Header logo is ei


2018


no image
Representation of sensory uncertainty in macaque visual cortex

Goris, R., Henaff, O., Meding, K.

Computational and Systems Neuroscience (COSYNE) 2018, March 2018 (poster)

[BibTex]

2018

[BibTex]


no image
A virtual reality environment for experiments in assistive robotics and neural interfaces

Bustamante, S.

Graduate School of Neural Information Processing, Eberhard Karls Universität Tübingen, Germany, 2018 (mastersthesis)

PDF [BibTex]

PDF [BibTex]


no image
Optimal Trajectory Generation and Learning Control for Robot Table Tennis

Koc, O.

Technical University Darmstadt, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
Distribution-Dissimilarities in Machine Learning

Simon-Gabriel, C. J.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
Generalized phase locking analysis of electrophysiology data

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N. K., Besserve, M.

7th AREADNE Conference on Research in Encoding and Decoding of Neural Ensembles, 2018 (poster)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


no image
Domain Adaptation Under Causal Assumptions

Lechner, T.

Eberhard Karls Universität Tübingen, Germany, 2018 (mastersthesis)

[BibTex]

[BibTex]


no image
Probabilistic Approaches to Stochastic Optimization

Mahsereci, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


no image
Reinforcement Learning for High-Speed Robotics with Muscular Actuation

Guist, S.

Ruprecht-Karls-Universität Heidelberg , 2018 (mastersthesis)

[BibTex]

[BibTex]


no image
Photorealistic Video Super Resolution

Pérez-Pellitero, E., Sajjadi, M. S. M., Hirsch, M., Schölkopf, B.

Workshop and Challenge on Perceptual Image Restoration and Manipulation (PIRM) at the 15th European Conference on Computer Vision (ECCV), 2018 (poster)

[BibTex]

[BibTex]


no image
Retinal image quality of the human eye across the visual field

Meding, K., Hirsch, M., Wichmann, F. A.

14th Biannual Conference of the German Society for Cognitive Science (KOGWIS 2018), 2018 (poster)

[BibTex]

[BibTex]


no image
Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

Schober, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
A machine learning approach to taking EEG-based computer interfaces out of the lab

Jayaram, V.

Graduate Training Centre of Neuroscience, IMPRS, Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]

2007


no image
MR-Based PET Attenuation Correction: Method and Validation

Hofmann, M., Steinke, F., Scheel, V., Charpiat, G., Brady, M., Schölkopf, B., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M16-6):1-2, November 2007 (poster)

Abstract
PET/MR combines the high soft tissue contrast of Magnetic Resonance Imaging (MRI) and the functional information of Positron Emission Tomography (PET). For quantitative PET information, correction of tissue photon attenuation is mandatory. Usually in conventional PET, the attenuation map is obtained from a transmission scan, which uses a rotating source, or from the CT scan in case of combined PET/CT. In the case of a PET/MR scanner, there is insufficient space for the rotating source and ideally one would want to calculate the attenuation map from the MR image instead. Since MR images provide information about proton density of the different tissue types, it is not trivial to use this data for PET attenuation correction. We present a method for predicting the PET attenuation map from a given the MR image, using a combination of atlas-registration and recognition of local patterns. Using "leave one out cross validation" we show on a database of 16 MR-CT image pairs that our method reliably allows estimating the CT image from the MR image. Subsequently, as in PET/CT, the PET attenuation map can be predicted from the CT image. On an additional dataset of MR/CT/PET triplets we quantitatively validate that our approach allows PET quantification with an error that is smaller than what would be clinically significant. We demonstrate our approach on T1-weighted human brain scans. However, the presented methods are more general and current research focuses on applying the established methods to human whole body PET/MRI applications.

PDF PDF [BibTex]

2007

PDF PDF [BibTex]


no image
Estimating receptive fields without spike-triggering

Macke, J., Zeck, G., Bethge, M.

37th annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37(768.1):1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


no image
Evaluation of Deformable Registration Methods for MR-CT Atlas Alignment

Scheel, V., Hofmann, M., Rehfeld, N., Judenhofer, M., Claussen, C., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M13-121):1, November 2007 (poster)

Abstract
Deformable registration methods are essential for multimodality imaging. Many different methods exist but due to the complexity of the deformed images a direct comparison of the methods is difficult. One particular application that requires high accuracy registration of MR-CT images is atlas-based attenuation correction for PET/MR. We compare four deformable registration algorithms for 3D image data included in the Open Source "National Library of Medicine Insight Segmentation and Registration Toolkit" (ITK). An interactive landmark based registration using MiraView (Siemens) has been used as gold standard. The automatic algorithms provided by ITK are based on the metrics Mattes mutual information as well as on normalized mutual information. The transformations are calculated by interpolating over a uniform B-Spline grid laying over the image to be warped. The algorithms were tested on head images from 10 subjects. We implemented a measure which segments head interior bone and air based on the CT images and l ow intensity classes of corresponding MRI images. The segmentation of bone is performed by individually calculating the lowest Hounsfield unit threshold for each CT image. The compromise is made by quantifying the number of overlapping voxels of the remaining structures. We show that the algorithms provided by ITK achieve similar or better accuracy than the time-consuming interactive landmark based registration. Thus, ITK provides an ideal platform to generate accurately fused datasets from different modalities, required for example for building training datasets for Atlas-based attenuation correction.

PDF [BibTex]

PDF [BibTex]


no image
Some Theoretical Aspects of Human Categorization Behavior: Similarity and Generalization

Jäkel, F.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, November 2007, passed with "ausgezeichnet", summa cum laude, published online (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Statistical Learning Theory Approaches to Clustering

Jegelka, S.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, November 2007 (diplomathesis)

PDF [BibTex]

PDF [BibTex]


no image
A time/frequency decomposition of information transmission by LFPs and spikes in the primary visual cortex

Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M., Logothetis, N., Panzeri, S.

37th Annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37, pages: 1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


no image
Mining expression-dependent modules in the human interaction network

Georgii, E., Dietmann, S., Uno, T., Pagel, P., Tsuda, K.

BMC Bioinformatics, 8(Suppl. 8):S4, November 2007 (poster)

PDF DOI [BibTex]

PDF DOI [BibTex]


no image
A Hilbert Space Embedding for Distributions

Smola, A., Gretton, A., Song, L., Schölkopf, B.

Proceedings of the 10th International Conference on Discovery Science (DS 2007), 10, pages: 40-41, October 2007 (poster)

Abstract
While kernel methods are the basis of many popular techniques in supervised learning, they are less commonly used in testing, estimation, and analysis of probability distributions, where information theoretic approaches rule the roost. However it becomes difficult to estimate mutual information or entropy if the data are high dimensional.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


no image
Studying the effects of noise correlations on population coding using a sampling method

Ecker, A., Berens, P., Bethge, M., Logothetis, N., Tolias, A.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 21, September 2007 (poster)

PDF [BibTex]

PDF [BibTex]


no image
Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference

Schölkopf, B., Platt, J., Hofmann, T.

Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006), pages: 1690, MIT Press, Cambridge, MA, USA, 20th Annual Conference on Neural Information Processing Systems (NIPS), September 2007 (proceedings)

Abstract
The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation and machine learning. It draws a diverse group of attendees--physicists, neuroscientists, mathematicians, statisticians, and computer scientists--interested in theoretical and applied aspects of modeling, simulating, and building neural-like or intelligent systems. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning, and applications. Only twenty-five percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains the papers presented at the December 2006 meeting, held in Vancouver.

Web [BibTex]

Web [BibTex]


no image
Near-Maximum Entropy Models for Binary Neural Representations of Natural Images

Berens, P., Bethge, M.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 19, September 2007 (poster)

Abstract
Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data---the model parameters can be derived in closed form and sampling is easy. We demonstrate its usefulness by studying a simple neural representation model of natural images. For the first time, we are able to directly compare predictions from a pairwise maximum entropy model not only in small groups of neurons, but also in larger populations of more than thousand units. Our results indicate that in such larger networks interactions exist that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics extrem ely well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

PDF [BibTex]

PDF [BibTex]


no image
Error Correcting Codes for the P300 Visual Speller

Biessmann, F.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, July 2007 (diplomathesis)

Abstract
The aim of brain-computer interface (BCI) research is to establish a communication system based on intentional modulation of brain activity. This is accomplished by classifying patterns of brain ac- tivity, volitionally induced by the user. The BCI presented in this study is based on a classical paradigm as proposed by (Farwell and Donchin, 1988), the P300 visual speller. Recording electroencephalo- grams (EEG) from the scalp while presenting letters successively to the user, the speller can infer from the brain signal which letter the user was focussing on. Since EEG recordings are noisy, usually many repetitions are needed to detect the correct letter. The focus of this study was to improve the accuracy of the visual speller applying some basic principles from information theory: Stimulus sequences of the speller have been modified into error-correcting codes. Additionally a language model was incorporated into the probabilistic letter de- coder. Classification of single EEG epochs was less accurate using error correcting codes. However, the novel code could compensate for that such that overall, letter accuracies were as high as or even higher than for classical stimulus codes. In particular at high noise levels, error-correcting decoding achieved higher letter accuracies.

PDF [BibTex]

PDF [BibTex]


no image
Learning the Influence of Spatio-Temporal Variations in Local Image Structure on Visual Saliency

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M.

10th T{\"u}binger Wahrnehmungskonferenz (TWK 2007), 10, pages: 1, July 2007 (poster)

Abstract
Computational models for bottom-up visual attention traditionally consist of a bank of Gabor-like or Difference-of-Gaussians filters and a nonlinear combination scheme which combines the filter responses into a real-valued saliency measure [1]. Recently it was shown that a standard machine learning algorithm can be used to derive a saliency model from human eye movement data with a very small number of additional assumptions. The learned model is much simpler than previous models, but nevertheless has state-of-the-art prediction performance [2]. A central result from this study is that DoG-like center-surround filters emerge as the unique solution to optimizing the predictivity of the model. Here we extend the learning method to the temporal domain. While the previous model [2] predicts visual saliency based on local pixel intensities in a static image, our model also takes into account temporal intensity variations. We find that the learned model responds strongly to temporal intensity changes ocurring 200-250ms before a saccade is initiated. This delay coincides with the typical saccadic latencies, indicating that the learning algorithm has extracted a meaningful statistic from the training data. In addition, we show that the model correctly predicts a significant proportion of human eye movements on previously unseen test data.

Web [BibTex]

Web [BibTex]


no image
Data-driven goodness-of-fit tests

Langovoy, MA.

Biologische Kybernetik, Georg-August-Universität Göttingen, Göttingen, Germany, July 2007 (phdthesis)

Web [BibTex]

Web [BibTex]


no image
Pattern detection

Blake, A., Romdhani, S., Schölkopf, B., Torr, P. H. S.

United States Patent, No 7236626, June 2007 (patent)

[BibTex]

[BibTex]


no image
Nonparametric Bayesian Discrete Latent Variable Models for Unsupervised Learning

Görür, D.

Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, April 2007, published online (phdthesis)

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Better Codes for the P300 Visual Speller

Biessmann, F., Hill, N., Farquhar, J., Schölkopf, B.

G{\"o}ttingen Meeting of the German Neuroscience Society, 7, pages: 123, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


no image
Do We Know What the Early Visual System Computes?

Bethge, M., Kayser, C.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 352, March 2007 (poster)

Abstract
Decades of research provided much data and insights into the mechanisms of the early visual system. Currently, however, there is great controversy on whether these findings can provide us with a thorough functional understanding of what the early visual system does, or formulated differently, of what it computes. At the Society for Neuroscience meeting 2005 in Washington, a symposium was held on the question "Do we know that the early visual system does", which was accompanied by a widely regarded publication in the Journal of Neuroscience. Yet, that discussion was rather specialized as it predominantly addressed the question of how well neural responses in retina, LGN, and cortex can be predicted from noise stimuli, but did not emphasize the question of whether we understand what the function of these early visual areas is. Here we will concentrate on this neuro-computational aspect of vision. Experts from neurobiology, psychophysics and computational neuroscience will present studies which approach this question from different viewpoints and promote a critical discussion of whether we actually understand what early areas contribute to the processing and perception of visual information.

PDF [BibTex]

PDF [BibTex]


no image
Implicit Wiener Series for Estimating Nonlinear Receptive Fields

Franz, MO., Macke, JH., Saleem, A., Schultz, SR.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 1199, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


no image
3D Reconstruction of Neural Circuits from Serial EM Images

Maack, N., Kapfer, C., Macke, J., Schölkopf, B., Denk, W., Borst, A.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 1195, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


no image
Identifying temporal population codes in the retina using canonical correlation analysis

Bethge, M., Macke, J., Gerwinn, S., Zeck, G.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 359, March 2007 (poster)

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Bayesian Neural System identification: error bars, receptive fields and neural couplings

Gerwinn, S., Seeger, M., Zeck, G., Bethge, M.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 360, March 2007 (poster)

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Applications of Kernel Machines to Structured Data

Eichhorn, J.

Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, March 2007, passed with "sehr gut", published online (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
A priori Knowledge from Non-Examples

Sinz, FH.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, March 2007 (diplomathesis)

PDF Web [BibTex]

PDF Web [BibTex]


no image
About the Triangle Inequality in Perceptual Spaces

Jäkel, F., Schölkopf, B., Wichmann, F.

Proceedings of the Computational and Systems Neuroscience Meeting 2007 (COSYNE), 4, pages: 308, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


no image
Center-surround filters emerge from optimizing predictivity in a free-viewing task

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M.

Proceedings of the Computational and Systems Neuroscience Meeting 2007 (COSYNE), 4, pages: 207, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


no image
Nonlinear Receptive Field Analysis: Making Kernel Methods Interpretable

Kienzle, W., Macke, J., Wichmann, F., Schölkopf, B., Franz, M.

Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 16, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


no image
Estimating Population Receptive Fields in Space and Time

Macke, J., Zeck, G., Bethge, M.

Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 44, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


no image
Machine Learning for Mass Production and Industrial Engineering

Pfingsten, T.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, February 2007 (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Development of a Brain-Computer Interface Approach Based on Covert Attention to Tactile Stimuli

Raths, C.

University of Tübingen, Germany, University of Tübingen, Germany, January 2007 (diplomathesis)

[BibTex]

[BibTex]


no image
A Machine Learning Approach for Estimating the Attenuation Map for a Combined PET/MR Scanner

Hofmann, M.

Biologische Kybernetik, Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, 2007 (diplomathesis)

[BibTex]

[BibTex]


no image
Machine Learning of Motor Skills for Robotics

Peters, J.

University of Southern California, Los Angeles, CA, USA, University of Southern California, Los Angeles, CA, USA, 2007, clmc (phdthesis)

Abstract
Autonomous robots that can assist humans in situations of daily life have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. A first step towards this goal is to create robots that can accomplish a multitude of different tasks, triggered by environmental context or higher level instruction. Early approaches to this goal during the heydays of artificial intelligence research in the late 1980s, however, made it clear that an approach purely based on reasoning and human insights would not be able to model all the perceptuomotor tasks that a robot should fulfill. Instead, new hope was put in the growing wake of machine learning that promised fully adaptive control algorithms which learn both by observation and trial-and-error. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this thesis, we investigate the ingredients for a general approach to motor skill learning in order to get one step closer towards human-like performance. For doing so, we study two major components for such an approach, i.e., firstly, a theoretically well-founded general approach to representing the required control structures for task representation and execution and, secondly, appropriate learning algorithms which can be applied in this setting. As a theoretical foundation, we first study a general framework to generate control laws for real robots with a particular focus on skills represented as dynamical systems in differential constraint form. We present a point-wise optimal control framework resulting from a generalization of Gauss' principle and show how various well-known robot control laws can be derived by modifying the metric of the employed cost function. The framework has been successfully applied to task space tracking control for holonomic systems for several different metrics on the anthropomorphic SARCOS Master Arm. In order to overcome the limiting requirement of accurate robot models, we first employ learning methods to find learning controllers for task space control. However, when learning to execute a redundant control problem, we face the general problem of the non-convexity of the solution space which can force the robot to steer into physically impossible configurations if supervised learning methods are employed without further consideration. This problem can be resolved using two major insights, i.e., the learning problem can be treated as locally convex and the cost function of the analytical framework can be used to ensure global consistency. Thus, we derive an immediate reinforcement learning algorithm from the expectation-maximization point of view which leads to a reward-weighted regression technique. This method can be used both for operational space control as well as general immediate reward reinforcement learning problems. We demonstrate the feasibility of the resulting framework on the problem of redundant end-effector tracking for both a simulated 3 degrees of freedom robot arm as well as for a simulated anthropomorphic SARCOS Master Arm. While learning to execute tasks in task space is an essential component to a general framework to motor skill learning, learning the actual task is of even higher importance, particularly as this issue is more frequently beyond the abilities of analytical approaches than execution. We focus on the learning of elemental tasks which can serve as the "building blocks of movement generation", called motor primitives. Motor primitives are parameterized task representations based on splines or nonlinear differential equations with desired attractor properties. While imitation learning of parameterized motor primitives is a relatively well-understood problem, the self-improvement by interaction of the system with the environment remains a challenging problem, tackled in the fourth chapter of this thesis. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm. In conclusion, in this thesis, we have contributed a general framework for analytically computing robot control laws which can be used for deriving various previous control approaches and serves as foundation as well as inspiration for our learning algorithms. We have introduced two classes of novel reinforcement learning methods, i.e., the Natural Actor-Critic and the Reward-Weighted Regression algorithm. These algorithms have been used in order to replace the analytical components of the theoretical framework by learned representations. Evaluations have been performed on both simulated and real robot arms.

[BibTex]

[BibTex]

2005


no image
Method and device for detection of splice form and alternative splice forms in DNA or RNA sequences

Rätsch, G., Sonnenburg, S., Müller, K., Schölkopf, B.

European Patent Application, International No PCT/EP2005/005783, December 2005 (patent)

[BibTex]

2005

[BibTex]


no image
Extension to Kernel Dependency Estimation with Applications to Robotics

BakIr, G.

Biologische Kybernetik, Technische Universität Berlin, Berlin, November 2005 (phdthesis)

Abstract
Kernel Dependency Estimation(KDE) is a novel technique which was designed to learn mappings between sets without making assumptions on the type of the involved input and output data. It learns the mapping in two stages. In a first step, it tries to estimate coordinates of a feature space representation of elements of the set by solving a high dimensional multivariate regression problem in feature space. Following this, it tries to reconstruct the original representation given the estimated coordinates. This thesis introduces various algorithmic extensions to both stages in KDE. One of the contributions of this thesis is to propose a novel linear regression algorithm that explores low-dimensional subspaces during learning. Furthermore various existing strategies for reconstructing patterns from feature maps involved in KDE are discussed and novel pre-image techniques are introduced. In particular, pre-image techniques for data-types that are of discrete nature such as graphs and strings are investigated. KDE is then explored in the context of robot pose imitation where the input is a an image with a human operator and the output is the robot articulated variables. Thus, using KDE, robot pose imitation is formulated as a regression problem.

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Kernel methods for dependence testing in LFP-MUA

Gretton, A., Belitski, A., Murayama, Y., Schölkopf, B., Logothetis, N.

35(689.17), 35th Annual Meeting of the Society for Neuroscience (Neuroscience), November 2005 (poster)

Abstract
A fundamental problem in neuroscience is determining whether or not particular neural signals are dependent. The correlation is the most straightforward basis for such tests, but considerable work also focuses on the mutual information (MI), which is capable of revealing dependence of higher orders that the correlation cannot detect. That said, there are other measures of dependence that share with the MI an ability to detect dependence of any order, but which can be easier to compute in practice. We focus in particular on tests based on the functional covariance, which derive from work originally accomplished in 1959 by Renyi. Conceptually, our dependence tests work by computing the covariance between (infinite dimensional) vectors of nonlinear mappings of the observations being tested, and then determining whether this covariance is zero - we call this measure the constrained covariance (COCO). When these vectors are members of universal reproducing kernel Hilbert spaces, we can prove this covariance to be zero only when the variables being tested are independent. The greatest advantage of these tests, compared with the mutual information, is their simplicity – when comparing two signals, we need only take the largest eigenvalue (or the trace) of a product of two matrices of nonlinearities, where these matrices are generally much smaller than the number of observations (and are very simple to construct). We compare the mutual information, the COCO, and the correlation in the context of finding changes in dependence between the LFP and MUA signals in the primary visual cortex of the anaesthetized macaque, during the presentation of dynamic natural stimuli. We demonstrate that the MI and COCO reveal dependence which is not detected by the correlation alone (which we prove by artificially removing all correlation between the signals, and then testing their dependence with COCO and the MI); and that COCO and the MI give results consistent with each other on our data.

Web [BibTex]

Web [BibTex]