to variance) and non-Poisson mean-versus-variance relationships are considered.

For large variability, the optimal stimulus-response curve will be shown to be discrete, in the sense that many stimuli values result in the same mean response [1]. The number of discrete levels increase (and the intervals of identically coded stimuli decrease in size) as the variance decreases. In the limit of small variability [2], an approximation to mutual information based on Fisher information [3] can be adapted to find closed form solutions for the optimal continuous stimulus-response curve, for arbitrary stimulus distributions [2]. When the variance is not small, this derivation can still be performed, and is still useful, since the outcome is a lower bound on the maximum mutual information. This approach can also be reversed to find the optimal stimulus distribution for a known stimulus-response curve.

Discussion will include: (i) example application to olfactory data; (ii) example application to a cochlear implant model; (iii) incorporation of constraints; (iv) comparison with similar optimizations using minimum mean square error [5]; (v) the many assumptions required to justify the maximum mutual information criteria; (vi) the long history of optimal discreteness in information theory [4] and the link between Fisher information and mutual information (e.g. [3]);

This talk will cover joint work with Nigel G. Stocks [1,2], Alexander Nikitin [1] (University of Warwick, UK) and Robert P. Morse (Aston University, UK) [1]. Mark D. McDonnell is funded by an Australian Research Council APD Fellowship, Grant No. DP0770747.

References:
[1] A. P. Nikitin and N. G. Stocks and R. P. Morse and M. D. McDonnell, "Neural Population Coding is Optimized by Discrete Tuning Curves", arXiv:0809.1549v1 (2008).
[2] Mark D. McDonnell and Nigel G. Stocks, "Maximally Informative Stimuli and Tuning Curves for Sigmoidal Rate-Coding Neurons and Populations," Physical Review Letters 101:058103 (2008).
[3] N. Brunel and J. Nadal, "Mutual information, Fisher information and population coding," Neural Computation 10:1731-1757 (1998).
[4] Mark D. McDonnell, "Information capacity of stochastic pooling networks is achieved by discrete inputs," Physical Review E 79:041107 (2009).
[5] M. Bethge, D. Rotermund and K. Pawelzik, "Optimal neural rate coding leads to bimodal firing rate distributions," Network: Computation in Neural Systems 14:303-319 (2003).

10:20 AM - 10:50 AM

Morning Break

10:50 AM - 11:30 AM

Speech Recognition Using Spiking Neural Networks

Benjamin Schrauwen, Electronics and Information Systems Department, Ghent University.

11:30 AM - 12:10 PM

Cliques in Neural Ensembles and Co-Evolutionary Learning in Liquid Architectures

Yehoshua (Josh) Y. Zeevi, I. Raichelgauz and K. Odinaev, Technion - Israel Institute of Technology and CORTICA Ltd, Haifa.

The “synfire chain” theory, advanced by M. Abeles, attributes the representation of components of external patterns to synchronous spatio-temporal activities of subsets of cortical neural networks. We define the concept of "Cliques" of neural activity as coherent states of complex spatio-temporal patterns of neural activity, which are presumed to correspond to complex percepts. A clique, thus, extends the concept of synfire-chains, in that it constitutes a spatio-temporal spiking activity sequence, within and across several synfire-chains, that coheres to signal the recognition of a complex pattern, or the arousal of complex percepts. It also extends in a way the over simplistic concept of Horace Barlow of "Grandmother Cells" to a more realistic model of "Grandmother Networks", and spatio-temporal patterns of activity therein. The question then is how does one test this model experimentally and, more importantly from an engineering approach to the development of advanced technology, how does one exploit this idea in the development of novel technologies, motivated by concepts and models emerging in computational brain sciences?

Considering first the latter, we have investigated the concept of cliques by using a computational framework of 'Liquid State Machines' (LSM); a computational paradigm proposed by W. Maas, T. Natschlager and H. Markram as a model of generic cortical microcircuits. We extend the computational power of this framework by closing the loop. This is consistent with the biological perception-action cycle. It is accomplished by applying, in parallel to the supervised learning of the readouts, a biologically-realistic reward-based learning mechanism, within the framework of the neural microcircuit (NM). This approach is inspired by neurobiological findings from ex-vivo multi-cellular electrical recordings and injection of dopamine to the neural culture of S. Marom and his group at the Technion. We show that by closing the loop, we obtain a much more effective performance with the new Co-Evolutionary Liquid Architecture. We illustrate the added value of the closed-loop approach to liquid architectures by executing, as an example, a multimedia classification task.

The Co-Evolutionary Liquid Architecture framework can be implemented in mapping processes of learning that take place in real biological networks for decisions and actions in the interface with the real-world stimuli and streaming content. The representation of complex patterns and concepts by neural cliques is highly compressive. Thus, Clique representation affords the Cortex to execute real-time processing of streaming content in real-time, in spite of the fact that neuronal components of cortical networks have long-time constants of the order of msec. Digital implementation can therefore accelerate the processing by at least several orders of magnitude and accomplish complex large-scale perceptual functions in real-time on-line. At present time, state-of-the-art technologies are effective at aggregating massive amounts of data in different verticals (e.g. images and videos), slicing and dicing it in different ways, searching and displaying it in an organized fashion. However, they don’t add any real “intelligence” to the mix, i.e. they don’t extract new knowledge from the data they aggregate. Thus, a new technological challenge of implementing a new layer of intelligence, by Cortical-motivated Technologies, has emerged.

12:10 PM - 2:00 PM

Lunch

Afternoon Session (2:00 PM - 5:30 PM)
Neural Encoding and Decoding
Chair: Simon R. Schultz

2:00 PM - 2:40 PM

Soft Clustering Decoding of Neural Codes

Alexander G. Dimitrov, Center for Computational Biology, Montana State University.

Methods based on Rate Distortion theory have been successfully used to cluster stimuli and neural responses in order to study neural codes at a level of detail supported by the amount of available data. They approximate the joint stimulus-response distribution by soft-clustering paired stimulus-response observations into smaller reproductions of the stimulus and response spaces. An optimal soft clustering is found by maximizing an information-theoretic cost function subject to both equality and inequality constraints, in hundreds to thousands of dimensions.

The method of annealing has been used to solve the corresponding high dimensional non-linear optimization problems. The annealing solutions undergo a series of bifurcations in order to reach the optimum, which we study using bifurcation theory in the presence of symmetries. The optimal models found by the Information Distortion methods have symmetries: any classification of the data can lead to another equivalent model simply by permuting the labels of the classes. These symmetries are described by SN, the algebraic group of all permutations on N symbols. The symmetry of the bifurcating solutions is dictated by the subgroup structure of SN. In this contribution we describe these symmetry breaking bifurcations in detail, and indicate some of the consequences of the form bifurcations.

2:40 PM - 3:20 PM

Distinguishing between Proximal and Distal Stimuli in Sensory Coding

Lars Schwabe, Department of Computer Science and Electrical Engineering, University of Rostock.

Theoretical investigations of sensory coding are often based on optimality assumptions (like efficient coding), possibly with added constraints on desirable properties of the neural code (like sparseness or a factorial code). Most theoretical investigations and experiments, however, neglect a distinction well known in psychophysics, namely the distinction between the proximal and the distal stimuli. In the context of sensory coding, the distal stimuli can be thought of as the “relevant” aspect of the environment (like the 3D properties of objects), whereas the proximal stimuli correspond to the signals sensed at the sensory periphery (like their 2D projection in the visual system).

I will briefly recapitulate some theoretical and experimental approaches to sensory coding and consider most of them as encoding the proximal stimuli. Then, I will apply the Information Bottleneck method (Tishby et al., 1999) in order to derive compressed representations of proximal stimuli, such that the compressed representation conveys maximal information about the corresponding distal stimuli. This approach can be considered as an implementation of Purves empirical theory of perception (Purves and Lotto, 2003), and I will illustrate it using examples from the visual and vestibular system. Ideas for the crucial and most challenging aspect of this approach will be presented and shall be discussed: How does the nervous system learn such representations without direct access to the distal stimuli?

3:20 PM - 3:50 PM

Afternoon Break

3:50 PM - 4:10 PM

How Neural Systems Adjust to Different Environments: a Novel Role for Gap Junction Coupling

Sheila Nirenberg, C. Pandarinath, I. Bomash, J. Victor, W. Tschetter, Department of Physiology and Biophysics, Weill Medical College, Cornell University.

The nervous system has an impressive ability to self-adjust – that is, as it moves from one environment to another, it can adjust itself to accommodate the new conditions. For example, as it moves into an environment with new stimuli, it can shift its attention; if the stimuli are low contrast, it can adjust its contrast sensitivity; if the signal-to-noise ratio is low, it can change its spatial and temporal integration properties. These changes are very well known at the behavioral level, but how the nervous system makes them happen isn’t clear.

Here we show a case where it was possible to obtain an answer. It’s a simple case, but one of the best-known examples of a behavioral shift – the shift in visual integration time that occurs as an animal switches from a day to a night environment. Our results show that the shift is produced by a mechanism in the retina – an increase in gap junction coupling among horizontal cells. Since coupling produces a shunt, the increase in coupling causes a substantial shunting of horizontal cell current, which effectively inactivates the horizontal cells. Since these cells play a key role in shaping integration time (they provide feedback to photoreceptors that keeps integration time short), inactivating them causes integration time to become longer. Thus, the coupling of the horizontal cells serves as a mechanism for shifting the visual system from one state to another.

These results raise a new, and possibly generalizable idea: that a neural system can shift itself from one state to another by changing the coupling of one of its cell classes. The coupling acts as a means to inactivate a cell class, effectively take it out of the system, and, by doing so, change the system’s behavior.

In sum, we tracked a behavioral shift down to the neural circuitry that implements it. This revealed a new, simple, and possibly generalizable, mechanism for how networks can rapidly adjust themselves to changing environmental demands.

4:10 PM - 4:50 PM

Phase of Firing Coding in Sensory Cortex

Stefano Panzeri, The Italian Institute of Technology, Genoa.

I will present some recent evidence that neurons in primary visual and auditory cortices encode information about natural visual or auditory stimuli in terms of spike timing relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. I will also describe the potential computational advantages of representing information in terms of phase of firing. These advantages are 1) higher information content than spike counts 2) ability to represent information about several effective stimuli in an easily decodable format 3) robustness to sensory noise. This is a joint work with Nikos Logothetis, Christoph Kayser and Marcelo Montemurro.

4:50 PM - 5:30 PM

Synaptic Encoding

Aurel A. Lazar, Department of Electrical Engineering, Columbia University.

Thursday (9:00 AM - 4:10 PM), July 23, 2009

Morning Session (9:00 AM - 12:10 PM)
Multi-Cell Analysis I
Chair: Stefano Panzeri

9:00 AM - 9:40 AM

Informational Robustness of the Hippocampal Spatial Map: Topological Analysis

Yuri Dabaghian (1), Facundo Memoli (2), Gurjeet Singh (2), Gunnar Carlsson (2), Loren Frank (1),
(1) Department of Physiology, University of California at San Francisco, CA. (2) Department of Mathematics, Stanford University, CA.

It is well known that the hippocampus plays crucial role in creating a spatial representation of the environment and in forming spatial memories. Each active hippocampal neuron (a place cell) tends to fire in its “place field’’ – a restricted region of the animal’s environment, so that the ensemble of active place cells encodes a spatial map. However the exact informational contents of this map are currently not clear. The hippocampal map may represent the connectivity of locations in the environment, i.e. be a topological map, or it may contain information about distances and angles and hence be more geometric in nature. The latter possibility is supported by the majority of current theories, which suggest that the hippocampus explicitly represents geometric elements of space derived from a path integration process that takes into account distances and angles of self motion information.

Several recent experiments indicate that the sequential structure of the hippocampal spatial map remains invariant with respect to a significant range of geometrical transformations of the environment [1,2], which indicates that the temporal ordering of spiking from hippocampal neural ensembles is the key determinant of the spatial information communicated to downstream neurons. This implies that the map itself is better understood as representing the topology of the animal’s environment and suggests that the actual role of the hippocampus is to encode topological memory maps, where the patterns of ongoing neural activity represent the connectivity of locations in the environment or the connectivity of elements of a memory trace. This hypothesis can be tested and studied both theoretically and experimentally. Specifically, the topological approach allows creating computational models that impose particular relationships on the parameters of the hippocampal map and predict some of its properties, such as the parameter ranges for informational stability of the map, which must agree with the experimentally observed parameters of firing activity in the hippocampus.

Hence we investigate the robustness of simulated hippocampal topological maps of different geometric complexity and dimensionality with respect to independent variations of place cell activity parameters, such as the distributions of the firing rate, the of sizes of place fields and the number of cells in the map, using the Persistent Homology method [2]. We find the maximal range of topological stability for each parameter independently and study the relationships between the parameters that ensure the stability of the map and then compare the results with the experimentally observed values and the dynamics of firing activity and find that our theoretical framework is consistent with experimental data. This provides a possibility to understand some of the physiological features of the hippocampal map based on the informational analysis of its firing activity.

Acknowledgments

This work was supported by NIH grants F32-NS054425-01 and MH080283, by the Sloan and Swartz Foundations, and by DARPA grants HR0011-05-1-0007 and FA8650-06-1-7629.

References

[1] K. Gothard, W. Skaggs, K. Moore, B. McNaughton, J. of Neuroscience, 16(2) (1996).
[2] K. Diba and G. Buzsáki, J. of Neuroscience, 28, 13448-13456 (2008).
[3] H. Edelsbrunner, D. Letscher and A. Zomorodian, Simplification, FOCS 2000: 454-463.

9:40 AM - 10:20 AM

Bayesian Population Decoding of Spiking Neurons

Matthias Bethge, Max Planck Institute for Biological Cybernetics, Tuebingen.

The timing of action potentials in spiking neurons depends on the temporal dynamics of their inputs, and contains information about temporal ﬂuctuations of a stimulus. Leaky integrate-and-ﬁre neurons constitute a popular class of encoding models in which spike times depend directly on the temporal structure of their inputs. However, optimal decoding rules for these models have only been studied explicitly in the noiseless case. Here, we study decoding rules for probabilistic inference of a continuous stimulus from the spike times of a population of leaky integrate-and-ﬁre neurons with noise threshold ﬂuctuations.

We derive three algorithms for approximating the posterior distribution over stimuli as a function of the observed spike trains. In addition to a reconstruction of the stimulus, we thus obtain an estimate of the uncertainty as well. Furthermore, we also derive a `spike-by-spike' online decoding scheme that recursively updates the posterior with the arrival of each new spike. We use these decoding rules to reconstruct time varying stimuli represented by a Gaussian process from spike trains of single neurons as well as neural populations.

Joint work with Sebastian Gerwinn and Jakob Macke.

10:20 AM - 10:50 AM

Morning Break

10:50 AM - 11:30 AM

Estimating Mutual Information of Multivariate Spike Count Distributions Using Copulas

Arno Onken (1,2), Steffen Grünewälder (1), and Klaus Obermayer (1,2)
(1) Technische Universität Berlin; (2) Bernstein Center for Computational Neuroscience, Berlin

Neural coding is typically analyzed by applying information theoretic measures like the mutual information between stimuli and spike count responses for a given bin size. In order to estimate the mutual information, a multivariate noise model of the spike counts is required. Here, we use copulas to construct discrete multivariate distributions that are appropriate to model dependent spike counts of several neurons.

With copulas it is possible to use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for modeling single neuron noise distributions than the most often applied normal approximation. Furthermore, copulas place a wide range of dependence structures at the disposal and can be used to analyze higher order interactions. We present a framework for model fitting of copula based distributions and apply Monte-Carlo techniques to estimate entropy and mutual information.

11:30 AM - 12:10 PM

Higher-Order Correlations in Large Neuronal Populations

Benjamin Staude, Sonja Grün and Stefan Rotter, Bernstein Center for Computational Neuroscience, Freiburg.

Spiking neurons are known to be quite sensitive for the higher-order correlation structure of their respective input populations (Kuhn et al. 2003). What is the role of these correlations in cortical information processing?

A prerequisite to answering this question is an appropriate framework to describe and effectively estimate the correlation structure of neuronal populations. Approaches available thus far suffer from the combinatorial explosion of the number of parameters that grows exponentially with the number of recorded neurons. As a consequence, methods that go beyond pairwise correlations and aim for estimating genuine higher-order effects require vast samples, rendering them essentially inapplicable to populations of more than ~10 neurons.

Here, we discuss the compound Poisson process as an intuitive and flexible model for correlated populations of spiking neurons. Based on this generative model, we present novel estimation techniques to infer the correlation structure of a neural population from sampled spike trains (Ehm et al. 2007; Staude et al. 2009). Our techniques can provide conclusive evidence for higher-order correlations in rather large populations of ~100 neurons, based on sample sizes that are compatible with current physiological in vivo recording technology.

Kuhn A, Aertsen A, Rotter S. Higher-order statistics of input ensembles and the response of simple model neurons. Neural Computation 15(1): 67-101, 2003.
Ehm W, Staude B, Rotter S. Decomposition of neuronal assembly activity via empirical de-Poissonization. Electronic Journal of Statistics 1: 473-495, 2007.
Staude B, Rotter S, Grün S. CuBIC: cumulant based inference of higher-order correlations in massively parallel spike trains. Under review.

12:00 PM - 2:00 PM

Lunch

Afternoon Session (2:00 PM - 4:50 PM)
Multi-Cell Analysis II
Chair: Yehoshua (Josh) Y. Zeevi

2:00 PM - 2:20 PM

Information-Geometric Measure of 3-Neuron Interactions Characterizes Scale-Dependence in Cortical Firing Patterns

Jonathan D. Victor and Ifije Ohiorhenuan, Department of Physiology and Biophysics, Weill Medical College of Cornell University.

2:20 PM - 3:00 PM

GELO - a Simple Stochastic Oscillator Traces Cellular and Coding Mechanisms

Gaby Schneider, Department of Informatics and Mathematics, University of Frankfurt.

Temporal coordination of neuronal spike trains, such as synchronous activity, oscillation, repetitive bursting or systematic temporal delays, have been hypothesized to be relevant for information processing. We present a simple stochastic model called the GELO which can describe and analyze these features in one theoretical framework.

Regular pacemakers and processes with repetitive bursts are described with the same set of parameters. The regularity of the oscillation and the degree of burstiness are estimated by fitting the model to the autocorrelation histogram. This allows a reliable burst detection in individual spike trains even in nonstationary conditions when burst surprise measures can fail. For parallel processes with a joint oscillation, the model can capture fine temporal structure across the units. By relating the auto correlation to the cross correlation histogram, it can also measure the degree to which all units share the same underlying oscillation. We illustrate the method with application to single spike trains recorded in the substantia nigra of mice and to a set of parallel spike-trains obtained from the visual cortex of the cat.

Acknowledgements: This is joint work with Markus Bingmer (Inst. of Mathematics, Frankfurt University), Felipe Gerhard and Danko Nikolic (FIAS, Frankfurt University), Jochen Roeper and Julia Schiemann (Institute of Neurophysiology, Frankfurt University). This work was supported by the German Bundesministerium fuer Bildung und Forschung (Bernstein Focus Neurotechnology, Frankfurt)

3:00 PM - 3:30 PM

Afternoon Break

3:30 PM - 4:10 PM

Maximum Entropy Decoding of Multivariate Neural Spike Trains

Simon R. Schultz, Department of Bioengineering, Imperial College.

4:10 PM - 4:50 PM

Using Information Theory to Trace Causal Relationships in Neurophysiological Data

Raul Vicente (1,2), German Gomez-Herrero (3), Wei Wu (1,2), Gordon Pipa (1,2), Jochen Triesch (2), Michael Wibral (4)

(1) Department of Neurophysiology, Max-Planck Institute for Brain Research, Frankfurt, (2) Frankfurt Institute for Advanced Studies (FIAS), Frankfurt, (3) Department of Signal Processing, Tampere University of Technology, Tampere, (4) MEG unit, Brain Imaging Center, Frankfurt.

The functional connectivity of the brain describes the network of statistically correlated activities of different brain areas. However, as it is well known correlation does not imply causality and most of synchronization measures are not able to distinguish context-dependent causal interactions (who drives whom?) among remote neural populations. There exists a great interest in the detection of this type of effective or causal networks since they can help in unveiling the neural circuitry of brain areas and its directed interactions involved in the processing of information.

Here, we assess the use of an information theoretic functional (transfer entropy) as a tool to discover patterns of causal relationships within the context of neurophysiological datasets. Transfer entropy can be understood as a direct implementation of the original concept of Wiener causality into an information theoretic framework and, thus naturally generalizing the limited linear regression modeling assumed in Granger causality. In particular, here I will discuss the robustness of transfer entropy to estimate causality against two common problems in neurophysiological recordings, namely, volume conduction and noise contamination. To go beyond the original pair-wise formulation of the transfer entropy, we also extend its definition and numerical estimator to the multivariate case which allows the distinction of direct from indirect causal interactions. We also make use of the typical multi-trial structure of a data set to propose a time resolved definition of transfer entropy able to capture causal relations between certain types of non-stationary time series. Finally, I will show results of the application of this causality approach to MEG datasets recorded during the performance of a Simon task.