This file was created by the Typo3 extension sevenpack version 0.7.14 --- Timezone: CEST Creation date: 2013-05-18 Creation time: 19-28-33 --- Number of references 50 article HaefnerGMB2013 Nature Neuroscience 2013 2 16 2 235–242 The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship that is often quantified by choice probabilities. Although choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. We derive the mathematical relationship between choice probabilities, read-out weights and correlated variability in the standard neural decision-making model. Our solution allowed us to prove and generalize earlier observations on the basis of numerical simulations and to derive new predictions. Notably, our results indicate how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we developed a test to decide whether the decoding weights of individual neurons are optimal for the task, even without knowing the underlying correlations. We confirmed the practicality of our approach using simulated data from a realistic population model. Thus, our findings provide a theoretical foundation for a growing body of experimental results on choice probabilities and correlations. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Macke Research Group Bethge Department Schölkopf http://www.nature.com/neuro/journal/v16/n2/pdf/nn.3309.pdf 10.1038/nn.3309 rhaefnerRMHaefner sgerwinnSGerwinn jakobJHMacke mbethgeMBethge article SchwartzMATB2012 Journal of Neurophysiology 2012 8 108 4 1069-1088 We explored the manner in which spatial information is encoded by retinal ganglion cell populations. We flashed a set of 36 shape stimuli onto the tiger salamander retina and used different decoding algorithms to read out information from a population of 162 ganglion cells. We compared the discrimination performance of linear decoders, which ignore correlation induced by common stimulation, against nonlinear decoders, which can accurately model these correlations. Similar to previous studies, decoders that ignored correlation suffered only a modest drop in discrimination performance for groups of up to ∼30 cells. However, for more realistic groups of 100+ cells, we found order-of-magnitude differences in the error rate. We also compared decoders that used only the presence of a single spike from each cell against more complex decoders that included information from multiple spike counts and multiple time bins. More complex decoders substantially outperformed simpler decoders, showing the importance of spike timing information. Particularly effective was the first spike latency representation, which allowed zero discrimination errors for the majority of shape stimuli. Furthermore, the performance of nonlinear decoders showed even greater enhancement compared to linear decoders for these complex representations. Finally, decoders that approximated the correlation structure in the population by matching all pairwise correlations with a maximum entropy model fit to all 162 neurons were quite successful, especially for the spike latency representation. Together, these results suggest a picture in which linear decoders allow a coarse categorization of shape stimuli, while nonlinear decoders, which take advantage of both correlation and spike timing, are needed to achieve high-fidelity discrimination. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf http://jn.physiology.org/content/early/2012/04/20/jn.00564.2011.full.pdf+html 10.1152/jn.00564.2011 GSchwartz jakobJMacke DAmodei HTang MJBerry article BuesingMS2012 Network 2012 3 23 1-2 24-47 Ongoing advances in experimental technique are making commonplace simultaneous recordings of the activity of tens to hundreds of cortical neurons at high temporal resolution. Latent population models, including Gaussian-process factor analysis and hidden linear dynamical system (LDS) models, have proven effective at capturing the statistical structure of such data sets. They can be estimated efficiently, yield useful visualisations of population activity, and are also integral building-blocks of decoding algorithms for brain-machine interfaces (BMI). One practical challenge, particularly to LDS models, is that when parameters are learned using realistic volumes of data the resulting models often fail to reflect the true temporal continuity of the dynamics; and indeed may describe a biologically-implausible unstable population dynamic that is, it may predict neural activity that grows without bound. We propose a method for learning LDS models based on expectation maximisation that constrains parameters to yield stable systems and at the same time promotes capture of temporal structure by appropriate regularisation. We show that when only little training data is available our method yields LDS parameter estimates which provide a substantially better statistical description of the data than alternatives, whilst guaranteeing stable dynamics. We demonstrate our methods using both synthetic data and extracellular multi-electrode recordings from motor cortex. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://informahealthcare.com/doi/abs/10.3109/0954898X.2012.677095 10.3109/0954898X.2012.677095 LBuesing jakobJHMacke MSahani article MackeBb2011 Frontiers in Computational Neuroscience 2011 7 5 35 1-2 Modern recording techniques such as multi-electrode arrays and two-photon imaging methods are capable of simultaneously monitoring the activity of large neuronal ensembles at single cell resolution. These methods finally give us the means to address some of the most crucial questions in systems neuroscience: what are the dynamics of neural population activity? How do populations of neurons perform computations? What is the functional organization of neural ensembles? While the wealth of new experimental data generated by these techniques provides exciting opportunities to test ideas about how neural ensembles operate, it also provides major challenges: multi-cell recordings necessarily yield data which is high-dimensional in nature. Understanding this kind of data requires powerful statistical techniques for capturing the structure of the neural population responses, as well as their relationship with external stimuli or behavioral observations. Furthermore, linking recorded neural population activity to the predictions of theoretical models of population coding has turned out not to be straightforward. These challenges motivated us to organize a workshop at the 2009 Computational Neuroscience Meeting in Berlin to discuss these issues. In order to collect some of the recent progress in this field, and to foster discussion on the most important directions and most pressing questions, we issued a call for papers for this Research Topic. We asked authors to address the following four questions: 1. What classes of statistical methods are most useful for modeling population activity? 2. What are the main limitations of current approaches, and what can be done to overcome them? 3. How can statistical methods be used to empirically test existing models of (probabilistic) population coding? 4. What role can statistical methods play in formulating novel hypotheses about the principles of information processing in neural populations? A total of 15 papers addressing questions related to these themes are now collected in this Research Topic. Three of these articles have resulted in “Focused reviews” in Frontiers in Neuroscience (Crumiller et al., 2011; Rosenbaum et al., 2011; Tchumatchenko et al., 2011), illustrating the great interest in the topic. Many of the articles are devoted to a better understanding of how correlations arise in neural circuits, and how they can be detected, modeled, and interpreted. For example, by modeling how pairwise correlations are transformed by spiking non-linearities in simple neural circuits, Tchumatchenko et al. (2010) show that pairwise correlation coefficients have to be interpreted with care, since their magnitude can depend strongly on the temporal statistics of their input-correlations. In a similar spirit, Rosenbaum et al. (2010) study how correlations can arise and accumulate in feed-forward circuits as a result of pooling of correlated inputs. Lyamzin et al. (2010) and Krumin et al. (2010) present methods for simulating correlated population activity and extend previous work to more general settings. The method of Lyamzin et al. (2010) allows one to generate synthetic spike trains which match commonly reported statistical properties, such as time varying firing rates as well signal and noise correlations. The Hawkes framework presented by Krumin et al. (2010) allows one to fit models of recurrent population activity to the correlation-structure of experimental data. Louis et al. (2010) present a novel method for generating surrogate spike trains which can be useful when trying to assess the significance and time-scale of correlations in neural spike trains. Finally, Pipa and Munk (2011) study spike synchronization in prefrontal cortex during working memory. A number of studies are also devoted to advancing our methodological toolkit for analyzing various aspects of population activity (Gerwinn et al., 2010; Machens, 2010; Staude et al., 2010; Yu et al., 2010). For example, Gerwinn et al. (2010) explain how full probabilistic inference can be performed in the popular model class of generalized linear models (GLMs), and study the effect of using prior distributions on the parameters of the stimulus and coupling filters. Staude et al. (2010) extend a method for detecting higher-order correlations between neurons via population spike counts to non-stationary settings. Yu et al. (2010) describe a new technique for estimating the information rate of a population of neurons using frequency-domain methods. Machens (2010) introduces a novel extension of principal component analysis for separating the variability of a neural response into different sources. Focusing less on the spike responses of neural populations but on aggregate signals of population activity, Boatman-Reich et al. (2010) and Hoerzer et al. (2010) describe methods for a quantitative analysis of field potential recordings. While Boatman-Reich et al. (2010) discuss a number of existing techniques in a unified framework and highlight the potential pitfalls associated with such approaches, Hoerzer et al. (2010) demonstrate how multivariate autoregressive models and the concept of Granger causality can be used to infer local functional connectivity in area V4 of behaving macaques. A final group of studies is devoted to understanding experimental data in light of computational models (Galán et al., 2010; Pandarinath et al., 2010; Shteingart et al., 2010). Pandarinath et al. (2010) present a novel mechanism that may explain how neural networks in the retina switch from one state to another by a change in gap junction coupling, and conjecture that this mechanism might also be found in other neural circuits. Galán et al. (2010) present a model of how hypoxia may change the network structure in the respiratory networks in the brainstem, and analyze neural correlations in multi-electrode recordings in light of this model. Finally, Shteingart et al. (2010) show that the spontaneous activation sequences they find in cultured networks cannot be explained by Zipf’s law, but rather require a wrestling model. The papers of this Research Topic thus span a wide range of topics in the statistical modeling of multi-cell recordings. Together with other recent advances, they provide us with a useful toolkit to tackle the challenges presented by the vast amount of data collected with modern recording techniques. The impact of novel statistical methods on the field and their potential to generate scientific progress, however, depends critically on how readily they can be adopted and applied by laboratories and researchers working with experimental data. An important step toward this goal is to also publish computer code along with the articles (Barnes, 2010) as a successful implementation of advanced methods also relies on many details which are hard to communicate in the article itself. In this way it becomes much more likely that other researchers can actually use the methods, and unnecessary re-implementations can be avoided. Some of the papers in this Research Topic already follow this goal (Gerwinn et al., 2010; Louis et al., 2010; Lyamzin et al., 2010). We hope that this practice becomes more and more common in the future and encourage authors and editors of Research Topics to make as much code available as possible, ideally in a format that can be easily integrated with existing software sharing initiatives (Herz et al., 2008; Goldberg et al., 2009). http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.frontiersin.org/Computational_Neuroscience/10.3389/fncom.2011.00035/full 10.3389/fncom.2011.00035 jakobJMacke berensPBerens mbethgeMBethge article MackeOb2011 Physical Review Letters 2011 5 106 20 1-4 Simultaneously recorded neurons exhibit correlations whose underlying causes are not known. Here, we use a population of threshold neurons receiving correlated inputs to model neural population recordings. We show analytically that small changes in second-order correlations can lead to large changes in higher-order redundancies, and that the resulting interactions have a strong impact on the entropy, sparsity, and statistical heat capacity of the population. Our findings for this simple model may explain some surprising effects recently observed in neural population recordings. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://prl.aps.org/pdf/PRL/v106/i20/e208102 10.1103/PhysRevLett.106.208102 208102 jakobJHMacke MOpper mbethgeMBethge article 6516 NeuroImage 2011 5 56 2 570-581 A striking feature of cortical organization is that the encoding of many stimulus features, for example orientation or direction selectivity, is arranged into topographic maps. Functional imaging methods such as optical imaging of intrinsic signals, voltage sensitive dye imaging or functional magnetic resonance imaging are important tools for studying the structure of cortical maps. As functional imaging measurements are usually noisy, statistical processing of the data is necessary to extract maps from the imaging data. We here present a probabilistic model of functional imaging data based on Gaussian processes. In comparison to conventional approaches, our model yields superior estimates of cortical maps from smaller amounts of data. In addition, we obtain quantitative uncertainty estimates, i.e. error bars on properties of the estimated map. We use our probabilistic model to study the coding properties of the map and the role of noise-correlations by decoding the stimulus from single trials of an imaging experiment. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WNP-5032NNX-1-3&_cdi=6968&_user=29041&_pii=S1053811910007007&_origin=&_coverDate=05%2F15%2F2011&_sk=999439997&view=c&wchp=dGLbVlz-zSkWl&md5=17cff103ca4f9e756eee9e6711fca3e4&ie=/sdarticle.pdf Biologische Kybernetik Max-Planck-Gesellschaft en 10.1016/j.neuroimage.2010.04.272 jakobJHMacke sgerwinnSGerwinn LWWhite MKaschube mbethgeMBethge article 7040 Frontiers in Neuroscience 2011 2 5 1 1-16 Reconstructing stimuli from the spike trains of neurons is an important approach for understanding the neural code. One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes. An important problem is to determine how much information about the continuously varying stimulus can be extracted from the time-points at which spikes were observed, especially if these time-points are subject to some sort of randomness. For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released. A simple decoding algorithm previously derived for the noiseless case can be extended to the stochastic case, but turns out to be biased. Here, we review a solution to this problem, by presenting a simple yet efficient algorithm which greatly reduces the bias, and therefore leads to better decoding performance in the stochastic case. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.frontiersin.org/Neuroscience/10.3389/fnins.2011.00001/abstract Biologische Kybernetik Max-Planck-Gesellschaft en 10.3389/fnins.2011.00001 1-9 sgerwinnSGerwinn jakobJHMacke mbethgeMBethge article LyamzinML2010 Frontiers in Computational Neuroscience 2010 10 4 144 1-11 As multi-electrode and imaging technology begin to provide us with simultaneous recordings of large neuronal populations, new methods for modeling such data must also be developed. Here, we present a model for the type of data commonly recorded in early sensory pathways: responses to repeated trials of a sensory stimulus in which each neuron has it own time-varying spike rate (as described by its PSTH) and the dependencies between cells are characterized by both signal and noise correlations. This model is an extension of previous attempts to model population spike trains designed to control only the total correlation between cells. In our model, the response of each cell is represented as a binary vector given by the dichotomized sum of a deterministic “signal” that is repeated on each trial and a Gaussian random “noise” that is different on each trial. This model allows the simulation of population spike trains with PSTHs, trial-to-trial variability, and pairwise correlations that match those measured experimentally. Furthermore, the model also allows the noise correlations in the spike trains to be manipulated independently of the signal correlations and single-cell properties. To demonstrate the utility of the model, we use it to simulate and manipulate experimental responses from the mammalian auditory and visual systems. We also present a general form of the model in which both the signal and noise are Gaussian random processes, allowing the mean spike rate, trial-to-trial variability, and pairwise signal and noise correlations to be specified independently. Together, these methods for modeling spike trains comprise a potentially powerful set of tools for both theorists and experimentalists studying population responses in sensory systems. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.frontiersin.org/Computational_Neuroscience/10.3389/fncom.2010.00144/abstract 10.3389/fncom.2010.00144 DRLyamzin jakobJHMacke NALesica article 6515 Journal of Vision 2010 5 10 5:22 1-24 One major challenge in the sensory sciences is to identify the stimulus features on which sensory systems base their computations, and which are predictive of a behavioral decision: they are a prerequisite for computational models of perception. We describe a technique (decision images) for extracting predictive stimulus features using logistic regression. A decision image not only defines a region of interest within a stimulus but is a quantitative template which defines a direction in stimulus space. Decision images thus enable the development of predictive models, as well as the generation of optimized stimuli for subsequent psychophysical investigations. Here we describe our method and apply it to data from a human face classification experiment. We show that decision images are able to predict human responses not only in terms of overall percent correct but also in terms of the probabilities with which individual faces are (mis-) classified by individual observers. We show that the most predictive dimension for gender categorization is neither aligned with the axis defined by the two class-means, nor with the first principal component of all faces-two hypotheses frequently entertained in the literature. Our method can be applied to a wide range of binary classification tasks in vision or other psychophysical contexts. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.journalofvision.org/content/10/5/22.full.pdf+html Biologische Kybernetik Max-Planck-Gesellschaft en 10.1167/10.5.22 jakobJHMacke felixFAWichmann article 6502 Frontiers in Computational Neuroscience 2010 4 4 12 1-42 Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://frontiersin.org/neuroscience/computationalneuroscience/paper/10.3389/fncom.2010.00012/pdf/ Biologische Kybernetik Max-Planck-Gesellschaft en 10.3389/fncom.2010.00012 sgerwinnSGerwinn jakobJMacke mbethgeMBethge article 6102 Frontiers in Computational Neuroscience 2009 10 3 21 1-28 The timing of action potentials in spiking neurons depends on the temporal dynamics of their inputs and contains information about temporal fluctuations in the stimulus. Leaky integrate-and-fire neurons constitute a popular class of encoding models, in which spike times depend directly on the temporal structure of the 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 threshold noise. 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 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. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.frontiersin.org/computationalneuroscience/paper/10.3389/neuro.10/021.2009/pdf/ Biologische Kybernetik Max-Planck-Gesellschaft en 10.3389/neuro.10.021.2009 sgerwinnSGerwinn jakobJHMacke mbethgeMBethge article 5157 Neural Computation 2009 2 21 2 397-423 Spike trains recorded from populations of neurons can exhibit substantial pairwise correlations between neurons and rich temporal structure. Thus, for the realistic simulation and analysis of neural systems, it is essential to have efficient methods for generating artificial spike trains with specified correlation structure. Here we show how correlated binary spike trains can be simulated by means of a latent multivariate gaussian model. Sampling from the model is computationally very efficient and, in particular, feasible even for large populations of neurons. The entropy of the model is close to the theoretical maximum for a wide range of parameters. In addition, this framework naturally extends to correlations over time and offers an elegant way to model correlated neural spike counts with arbitrary marginal distributions. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/macke2009_5157[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.mitpressjournals.org/doi/pdf/10.1162/neco.2008.02-08-713 Biologische Kybernetik Max-Planck-Gesellschaft en 10.1162/neco.2008.02-08-713 jakobJHMacke berensPBerens aeckerASEcker atoliasASTolias mbethgeMBethge article 4877 Magnetic Resonance Imaging 2008 9 26 7 1007-1014 Pattern recognition methods have shown that functional magnetic resonance imaging (fMRI) data can reveal significant information about brain activity. For example, in the debate of how object categories are represented in the brain, multivariate analysis has been used to provide evidence of a distributed encoding scheme [Science 293:5539 (2001) 2425–2430]. Many follow-up studies have employed different methods to analyze human fMRI data with varying degrees of success [Nature reviews 7:7 (2006) 523–534]. In this study, we compare four popular pattern recognition methods: correlation analysis, support-vector machines (SVM), linear discriminant analysis (LDA) and Gaussian naïve Bayes (GNB), using data collected at high field (7 Tesla) with higher resolution than usual fMRI studies. We investigate prediction performance on single trials and for averages across varying numbers of stimulus presentations. The performance of the various algorithms depends on the nature of the brain activity being categorized: for several tasks, many of the methods work well, whereas for others, no method performs above chance level. An important factor in overall classification performance is careful preprocessing of the data, including dimensionality reduction, voxel selection and outlier elimination. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/sdarticle_4877[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Department Logothetis Research Group Bethge http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6T9D-4T5BWJY-5-7&_cdi=5112&_user=29041&_orig=browse&_coverDate=09%2F30%2F2008&_sk=999739992&view=c&wchp=dGLbVzz-zSkWb&md5=25e9 Biologische Kybernetik Max-Planck-Gesellschaft en http://dx.doi.org/10.1016/j.mri.2008.02.016 shihpiS-PKu arthurAGretton jakobJMacke nikosNKLogothetis article 4667 Journal of Neuroscience Methods 2008 1 167 2 349-357 A new technique, ”Serial Block Face Scanning Electron Microscopy” (SBFSEM), allows for automatic sectioning and imaging of biological tissue with a scanning electron microscope. Image stacks generated with this technology have a resolution sufficient to distinguish different cellular compartments, including synaptic structures, which should make it possible to obtain detailed anatomical knowledge of complete neuronal circuits. Such an image stack contains several thousands of images and is recorded with a minimal voxel size of 10-20nm in the x and y- and 30nm in z-direction. Consequently, a tissue block of 1mm3 (the approximate volume of the Calliphora vicina brain) will produce several hundred terabytes of data. Therefore, highly automated 3D reconstruction algorithms are needed. As a first step in this direction we have developed semiautomated segmentation algorithms for a precise contour tracing of cell membranes. These algorithms were embedded into an easy-to-operate user interface, which allows direct 3D observation of the extracted objects during the segmentation of image stacks. Compared to purely manual tracing, processing time is greatly accelerated. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/Macke_Maack_07_JNeuMeth_Segmentation_[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6T04-4PCXG9T-1-1&_cdi=4852&_user=29041&_orig=browse&_coverDate=08%2F10%2F2007&_sk=999999999&view=c&wch Biologische Kybernetik Max-Planck-Gesellschaft en 10.1016/j.jneumeth.2007.07.021 jakobJHMacke NMaack RGupta WDenk bsBSchölkopf ABorst inproceedings BusingMS2013 2012 12 1691-1699 Latent linear dynamical systems with generalised-linear observation models arise in a variety of applications, for example when modelling the spiking activity of populations of neurons. Here, we show how spectral learning methods for linear systems with Gaussian observations (usually called subspace identification in this context) can be extended to estimate the parameters of dynamical system models observed through non-Gaussian noise models. We use this approach to obtain estimates of parameters for a dynamical model of neural population data, where the observed spike-counts are Poisson-distributed with log-rates determined by the latent dynamical process, possibly driven by external inputs. We show that the extended system identification algorithm is consistent and accurately recovers the correct parameters on large simulated data sets with much smaller computational cost than approximate expectation-maximisation (EM) due to the non-iterative nature of subspace identification. Even on smaller data sets, it provides an effective initialization for EM, leading to more robust performance and faster convergence. These benefits are shown to extend to real neural data. http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2013/NIPS-2012-Buesing.pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://books.nips.cc/nips25.html Bartlett, P. , F.C.N. Pereira, L. Bottou, C.J.C. Burges, K.Q. Weinberger Advances in Neural Information Processing Systems 25 Lake Tahoe, NV, USA Twenty-Sixth Annual Conference on Neural Information Processing Systems (NIPS 2012) LBuesing jakobJHMacke MSahani inproceedings MackeBCYSS2012 2012 1 1350-1358 Neurons in the neocortex code and compute as part of a locally interconnected population. Large-scale multi-electrode recording makes it possible to access these population processes empirically by fitting statistical models to unaveraged data. What statistical structure best describes the concurrent spiking of cells within a local network? We argue that in the cortex, where firing exhibits extensive correlations in both time and space and where a typical sample of neurons still reflects only a very small fraction of the local population, the most appropriate model captures shared variability by a low-dimensional latent process evolving with smooth dynamics, rather than by putative direct coupling. We test this claim by comparing a latent dynamical model with realistic spiking observations to coupled generalised linear spike-response models (GLMs) using cortical recordings. We find that the latent dynamical approach outperforms the GLM in terms of goodness-offit, and reproduces the temporal correlations in the data more accurately. We also compare models whose observations models are either derived from a Gaussian or point-process models, finding that the non-Gaussian model provides slightly better goodness-of-fit and more realistic population spike counts. http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2012/NIPS-2011-Macke.pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://nips.cc/Conferences/2011/ Shawe-Taylor , J. , R.S. Zemel, P. Bartlett, F. Pereira, K.Q. Weinberger Curran

Red Hook, NY, USA

Advances in Neural Information Processing Systems 24 Granada, Spain Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS 2011) 978-1-618-39599-3 jakobJHMacke LBüsing JPCunningham BMYu KVShenoy MSahani inproceedings MackeML2012 2012 1 2034-2042 Maximum entropy models have become popular statistical models in neuroscience and other areas in biology, and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e. the true entropy of the data can be severely underestimated. Here we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We show that if the data is generated by a distribution that lies in the model class, the bias is equal to the number of parameters divided by twice the number of observations. However, in practice, the true distribution is usually outside the model class, and we show here that this misspecification can lead to much larger bias. We provide a perturbative approximation of the maximally expected bias when the true model is out of model class, and we illustrate our results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data. http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2012/NIPS-2011-Macke-2.pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://nips.cc/Conferences/2011/ Shawe-Taylor , J. , R.S. Zemel, P. Bartlett, F. Pereira, K.Q. Weinberger Curran

Red Hook, NY, USA

Advances in Neural Information Processing Systems 24 Granada, Spain Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS 2011) 978-1-618-39599-3 jakobJHMacke IMurray PLatham inproceedings 6121 Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009 2010 4 1195-1203 Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial and temporal scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or pinwheel counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and quantitative model comparisons. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/NIPS2009-Macke_6121[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://nips.cc/Conferences/2009/ Bengio, Y. , D. Schuurmans, J. Lafferty, C. Williams, A. Culotta Curran

Red Hook, NY, USA

Advances in Neural Information Processing Systems 22 Biologische Kybernetik Max-Planck-Gesellschaft Vancouver, BC, Canada 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009) en 978-1-615-67911-9 jakobJHMacke sgerwinnSGerwinn MKaschube LEWhite mbethgeMBethge inproceedings 4728 Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007 2008 9 529-536 Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons. Here we present a Bayesian treatment of such models. Using the expectation propagation algorithm, we are able to approximate the full posterior distribution over all weights. In addition, we use a Laplacian prior to favor sparse solutions. Therefore, stimulus features that do not critically influence neural activity will be assigned zero weights and thus be effectively excluded by the model. This feature selection mechanism facilitates both the interpretation of the neuron model as well as its predictive abilities. The posterior distribution can be used to obtain confidence intervals which makes it possible to assess the statistical significance of the solution. In neural data analysis, the available amount of experimental measurements is often limited whereas the parameter space is large. In such a situation, both regularization by a sparsity prior and uncertainty estimates for the model parameters are essential. We apply our method to multi-electrode recordings of retinal ganglion cells and use our uncertainty estimate to test the statistical significance of functional couplings between neurons. Furthermore we used the sparsity of the Laplace prior to select those filters from a spike-triggered covariance analysis that are most informative about the neural response. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/BayesLNP_4728[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://nips.cc/Conferences/2007/ Platt, J. C., D. Koller, Y. Singer, S. Roweis Curran

Red Hook, NY, USA

Advances in neural information processing systems 20 Biologische Kybernetik Max-Planck-Gesellschaft Vancouver, BC, Canada Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007) en 978-1-605-60352-0 sgerwinnSGerwinn jakobJMacke seegerMSeeger mbethgeMBethge inproceedings 4738 Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007 2008 9 969-976 Stimulus selectivity of sensory neurons is often characterized by estimating their receptive field properties such as orientation selectivity. Receptive fields are usually derived from the mean (or covariance) of the spike-triggered stimulus ensemble. This approach treats each spike as an independent message but does not take into account that information might be conveyed through patterns of neural activity that are distributed across space or time. Can we find a concise description for the processing of a whole population of neurons analogous to the receptive field for single neurons? Here, we present a generalization of the linear receptive field which is not bound to be triggered on individual spikes but can be meaningfully linked to distributed response patterns. More precisely, we seek to identify those stimulus features and the corresponding patterns of neural activity that are most reliably coupled. We use an extension of reverse-correlation methods based on canonical correlation analysis. The resulting population receptive fields span the subspace of stimuli that is most informative about the population response. We evaluate our approach using both neuronal models and multi-electrode recordings from rabbit retinal ganglion cells. We show how the model can be extended to capture nonlinear stimulus-response relationships using kernel canonical correlation analysis, which makes it possible to test different coding mechanisms. Our technique can also be used to calculate receptive fields from multi-dimensional neural measurements such as those obtained from dynamic imaging methods. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/NIPS2007-Macke_4738[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://nips.cc/Conferences/2007/ Platt, J. C., D. Koller, Y. Singer, S. Roweis Curran

Red Hook, NY, USA

Advances in neural information processing systems 20 Biologische Kybernetik Max-Planck-Gesellschaft Vancouver, BC, Canada Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007) en 978-1-605-60352-0 jakobJHMacke gzeckGZeck mbethgeMBethge inproceedings 4266 Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference 2007 9 777-784 Attempting to model human categorization and similarity judgements is both a very interesting but also an exceedingly difficult challenge. Some of the difficulty arises because of conflicting evidence whether human categorization and similarity judgements should or should not be modelled as to operate on a mental representation that is essentially metric. Intuitively, this has a strong appeal as it would allow (dis)similarity to be represented geometrically as distance in some internal space. Here we show how a single stimulus, carefully constructed in a psychophysical experiment, introduces l2 violations in what used to be an internal similarity space that could be adequately modelled as Euclidean. We term this one influential data point a conflictual judgement. We present an algorithm of how to analyse such data and how to identify the crucial point. Thus there may not be a strict dichotomy between either a metric or a non-metric internal space but rather degrees to which potentially large subsets of stimuli are represented metrically with a small subset causing a global violation of metricity. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/NIPS2006-Laub_4266[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://nips.cc/Conferences/2006/ Schölkopf, B. , J. Platt, T. Hofmann MIT Press

Cambridge, MA, USA

Advances in Neural Information Processing Systems 19 Biologische Kybernetik Max-Planck-Gesellschaft Vancouver, BC, Canada Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006) en 0-262-19568-2 JLaub jakobJHMacke klausK-RMüller felixFAWichmann inproceedings 4305 Human Vision and Electronic Imaging XII: Proceedings of the SPIE Human Vision and Electronic Imaging Conference 2007 2007 2 1-12 There are two aspects to unsupervised learning of invariant representations of images: First, we can reduce the dimensionality of the representation by finding an optimal trade-off between temporal stability and informativeness. We show that the answer to this optimization problem is generally not unique so that there is still considerable freedom in choosing a suitable basis. Which of the many optimal representations should be selected? Here, we focus on this second aspect, and seek to find representations that are invariant under geometrical transformations occuring in sequences of natural images. We utilize ideas of steerability and Lie groups, which have been developed in the context of filter design. In particular, we show how an anti-symmetric version of canonical correlation analysis can be used to learn a full-rank image basis which is steerable with respect to rotations. We provide a geometric interpretation of this algorithm by showing that it finds the two-dimensional eigensubspaces of the avera ge bivector. For data which exhibits a variety of transformations, we develop a bivector clustering algorithm, which we use to learn a basis of generalized quadrature pairs (i.e. complex cells) from sequences of natural images. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/SPIE2007-Bethge_4305[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.ece.northwestern.edu/~pappas/hvei/past/6806.html Rogowitz, B. E. SPIE

Bellingham, WA, USA

Human Vision and Electronic Imaging XII Biologische Kybernetik Max-Planck-Gesellschaft San Jose, CA, USA SPIE Human Vision and Electronic Imaging Conference 2007 en 10.1117/12.711119 mbethgeMBethge sgerwinnSGerwinn jakobJHMacke techreport 5865 2009 3 183 Simultaneously recorded neurons often exhibit correlations in their spiking activity. These correlations shape the statistical structure of the population activity, and can lead to substantial redundancy across neurons. Here, we study the effect of pairwise correlations on the population spike count statistics and redundancy in populations of threshold-neurons in which response-correlations arise from correlated Gaussian inputs. We investigate the scaling of the redundancy as the population size is increased, and compare the asymptotic redundancy in our models to the corresponding maximum- and minimum entropy models. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/MPIK-TR-183_[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge Biologische Kybernetik Max-Planck-Gesellschaft Max Planck Institute for Biological Cybernetics, Tübingen, Germany en jakobJHMacke MOpper mbethgeMBethge poster MackeML2013 2013 3 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Macke http://www.cosyne.org/c/index.php?title=Cosyne_13 Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2013) accepted jakobJMacke iainIMurray PLatham poster BuesingMB2013 2013 3 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Macke Research Group Bethge Department Schölkopf http://www.cosyne.org/c/index.php?title=Cosyne_13 Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2013) accepted LBuesing jakobJMacke mbethgeMBethge poster MackeBCYSS2012_2 2012 5 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Ashburn, VA, USA Janelia Farm Conference 2012: Machine Learning, Statistical Inference, and Neuroscience jakobJHMacke LBüsing JPCunningham BMYu KVShenoy MSahani poster HaefnerGMB2011 2011 11 41 17.09 When monkeys make a perceptual decision about ambiguous visual stimuli, individual sensory neurons in MT and other areas have been shown to covary with the decision. This observation suggests that the response variability in those very neurons causes the animal to choose one over the other option. However, the fact that sensory neurons are correlated has greatly complicated attempts to link those covariances (and the associated choice probabilities) to a direct involvement of any particular neuron in a decision-making task. Here we report on an analytical treatment of choice probabilities in a population of correlated sensory neurons read out by a linear decoder. We present a closed-form solution that links choice probabilities, noise correlations and decoding weights for the case of fixed integration time. This allowed us to analytically prove and generalize a prior numerical finding about the choice probabilities being only due to the difference between the correlations within and between decision pools (Nienborg & Cumming 2010) and derive simplified expressions for a range of interesting cases. We investigated the implications for plausible correlation structures like pool-based and limited-range correlations. We found that the relationship between choice probabilities and decoding weights is in general non-monotonic and highly sensitive to the underlying correlation structure. In fact, given empirical measures of the interneuronal correlations and CPs, our formulas allow to infer the individual neuronal decoding weights. We confirmed the feasibility of this approach using synthetic data. We then applied our analytical results to a published dataset of empirical noise correlations and choice probabilities (Cohen & Newsome 2008 and 2009) recorded during a classic motion discriminating task (Britten et al 1992). We found that the data are compatible with an optimal read-out scheme in which the responses of neurons with the correct direction preference are summed and those with perpendicular preference, but positively correlated noise, are subtracted. While the correlation data of Cohen & Newsome (being based on individual extracellular electrode recordings) do not give access to the full covariance structure of a neural population, our analytical formulas will make it possible to accurately infer individual read-out weights from simultaneous population recordings. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.sfn.org/am2011/ Washington, DC, USA 41st Annual Meeting of the Society for Neuroscience (Neuroscience 2011) rhaefnerRMHaefner sgerwinnSGerwinn jakobJHMacke mbethgeMBethge poster MackeBCYSS2011 2011 2 I-34 Neural population activity reflects not only variations in stimulus drive ( captured by many neural encoding models) but also the rich computational dynamics of recurrent neural circuitry. Identifying this dynamical structure, and relating it to external stimuli and behavioural events, is a crucial step towards understanding neural computation. One data-driven approach is to fit hidden low-dimensional dynamical systems models to the high-dimensional spiking observations collected by microelectrode arrays (Yu et al, 2006, 2009). This approach yields low-dimensional representations of population-activity, allowing analysis and visualization of population dynamics with single trial resolution. Here, we compare two models using latent linear dynamics, with the dependence of spiking observations on the dynamical state being either linear with Gaussian observations (GaussLDS), or generalised linear with Poisson observations and an exponential nonlinearity (PoissonLDS) (Kulkarni & Paninski, 2007). Both models were fit by Expectation-Maximisation to multi-electrode recordings from pre-motor cortex in behaving monkeys during the delay-period of a delayed reach task. We evaluated the accuracy of different approximations for the E-step necessary for PoissonLDS using elliptical slice sampling. We quantified model-performance using a cross-prediction approach (Yu et al). Although only the Poisson noise model takes the discrete nature of spiking into account, we found no consistent improvement of the Poisson-model over GaussLDS: PoissonLDS was generally more accurate for low dimensions, but slightly under-performed GaussLDS in higher dimensions (cf. Lawhern et al. 2010). We also examined the ability of such models to capture conventional population metrics such as pairwise correlations and the distribution of synchronous spikes counts. We found that both models were able to reproduce these quantities with very low dynamical dimension, although the non-positivity of the Gaussian model introduced a bias. Thus, despite its verisimilitude, the Poisson observation model does not always yield more accurate predictions in real data. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.cosyne.org/c/index.php?title=Cosyne_11_posters Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2011) jakobJHMacke LBüsing JPCunningham BMYu KVShenoy MSahani poster MackeOB2011_2 2011 2 III-68 Finding models for capturing the statistical structure of multi-neuron firing patterns is a major challenge in sensory neuroscience. Recently, Maximum Entropy (MaxEnt) models have become popular tools for studying neural population recordings [4, 3]. These studies have found that small populations in retinal, but not in local cortical circuits, are well described by models based on pairwise correlations. It has also been found that entropy in small populations grows sublinearly [4], that sparsity in the population code is related to correlations [3], and it has been conjectured that neural populations might be at a ícritical pointí. While there have been many empirical studies using MaxEnt models, there has arguably been a lack of analytical studies that might explain the diversity of their findings. In particular, theoretical models would be of great importance for investigating their implications for large populations. Here, we study these questions in a simple, tractable population model of neurons receiving Gaussian inputs [1, 2]. Although the Gaussian input has maximal entropy, the spiking-nonlinearities yield non-trivial higher-order correlations (íhocsí). We find that the magnitude of hocs is strongly modulated by pairwise correlations, in a manner which is consistent with neural recordings. In addition, we show that the entropy in this model grows sublinearly for small, but linearly for large populations. We characterize how the magnitude of hocs grows with population size. Finally, we find that the hocs in this model lead to a diverging specific heat, and therefore, that any such model appears to be at a critical point. We conclude that common input might provide a mechanistic explanation for a wide range of recent empirical observations. [1] SI Amari, H Nakahara, S Wu, Y Sakai. Neural Comput, 2003. [2] JH Macke, M Opper, M Bethge. ArXiv, 2010. [3] IE Ohiorhenuan, et. al Nature, 2010. [4] E Schneidman, MJ Berry, R Segev, W Bialek. Nature, 2006. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.cosyne.org/c/index.php?title=Cosyne_11_posters3 Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2011) jakobJHMacke MOpper mbethgeMBethge poster 7074 2010 11 40 483.18 A striking feature of cortical organization is that the encoding of many stimulus features, such as orientation preference, is arranged into topographic maps. The structure of these maps has been extensively studied using functional imaging methods, for example optical imaging of intrinsic signals, voltage sensitive dye imaging or functional magnetic resonance imaging. As functional imaging measurements are usually noisy, statistical processing of the data is necessary to extract maps from the imaging data. We here present a probabilistic model of functional imaging data based on Gaussian processes. In comparison to conventional approaches, our model yields superior estimates of cortical maps from smaller amounts of data. In addition, we obtain quantitative uncertainty estimates, i.e. error bars on properties of the estimated map. We use our probabilistic model to study the coding properties of the map and the role of noise correlations by decoding the stimulus from single trials of an imaging experiment. In addition, we show how our method can be used to reconstruct maps from sparse measurements, for example multi-electrode recordings. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.sfn.org/am2010/index.aspx?pagename=abstracts_main Biologische Kybernetik Max-Planck-Gesellschaft San Diego, CA, USA 40th Annual Meeting of the Society for Neuroscience (Neuroscience 2010) en jakobJHMacke GSebastian LEWhite MKaschube mbethgeMBethge poster 6242 Journal of Vision 2009 8 9 8 31 One of the main challenges in the sensory sciences is to identify the stimulus features on which the sensory systems base their computations: they are a pre-requisite for computational models of perception. We describe a technique---decision-images--- for extracting critical stimulus features based on logistic regression. Rather than embedding the stimuli in noise, as is done in classification image analysis, we want to infer the important features directly from physically heterogeneous stimuli. A Decision-image not only defines the critical region-of-interest within a stimulus but is a quantitative template which defines a direction in stimulus space. Decision-images thus enable the development of predictive models, as well as the generation of optimized stimuli for subsequent psychophysical investigations. Here we describe our method and apply it to data from a human face discrimination experiment. We show that decision-images are able to predict human responses not only in terms of overall percent correct but are able to predict, for individual observers, the probabilities with which individual faces are (mis-) classified. We then test the predictions of the models using optimized stimuli. Finally, we discuss possible generalizations of the approach and its relationships with other models. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.journalofvision.org/9/8/31/ Biologische Kybernetik Max-Planck-Gesellschaft Naples, FL, USA 9th Annual Meeting of the Vision Sciences Society (VSS 2009) en 10.1167/9.8.31 jakobJHMacke felixFAWichmann poster 5845 Frontiers in Systems Neuroscience 2009 3 2009 Conference Abstracts: Computational and Systems Neuroscience Neurons in the early visual cortex of mammals exhibit a striking organization with respect to their functional properties. A prominent example is the layout of orientation preferences in primary visual cortex, the orientation preference map (OPM). Functional imaging techniques, such as optical imaging of intrinsic signals have been used extensively for the measurement of OPMs. As the signal-to-noise ratio in individual pixels if often low, the signals are usually spatially smoothed with a fixed linear filter to obtain an estimate of the functional map. Here, we consider the estimation of the map from noisy measurements as a Bayesian inference problem. By combining prior knowledge about the structure of OPMs with experimental measurements, we want to obtain better estimates of the OPM with smaller trial numbers. In addition, the use of an explicit, probabilistic model for the data provides a principled framework for setting parameters and smoothing. We model the underlying map as a bivariate Gaussian process (GP, a.k.a. Gaussian random field), with a prior covariance function that reflects known properties of OPMs. The posterior mean of the map can be interpreted as an optimally smoothed map. Hyper-parameters of the model can be chosen by optimization of the marginal likelihood. In addition, the GP also returns a predicted map for any location, and can therefore be used for extending the map to pixel at which no, or only unreliable data was obtained. We also obtain a posterior distribution over maps, from which we can estimate the posterior uncertainty of statistical properties of the maps, such as the pinwheel density. Finally, our probabilistic model of both the signal and the noise can be used for decoding, and for estimating the informational content of the map. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.cosyne.org/c/index.php?title=Cosyne_09 Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2009) en 10.3389/conf.neuro.06.2009.03.310 jakobJMacke sgerwinnSGerwinn LWhite MKaschube mbethgeMBethge poster 5843 Frontiers in Systems Neuroscience 2009 3 2009 Conference Abstracts: Computational and Systems Neuroscience http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.cosyne.org/c/index.php?title=Cosyne_09 Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA, Computational and Systems Neuroscience Meeting (COSYNE 2009) en 10.3389/conf.neuro.06.2009.03.026 sgerwinnSGerwinn jakobJMacke mbethgeMBethge poster 5844 Frontiers in Systems Neuroscience 2009 3 2009 Conference Abstracts: Computational and Systems Neuroscience Understanding the structure of multi-neuronal firing patterns in ensembles of cortical neurons is a major challenge for systems neuroscience. The dependence of network properties on the statistics of the sensory input can provide important insights into the computations performed by neural ensembles. Here, we study the functional properties of neural populations in the primary visual cortex of awake, behaving macaques by varying visual input statistics in a controlled way. Using arrays of chronically implanted tetrodes, we record simultaneously from up to thirty well-isolated neurons while presenting sets of images with three different correlation structures: spatially uncorrelated white noise (whn), images matching the second-order correlations of natural images (phs) and natural images including higher-order correlations (nat). We find that groups of six nearby cortical neurons show little redundancy in their firing patterns (represented as binary vectors, 10ms bins) but rather act almost independently (mean multi-information 0.85 bits/s, range 0.16 - 1.90 bits/s, mean fraction of marginal entropy 0.34 %, N=46). Although network correlations are weak, they are statistically significant. While relatively few groups showed significant redundancies under stimulation with white noise (67.4 ± 3.2%; mean fraction of groups ± S.E.M.), many more did so in the other two conditions (phs: 95.7 ± 0.6%; nat: 89.1 ± 1.4%). Additional higher-order correlations in natural images compared to phase scrambled images did not increase but rather decrease the redundancy in the cortical representation: Network correlations are significantly higher in phs than in nat, as is the number of significantly correlated groups. Multi-information measures the reduction in entropy due to any form of correlation. By using second order maximum entropy modeling, we find that a large fraction of multi-information is accounted for by pairwise correlations (whn: 75.0 ± 3.3%; phs: 82.8 ± 2.1%; nat: 80.8 ± 2.4%; groups with significant redundancy). Importantly, stimulation with natural images containing higher-order correlations only lead to a slight increase in the fraction of redundancy due to higher-order correlations in the cortical representation (mean difference 2.26 %, p=0.054, Sign test). While our results suggest that population activity in V1 may be modeled well using pairwise correlations only, they leave roughly 20-25 % of the multi-information unexplained. Therefore, choosing a particular form of higher-order interactions may improve model quality. Thus, in addition to the independent model, we evaluated the quality of three different models: (a) The second-order maximum entropy model, which minimizes higher-order correlations, (b) a model which assumes that correlations are a product of common inputs (Dichotomized Gaussian) and (c) a mixture model in which correlations are induced by a discrete number of latent states. We find that an independent model is sufficient for the white noise condition but neither for phs or nat. In contrast, all of the correlation models (a-c) perform similarly well for the conditions with correlated stimuli. Our results suggest that under natural stimulation redundancies in cortical neurons are relatively weak. Higher-order correlations in natural images do not increase but rather decrease the redundancies in the cortical representation. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.cosyne.org/c/index.php?title=Cosyne_09 Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2009) en 10.3389/conf.neuro.06.2009.03.298 berensPBerens jakobJHMacke aeckerASEcker RJCotton mbethgeMBethge atoliasASTolias poster MackeBEOTB2008 2008 7 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge Department Logothetis http://www.theswartzfoundation.org/summer-meeting-2008.asp Princeton, NJ, USA Annual Meeting 2008 of Sloan-Swartz Centers for Theoretical Neurobiology jakobJHMacke berensPBerens aeckerASEcker MOpper atoliasASTolias mbethgeMBethge poster 5857 2008 6 67 Pattern recognition methods have shown that fMRI data can reveal significant information about brain activity. For example, in the debate of how object-categories are represented in the brain, multivariate analysis has been used to provide evidence of distributed encoding schemes. Many follow-up studies have employed different methods to analyze human fMRI data with varying degrees of success. In this study we compare four popular pattern recognition methods: correlation analysis, support-vector machines (SVM), linear discriminant analysis and Gaussian naïve Bayes (GNB), using data collected at high field (7T) with higher resolution than usual fMRI studies. We investigate prediction performance on single trials and for averages across varying numbers of stimulus presentations. The performance of the various algorithms depends on the nature of the brain activity being categorized: for several tasks, many of the methods work well, whereas for others, no methods perform above chance level. An important factor in overall classification performance is careful preprocessing of the data, including dimensionality reduction, voxel selection, and outlier elimination. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Department Logothetis Research Group Bethge http://www.areadne.org/2008/home.html Biologische Kybernetik Max-Planck-Gesellschaft Santorini, Greece AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles en shihpiS-PKu arthurAGretton jakobJMacke atoliasATTolias nikosNKLogothetis poster 5101 2008 6 48 In order to understand how neural systems perform computations and process sensory information, we need to understand the structure of firing patterns in large populations of neurons. Spike trains recorded from populations of neurons can exhibit substantial pair wise correlations between neurons and rich temporal structure. Thus, efficient methods for generating artificial spike trains with specified correlation structure are essential for the realistic simulation and analysis of neural systems. Here we show how correlated binary spike trains can be modeled by means of a latent multivariate Gaussian model. Sampling from our model is computationally very efficient, and in particular, feasible even for large populations of neurons. We show empirically that the spike trains generated with this method have entropy close to the theoretical maximum. They are therefore consistent with specified pair-wise correlations without exhibiting systematic higher-order correlations. We compare our model to alternative approaches and discuss its limitations and advantages. In addition, we demonstrate its use for modeling temporal correlations in a neuron recorded in macaque primary visual cortex. Neural activity is often summarized by discarding the exact timing of spikes, and only counting the total number of spikes that a neuron (or population) fires in a given time window. In modeling studies, these spike counts have often been assumed to be Poisson distributed and neurons to be independent. However, correlations between spike counts have been reported in various visual areas. We show how both temporal and inter-neuron correlations shape the structure of spike counts, and how our model can be used to generate spike counts with arbitrary marginal distributions and correlation structure. We demonstrate its capabilities by modeling a population of simultaneously recorded neurons from the primary visual cortex of a macaque, and we show how a model with correlations accounts for the data far better than a model that assumes independence. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.areadne.org/2008/home.html Biologische Kybernetik Max-Planck-Gesellschaft Santorini, Greece AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles en mbethgeMBethge jakobJHMacke berensPBerens aeckerASEcker atoliasASTolias poster 5100 2008 6 46 Understanding the structure of multi-neuronal firing patterns has been a central quest and major challenge for systems neuroscience. In particular, how do pairwise interactions between neurons shape the firing patterns of neuronal ensembles in the cortex? To study this question, we recorded simultaneously from multiple single neurons in the primary visual cortex of an awake, behaving macaque using an array of chronically implanted tetrodes1. High contrast flashed and moving bars were used for stimulation, while the monkey was required to maintain fixation. In a similar vein to recent studies of in vitro preparations2,3,5, we applied maximum entropy analysis for the first time to the binary spiking patterns of populations of cortical neurons recorded in vivo from the awake macaque. We employed the Dichotomized Gaussian distribution, which can be seen as a close approximation to the pairwise maximum-entropy model for binary data4. Surprisingly, we find that even pairs of neurons with nearby receptive fields (receptive field center distance < 0.15°) have only weak correlations between their binary responses computed in bins of 10 ms (median absolute correlation coefficient: 0.014, 0.010-0.019, 95% confidence intervals, N=95 pairs; positive correlations: 0.015, N=59; negative correlations: -0.013, N=36). Accordingly, the distribution of spiking patterns of groups of 10 neurons is described well with a model that assumes independence between individual neurons (Jensen-Shannon-Divergence: 1.06×10-2 independent model, 0.96×10-2 approximate second-order maximum-entropy model4; H/H1=0.992). These results suggest that the distribution of firing patterns of small cortical networks in the awake animal is predominantly determined by the mean activity of the participating cells, not by their interactions. Meaningful computations, however, are performed by neuronal populations much larger than 10 neurons. Therefore, we investigated how weak pairwise correlations affect the firing patterns of artificial populations4 of up to 1000 cells with the same correlation structure as experimentally measured. We find that in neuronal ensembles of this size firing patterns with many active or silent neurons occur considerably more often than expected from a fully independent population (e.g. 130 or more out of 1000 neurons are active simultaneously roughly every 300 ms in the correlated model and only once every 3-4 seconds in the independent model). These results suggest that the firing patterns of cortical networks comparable in size to several minicolumns exhibit a rich structure, even if most pairs appear relatively independent when studying small subgroups thereof. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.areadne.org/2008/home.html Biologische Kybernetik Max-Planck-Gesellschaft Santorini, Greece AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles en berensPBerens aeckerASEcker MSubramaniyan jakobJHMacke PHauck mbethgeMBethge atoliasASTolias poster MackeSB2008 2008 6 73 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://www.areadne.org/2008/home.html Santorini, Greece AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles jakobJHMacke GSchwartz MBerry poster 4952 2008 3 5 172 a large number of retinal ganglion cells, one should be able to construct a decoding algorithm to discriminate different visual stimuli. Despite the inherent noise in the response of the ganglion cell population, everyday visual experience is highly deterministic. We have designed an experiment to study the nature of the population code of the retina in the “low error” regime. We presented 36 different black and white shapes, each with the same number of black pixels, to the retina of a tiger salamander while recording retinal ganglion cell responses using a multi-electrode array. Each shape was presented over 100 trials for 0.5 s each and trials were randomly interleaved. Spike trains were recorded from 162 ganglion cells in 13 experiments. We removed noise correlations by shuffling trials, as we wanted to focus on the role of correlations induced by the stimulus (signal correlations). We designed decoding algorithms for this population response in order to detect each target shape against the distracter set of the 35 other shapes. Binary response vectors were constructed using a 100 ms bin following the presentation of each shape. First, we used a simple decoder that assumes that all neurons are independent. This decoder is a linear classifier. A second decoder, which takes into account correlations between neurons, was constructed by fitting Ising models1 to the population response using up to 162 neurons for each model. We also constructed the statistically optimal decoder based on a mixture model, which accounts for signal correlations. Using populations of many neurons, the optimal and Ising decoders performed considerably better than the “independent” decoder. For certain shapes, the optimal decoder had 100 times fewer false positives than the independent decoder at 99% hit rate, and, in the median across shapes, the performance enhancement was 8-fold. While the decoder using an Ising model fit to the pairwise correlations did not achieve optimality, it was up to 50 times more accurate than the independent decoder, and 3 times more accurate in the median across shapes. Some shape discriminations were performed at zero error out of 3500 trials using the optimal and Ising decoders on only a subset of the recorded cells while none reached this “low error” level using the independent decoder even on all 162 cells (see figure). We find that discrimination with very low error using large populations requires a decoder that models signal correlations. Linear classifiers were unable to reach the “low error” regime. The Ising model of the population response is successfully applied to groups of up to 162 cells and offers a biologically feasible mechanism by which downstream neurons could account for correlations in their inputs. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/COSYNE2008-Schwartz_4952[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge http://cosyne.org/c/index.php?title=Cosyne_08 Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA, Computational and Systems Neuroscience Meeting (COSYNE 2008) en GSchwartz jakobJMacke MBerry poster 4347 Neuroforum 2007 4 13 Supplement 1195 The neural processing of visual motion is of essential importance for course control. A basic model suggesting a possible mechanism of how such a computation could be implemented in the fly visual system is the so called "correlation-type motion detector" proposed by Reichardt and Hassenstein in the 1950s. The basic requirement to reconstruct the neural circuit underlying this computation is the availability of electron microscopic 3D data sets of whole ensembles of neurons constituting the fly visual ganglia. We apply a new technique,"Serial Block Face Scanning Electron Microscopy" (SBFSEM), that allows for an automatic sectioning and imaging of biological tissue with a scanning electron microscope [Denk, Horstman (2004) Serial block face scanning electron microscopy to reconstruct three-dimensional tissue nanostructure. PLOS Biology 2: 1900-1909]. Image Stacks generated with this technology have a resolution sufficient to distinguish different cellular compartments, especially synaptic structures. Consequently detailed anatomical knowledge of complete neuronal circuits can be obtained. Such an image stack contains several thousands of images and is recorded with a minimal voxel size of 25nm in x and y and 30nm in z direction. Consequently a tissue block of 1mm³ (volume of the Calliphora vicina brain) produces several hundreds terabyte of data. Therefore new concepts for managing large data sets and for automated 3D reconstruction algorithms need to be developed. We developed an automated image segmentation and 3D reconstruction software, which allows a precise contour tracing of cell membranes and simultaneously displays the resulting 3D structure. In detail, the software contains two stand-alone packages: Neuron2D and Neuron3D, both offer an easy-to-operate Graphical-User-Interface. Neuron2D software provides the following image processing functions: • Image Viewer: Display image stacks in single or movie mode and optional calculates intensity distribution of each image. • Image Preprocessing: Filter process of image stacks. Implemented filters are a Gaussian 2D and a Non-Linear-Diffusion Filter. The filter step enhances the contrast between contour lines and image background, leading to an enhanced signal to noise ratio which further improves detection of membrane structures. • Image Segmentation: The implemented algorithm extracts contour lines from the preceding image and automatically traces the contour lines in the following images (z-direction), taking into account the previous image segmentation. In addition, a manual interaction is possible. To visualize 3D structures of neuronal circuits the additional software Neuron3D was developed. The reconstruction of neuronal surfaces from contour lines, obtained in Neuron2D, is implemented as a graph theory approach. The reconstructed anatomical data can further provide a subset for computational models of neuronal circuits in the fly visual system. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.neuro.uni-goettingen.de/nbc.php?sel=archiv Biologische Kybernetik Max-Planck-Gesellschaft Göttingen, Germany 31st Göttingen Neurobiology Conference en NMaack CKapfer jakobJHMacke bsBSchölkopf WDenk ABorst poster 4345 Neuroforum 2007 4 13 Supplement 359 Right from the first synapse in the retina, the visual information gets distributed across several parallel channels with different temporal filtering properties (Wässle, 2004). Yet, the prevalent system identification tool for characterizing neural responses, the spike-triggered average, only allows one to investigate the individual neural responses independently of each other. Here, we present a novel data analysis tool for the identification of temporal population codes based on canonical correlation analysis (Hotelling, 1936). Canonical correlation analysis allows one to find `population receptive fields' (PRF) which are maximally correlated with the temporal response of the entire neural population. The method is a convex optimization technique which essentially solves an eigenvalue problem and is not prone to local minima. We apply the method to simultaneous recordings from rabbit retinal ganlion cells in a whole mount preparation (Zeck et al, 2005). The cells respond to a 16 by 16 pixel m-sequence stimulus presented at a frame rate of 1/(20 msec). The response of 27 ganglion cells is correlated with each input frame in an interval between zero and 200 msec relative to the stimulus. The 200 msec response period is binned into 14 equal-sized bins. As shown in the figure, we obtain six predictive population receptive fields (left column), each of which gives rise to a different population response (right column). The x-axis of the color-coded images used to describe the population response kernels (right column) corresponds to the index of the 27 different neurons, while the y-axis indicates time relative to the stimulus from 0 (top) to 200 msec (bottom). The six population receptive fields do not only provide a more concise description of the population response but can also be estimated much more reliably than the receptive fields of individual neurons. In conclusion, we suggest to characterize retinal ganglion cell responses in terms of population receptive fields, rather than discussing stimulus-neuron and neuron-neuron dependencies separately. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/TS24-2C_4345[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.neuro.uni-goettingen.de/nbc.php?sel=archiv Biologische Kybernetik Max-Planck-Gesellschaft Göttingen, Germany 31st Göttingen Neurobiology Conference en mbethgeMBethge jakobJHMacke sgerwinnSGerwinn gzeckGZeck poster 4265 Neuroforum 2007 4 13 Supplement 1199 The representation of the nonlinear response properties of a neuron by a Wiener series expansion has enjoyed a certain popularity in the past, but its application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. A recently developed estimation method [1] utilizes the kernel techniques widely used in the machine learning community to implicitly represent the Wiener series as an element of an abstract dot product space. In contrast to the classical estimation methods for the Wiener series, the estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity. From the neural system identification point of view, the proposed estimation method has several advantages: 1. Due to the linear dependence of the estimation complexity on input dimensionality, system identification can be also done for systems acting on high-dimensional inputs such as images or video sequences. 2. Compared to classical cross-correlation techniques (such as spike-triggered average or covariance estimates), similar accuracies can be achieved with a considerably smaller amount of data. 3. The new technique does not need white noise as input, but works for arbitrary classes of input signals such as, e.g., natural image patches. 4. Regularisation concepts from machine learning to identify systems with noise-contaminated output signals. We present an application of the implicit Wiener series to find the low-dimensional stimulus subspace which accounts for most of the neuron's activity. We approximate the second-order term of a full Wiener series model with a set of parallel cascades consisting of a linear receptive field and a static nonlinearity. This type of approximation is known as reduced set technique in machine learning. We compare our results on simulated and physiological datasets to existing identification techniques in terms of prediction performance and accuracy of the obtained subspaces. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.neuro.uni-goettingen.de/nbc.php?sel=archiv Biologische Kybernetik Max-Planck-Gesellschaft Göttingen, Germany 31st Göttingen Neurobiology Conference en mofMOFranz jakobJHMacke ASaleem SRSchultz poster 4668 2007 2 44 Right from the first synapse in the retina, visual information gets distributed across several parallel channels with different temporal filtering properties. Yet, commonly used system identification tools for characterizing neural responses, such as the spike-triggered average, only allow one to investigate the individual neural responses independently of each other. Conversely, many population coding models of neurons and correlations between neurons concentrate on the encoding of a single-variate stimulus. We seek to identify the features of the visual stimulus that are encoded in the temporal response of an ensemble of neurons, and the corresponding spike-patterns that indicate the presence of these features. We present a novel data analysis tool for the identification of such temporal population codes based on canonical correlation analysis (Hotelling, 1936). The “population receptive fields” (PRFs) are defined to be those dimensions of the stimulus-space that are maximally correlated with the temporal response of the entire neural population, irrespective of whether the stimulus features are encoded by the responses of single neurons or by patterns of spikes across neurons or time. These dimensions are identified by canonical correlation analysis, a convex optimization technique which essentially solves an eigenvalue problem and is not prone to local minima. Each receptive field can be represented by the weighted sum of a small number of functions that are separable in space-time. Therefore, non-separable receptive fields can be estimated more efficiently than with spiketriggered techniques, which makes our method advantageous even for the estimation of single-cell receptive fields. The method is demonstrated by applying it to data from multi-electrode recordings from rabbit retinal ganglion cells in a whole mount preparation (Zeck et al, 2005). The figure displays the first 6 PRFs of a population of 27 cells from one such experiment. The recovered stimulus-features look qualitatively different to the receptive fields of single retinal ganglion cells. In addition, we show how the model can be extendended to capture nonlinear stimulus-response relationships and to test different coding-mechanisms by the use of kernel-canonical correlation analysis. In conclusion, we suggest to characterize responses of ensembles of neurons in terms of PRFs, rather than discussing stimulus-neuron and neuron-neuron dependencies separately. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/Cosyne-2007-I-37_[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.cosyne.org/wiki/Cosyne_07_Program Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2007) en jakobJHMacke gzeckGZeck mbethgeMBethge poster 4358 2007 2 16 Identification of stimulus-response functions is a central problem in systems neuroscience and related areas. Prominent examples are the estimation of receptive fields and classification images [1]. In most cases, the relationship between a high-dimensional input and the system output is modeled by a linear (first-order) or quadratic (second-order) model. Models with third or higher order dependencies are seldom used, since both parameter estimation and model interpretation can become very difficult. Recently, Wu and Gallant [3] proposed the use of kernel methods, which have become a standard tool in machine learning during the past decade [2]. Kernel methods can capture relationships of any order, while solving the parameter estmation problem efficiently. In short, the stimuli are mapped into a high-dimensional feature space, where a standard linear method, such as linear regression or Fisher discriminant, is applied. The kernel function allows for doing this implicitly, with all computations carried out in stimulus space. As a consequence, the resulting model is nonlinear, but many desirable properties of linear methods are retained. For example, the estimation problem has no local minima, which is in contrast to other nonlinear approaches, such as neural networks [4]. Unfortunately, although kernel methods excel at modeling complex functions, the question of how to interpret the resulting models remains. In particular, it is not clear how receptive fields should be defined in this context, or how they can be visualized. To remedy this, we propose the following definition: noting that the model is linear in feature space, we define a nonlinear receptive field as a stimulus whose image in feature space maximizes the dot-product with the learned model. This can be seen as a generalization of the receptive field of a linear filter: if the feature map is the identity, the kernel method becomes linear, and our receptive field definition coincides with that of a linear filter. If it is nonlinear, we numerically invert the feature space mapping to recover the receptive field in stimulus space. Experimental results show that receptive fields of simulated visual neurons, using natural stimuli, are correctly identified. Moreover, we use this technique to compute nonlinear receptive fields of the human fixation mechanism during free-viewing of natural images. http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/Cosyne-2007-I-9_4358[0].pdf http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge http://www.cosyne.org/wiki/Cosyne_07_Program Biologische Kybernetik Max-Planck-Gesellschaft Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2007) en kienzleWKienzle jakobJHMacke felixFAWichmann bsBSchölkopf mofMOFranz conference HafnerGMB2010 Frontiers in Neuroscience 2010 2 Conference Abstract: Computational and Systems Neuroscience 2010 Understanding how the activity of sensory neurons contribute to perceptual decision making is one of the major questions in neuroscience. In the current standard model, the output of opposing pools of noisy, correlated sensory neurons is integrated by downstream neurons whose activity elicits a decision-dependent behavior [1][2]. The predictions of the standard model for empirical measurements like choice probability (CP), psychophysical kernel (PK) and reaction time distribution crucially depend on the spatial and temporal correlations within the pools of sensory neurons. This dependency has so far only been investigated numerically and for time-invariant correlations and variances. However, it has recently been shown that the noise variance undergoes significant changes over the course of the stimulus presentation [3]. The same is true for inter-neuronal correlations that have been shown to change with task and attentional state [4][5]. In the first part of our work we compute analytically the time course of CPs and PKs in the presence of arbitrary noise correlations and variances for the case of non-leaky integration and Gaussian noise. This allows general insights and is especially needed in the light of the experimental transition from single-cell to multi-cell recordings. Then we simulate the implications of realistic noise in several variants of the standard model (leaky and non-leaky integration, integration over the entire stimulus presentation or until a bound, with and without urgency signal) and compare them to physiological data. We find that in the case of non-leaky integration over the entire stimulus duration, the PK only depends on the overall level of noise variance, not its time course. That means that the PK remains constant regardless of the temporal changes in the noise. This finding supports an earlier conclusion that an observed decreasing PK suggests that the brain is not integrating over the entire stimulus duration but only until it has accumulated sufficient evidence, even in the case of no urgency [6]. The time course of the CP, on the other hand, strongly depends on the time course of the noise variances and on the temporal and interneuronal correlations. If noise variance or interneuronal correlation increases, CPs increase as well. This dissociation of PK and CP allows an alternative solution to the puzzle recently posed by [7] in a bottom-up framework by combining integration to a bound with an increase in noise variance/correlation. In addition, we derive how the distribution of reaction times depends on noise variance and correlation, further constraining the model using empirical observations. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge Department Schölkopf Abstract Talk http://www.frontiersin.org/10.3389/conf.fnins.2010.03.00023/event_abstract Salt Lake City, UT, USA Computational and Systems Neuroscience Meeting (COSYNE 2010) 10.3389/conf.fnins.2010.03.00023 rhaefnerRHäfner sgerwinnSGerwinn jakobJMacke mbethgeMBethge conference MackeOB2008 Frontiers in Computational Neuroscience 2008 10 2008 Conference Abstract: Bernstein Symposium 2008 http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Research Group Bethge Abstract Talk http://www.frontiersin.org/community/AbstractDetails.aspx?ABS_DOI=10.3389/conf.neuro.10.2008.01.086&eid=108&sname=Bernstein_Symposium_2008 München, Germany Bernstein Symposium 2008 10.3389/conf.neuro.10.2008.01.086 jakobJHMacke MOpper mbethgeMBethge conference KuGML2008 2008 10 9 11 Pattern recognition methods have shown that fMRI data can reveal signicant information about brain activity. For example, in the debate of how object{categories are represented in the brain, multivariate analysis has been used to provide evidence of a distributed encoding scheme. Many follow{up studies have employed dierent methods to analyze human fMRI data with varying degrees of success. In this presentation I would like to discuss and compare four popular pattern recognition methods: correlation analysis, support{vector machines (SVM), linear discriminant analysis and Gaussian nave Bayes (GNB), using data collected at high eld (7T) with higher resolution than usual fMRI studies. We investigate prediction performance on single trials and for averages across varying numbers of stimulus presentations. The performance of the various algorithms depends on the nature of the brain activity being categorized: for several tasks, many of the methods work well, whereas for others, no methods perform above chance level. An important factor in overall classication performance is careful preprocessing of the data, including dimensionality reduction, voxel selection, and outlier elimination. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Logothetis Department Schölkopf Research Group Bethge Abstract Talk http://www.neuroschool-tuebingen-nena.de/index.php?id=284 Ellwangen, Germany 9th Conference of the Junior Neuroscientists of Tübingen (NeNa 2008) shipiS-PKu arthurAGretton jakobJMacke nikosNKLogothetis conference 5408 2007 11 37 768.1 The prevalent means of characterizing stimulus selectivity in sensory neurons is to estimate their receptive field properties such as orientation selectivity. Receptive fields are usually derived from the mean (or covariance) of the spike-triggered stimulus ensemble. This approach treats each spike as an independent message but ignores the possibility that information might be conveyed through patterns of neural activity that are distributed across space or time. In the retina for example, visual stimuli are analyzed by several parallel channels with different spatiotemporal filtering properties. How can we define the receptive field of a whole population of neurons, not just a single neuron? Imaging methods (such as voltage-sensitive dye imaging) yield measurements of neural activity that do not contain spiking events at all. How can receptive fields be derived from this kind of data? Even for single neurons, there is evidence that multiple features of the neural response, for example spike patterns or latencies, can carry information. How can these features be taken into account in the estimation process? Here, we address the question of how receptive fields can be calculated from such distributed representations. We seek to identify those stimulus features and the corresponding patterns of neural activity that are most reliably coupled, as measured by the mutual information between the two signals. As an efficient implementation of this strategy, we use an extension of reverse-correlation methods based on canonical correlation analysis [1]. We evaluate our approach using both simulated data and multi-electrode recordings from rabbit retinal ganglion cells [2]. In addition, we show how the model can be extended to capture nonlinear stimulus-response relationships and to test different coding mechanisms using kernel canonical correlation analysis [3]. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge Abstract Talk http://www.sfn.org/am2007/ Biologische Kybernetik Max-Planck-Gesellschaft San Diego, CA, USA 37th Annual Meeting of the Society for Neuroscience (Neuroscience 2007) en jakobJHMacke gzeckGZeck mbethgeMBethge conference Macke2006 2006 11 7 10 neurons- during a visual task is an important pre-requisite for computational models of visual cognition. We describe a technique for estimating high-dimensional decision-images, and apply the method to a psychophysical gender discrimination task. The use of regularization makes it possible to map out decision-images using a relatively small number of stimuli. Statistical analysis of the result shows a remarkable fit to the datasets collected—remarkable, as gender discrimination is a rather high-level visual task, and thus believed to be complex, but our model is conceptually rather simple. We demonstrate that the decision-images are sensitive to subtle changes in lighting, texture, and pose, and to individual differences in gender discrimination exhibited by our subjects. We show how decision-images can be used to create new stimuli, and how the approach can be generalized to non-linear and multi-scale decision-images. In addition, connections to reverse correlation techniques for receptive field estimation are described. http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de http://www.kyb.tuebingen.mpg.de Department Schölkopf Research Group Bethge Abstract Talk http://www.neuroschool-tuebingen-nena.de/index.php?id=284 Oberjoch, Germany 7th Conference of the Junior Neuroscientists of Tuebingen (NeNa 2006) jakobJMacke