Scene Graph Generation (SGG) suffers from a long-tailed distribution, where a few predicate classes dominate while many others are underrepresented, leading to biased models that underperform on rare relations. Unbiased-SGG methods address this by implementing debiasing strategies, but often at the cost of spatial understanding—resulting in over-reliance on semantic priors. We introduce Salience-SGG, a novel framework featuring an Iterative Salience Decoder (ISD) that emphasizes triplets with salient spatial structures. To support this, we propose semantic-agnostic salience labels guiding ISD. Evaluations on Visual Genome, Open Images V6, and GQA-200 show that Salience-SGG achieves state-of-the-art performance and improves existing Unbiased-SGG methods in their spatial understanding as demonstrated by the Pairwise Localization Average Precision. Code is available at: https://github.com/runfeng-q/Salience-SGG.

The complexity of natural scenes makes it challenging to experimentally study the mechanisms behind human gaze behavior when viewing dynamic environments. Historically, eye movements were believed to be driven primarily by space-based attention towards locations with salient features. Increasing evidence suggests, however, that visual attention does not select locations with high saliency but operates on attentional units given by the objects in the scene. We present a new computational framework to investigate the importance of objects for attentional guidance. This framework is designed to simulate realistic scanpaths for dynamic real-world scenes, including saccade timing and smooth pursuit behavior. Individual model components are based on psychophysically uncovered mechanisms of visual attention and saccadic decision-making. All mechanisms are implemented in a modular fashion with a small number of well-interpretable parameters. To systematically analyze the importance of objects in guiding gaze behavior, we implemented five different models within this framework: two purely spatial models, where one is based on low-level saliency and one on high-level saliency, two object-based models, with one incorporating low-level saliency for each object and the other one not using any saliency information, and a mixed model with object-based attention and selection but space-based inhibition of return. We optimized each model's parameters to reproduce the saccade amplitude and fixation duration distributions of human scanpaths using evolutionary algorithms. We compared model performance with respect to spatial and temporal fixation behavior, including the proportion of fixations exploring the background, as well as detecting, inspecting, and returning to objects. A model with object-based attention and inhibition, which uses saliency information to prioritize between objects for saccadic selection, leads to scanpath statistics with the highest similarity to the human data. This demonstrates that scanpath models benefit from object-based attention and selection, suggesting that object-level attentional units play an important role in guiding attentional processing.

[This corrects the article DOI: 10.1371/journal.pcbi.1007822.].

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network's state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description. We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models.

Identification and localization of sounds are both integral parts of computational auditory scene analysis. Although each can be solved separately, the goal of forming coherent auditory objects and achieving a comprehensive spatial scene understanding suggests pursuing a joint solution of the two problems. This article presents an approach that robustly binds localization with the detection of sound events in a binaural robotic system. Both tasks are joined through the use of spatial stream segregation which produces probabilistic time-frequency masks for individual sources attributable to separate locations, enabling segregated sound event detection operating on these streams. We use simulations of a comprehensive suite of test scenes with multiple co-occurring sound sources, and propose performance measures for systematic investigation of the impact of scene complexity on this segregated detection of sound types. Analyzing the effect of spatial scene arrangement, we show how a robot could facilitate high performance through optimal head rotation. Furthermore, we investigate the performance of segregated detection given possible localization error as well as error in the estimation of number of active sources. Our analysis demonstrates that the proposed approach is an effective method to obtain joint sound event location and type information under a wide range of conditions.

Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Astrocytes integrate and process synaptic information and exhibit calcium (Ca2+) signals in response to incoming information from neighboring synapses. The generation of Ca2+ signals is mostly attributed to Ca2+ release from internal Ca2+ stores evoked by an elevated metabotropic glutamate receptor (mGluR) activity. Different experimental results associated the generation of Ca2+ signals to the activity of the glutamate transporter (GluT). The GluT itself does not influence the intracellular Ca2+ concentration, but it indirectly activates Ca2+ entry over the membrane. A closer look into Ca2+ signaling in different astrocytic compartments revealed a spatial separation of those two pathways. Ca2+ signals in the soma are mainly generated by Ca2+ release from internal Ca2+ stores (mGluR-dependent pathway). In astrocytic compartments close to the synapse most Ca2+ signals are evoked by Ca2+ entry over the plasma membrane (GluT-dependent pathway). This assumption is supported by the finding, that the volume ratio between the internal Ca2+ store and the intracellular space decreases from the soma towards the synapse. We extended a model for mGluR-dependent Ca2+ signals in astrocytes with the GluT-dependent pathway. Additionally, we included the volume ratio between the internal Ca2+ store and the intracellular compartment into the model in order to analyze Ca2+ signals either in the soma or close to the synapse. Our model results confirm the spatial separation of the mGluR- and GluT-dependent pathways along the astrocytic process. The model allows to study the binary Ca2+ response during a block of either of both pathways. Moreover, the model contributes to a better understanding of the impact of channel densities on the interaction of both pathways and on the Ca2+ signal.

In realistic acoustic scenes, the detection of particular types of environmental sounds is often impeded by the simultaneous presence of multiple sound sources. In this work, we use simulations to systematically investigate the impact of superimposed distractor sources on sound type classification in a binaural robotic system and suggest techniques for increasing the robustness under such conditions. First, we demonstrate that by superimposing target sounds with strongly varying general environmental sounds during training, sound type classifiers are less affected by the presence of a distractor source. Moreover, we show that generalization performance of such models depends on how similar the angular source configuration and the signal-to-noise ratio are to the conditions under which the models were trained. Based on these results, we demonstrate how robust models can be obtained by including a variety of different conditions in the training data, a procedure called multi-conditional training. We evaluate this technique training both with ambient sources as well as with point sources with varying angular configurations, and show that this is an effective approach to produce models with close-to-optimal performance under a wide range of conditions. Moreover, we investigate the impact of head orientation and find that it has a significant influence on classification performance.

In this letter, we propose a definition of the operational mode of a neuron, that is, whether a neuron integrates over its input or detects coincidences. We complete the range of possible operational modes by a new mode we call gap detection, which means that a neuron responds to gaps in its stimulus. We propose a measure consisting of two scalar values, both ranging from -1 to +1: the neural drive, which indicates whether its stimulus excites the neuron, serves as background noise, or inhibits it; the neural mode, which indicates whether the neuron's response is the result of integration over its input, of coincidence detection, or of gap detection; with all three modes possible for all neural drive values. This is a pure spike-based measure and can be applied to measure the influence of either all or subset of a neuron's stimulus. We derive the measure by decomposing the reverse correlation, test it in several artificial and biological settings, and compare it to other measures, finding little or no correlation between them. We relate the results of the measure to neural parameters and investigate the effect of time delay during spike generation. Our results suggest that a neuron can use several different modes simultaneously on different subsets of its stimulus to enable it to respond to its stimulus in a complex manner.

Transcranial brain stimulation and evidence of ephaptic coupling have recently sparked strong interests in understanding the effects of weak electric fields on the dynamics of brain networks and of coupled populations of neurons. The collective dynamics of large neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type as their elements. These models, however, lack the dendritic morphology required to biophysically describe the effect of an extracellular electric field on the neuronal membrane voltage. Here, we extend the IF point neuron models to accurately reflect morphology dependent electric field effects extracted from a canonical spatial "ball-and-stick" (BS) neuron model. Even in the absence of an extracellular field, neuronal morphology by itself strongly affects the cellular response properties. We, therefore, derive additional components for leaky and nonlinear IF neuron models to reproduce the subthreshold voltage and spiking dynamics of the BS model exposed to both fluctuating somatic and dendritic inputs and an extracellular electric field. We show that an oscillatory electric field causes spike rate resonance, or equivalently, pronounced spike to field coherence. Its resonance frequency depends on the location of the synaptic background inputs. For somatic inputs the resonance appears in the beta and gamma frequency range, whereas for distal dendritic inputs it is shifted to even higher frequencies. Irrespective of an external electric field, the presence of a dendritic cable attenuates the subthreshold response at the soma to slowly-varying somatic inputs while implementing a low-pass filter for distal dendritic inputs. Our point neuron model extension is straightforward to implement and is computationally much more efficient compared to the original BS model. It is well suited for studying the dynamics of large populations of neurons with heterogeneous dendritic morphology with (and without) the influence of weak external electric fields.

Pairwise clustering methods are able to handle relational data, in which a set of objects is described via a matrix of pairwise (dis)similarities. Using the framework of source coding, it has been shown that pairwise clustering can be considered as entropy maximization problem under the constraint of keeping the distortion at a small value. This can be optimized via deterministic annealing. For the purpose of improving this optimization procedure, we have previously suggested two incremental pairwise clustering methods. However, they either only allow an even number of clusters, or cannot be applied to large proximity matrices. In this paper, we propose an incremental pairwise clustering method that resolves these issues. We compare the computational efficiency of the proposed algorithm to the previous incremental methods using simulations. Moreover, we apply the method to identify functionally connected brain networks by clustering a high-dimensional connectivity matrix obtained from resting state functional magnetic resonance imaging data.

We propose a general framework of risk-averse reinforcement learning for algorithmic trading. Our approach is tested in an experiment based on 1.5 years of millisecond time-scale limit order data from NASDAQ, which contain the data around the 2010 flash crash. The results show that our algorithm outperforms the risk-neutral reinforcement learning algorithm by 1) keeping the trading cost at a substantially low level at the spot when the flash crash happened, and 2) significantly reducing the risk over the whole test period.

How can we test for group differences in multidimensional input patterns, such as functional magnetic resonance imaging measurements or gene expression values? One solution is to split the available data into training and test set, and to estimate the generalization accuracy of a classifier that predicts the group variable from the input pattern. If this lies significantly above chance level, we can reject the null hypothesis of no association. This test is straightforward for balanced data, where all groups are equally frequent in the data set. However, data sets collected in observational studies are often imbalanced. Then accuracy is no longer a suitable measure of performance, and balanced accuracy should be used instead. In this paper, we give an overview on existing analytical tests and use the framework of prediction theory to derive a new test for the balanced accuracy of a classifier. We then use numerical simulations to evaluate the type I error rate and the power of two tests for imbalanced data.

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman & Tversky, 1979 ), for example, different risk preferences for gains and losses, as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework, we apply it to quantify human behavior in a sequential investment task. We find that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses that is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals shows a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex, and insula that is not present if standard Q-values are used.

Spatial selective attention pattern recognition plays a significant role in specific people's (e.g.: pilot's) state monitoring. Steady-State Visual Evoked Potentials (SSVEP) were recorded from the scalp of 6 subjects who were cued to attend to a flickering sequence displayed in one visual field while ignoring a similar one with a different flickering rate in the opposite field. The SSVEP to either flickering stimulus was enhanced when attention was lead to the same direction rather than to the opposite direction. The most significant enlargement is generally located on the posterior scalp contralateral to the visual field of stimulation. This attention-caused amplitude enhancement of SSVEP can be used to measure the attention shifting. In this paper, we developed an algorithm to extract short SSVEP, selectively combine them to form a joint temporal spatial selective attention feature, and use Support Vector Machine (SVM) to classify different attention pattern joint features. By segmenting the long single trial SSVEP (12s) data into short pieces (1s), we are able to largely decrease the training time while still keeping a high recognition accuracy (>93%) for most subjects, which makes it possible to monitor spatial selective attention on time.

We suggest a multivariate genotype-phenotype association test for functional magnetic resonance imaging (fMRI) data. The method uses a voxel selection and ranking scheme based on iterative adaptive Lasso for defining a functional region of interest. A classifier-based test is used to assess the significance of potential associations between the differential activity pattern within that region and a set of candidate genetic variants. We applied the method to a small sample dataset from an ongoing imaging genetics study and identified a significant genetic association to a stimulus-locked imaging phenotype.

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness-of-fit test, which tests--for a given divergence measure of interest--whether the experimental data lead to the rejection of the null hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.

Studies of Gaver (W. W. Gaver, “How do we hear in the world? Explorations in ecological acoustics,” Ecological Psychology, 1993) revealed that humans categorize everyday sounds considering the processes that have generated them: He defined these categories in a taxonomy according to the aggregate states of the involved materials (solid, liquid, gas) and the physical nature of the sound generating interaction such as deformation, friction, etc., for solids. We exemplified this taxonomy in an everyday sound database that contains recordings of basic isolated sound events of these categories. We used a sparse method to represent and to visualize these sound events. This representation relies on a sparse decomposition of sounds into atomic filter functions in the time-frequency domain. The filter functions maximally correlated with a given sound are selected automatically to perform the decomposition. The obtained sparse point pattern depicts the skeleton of the given sound. The visualization of these point patterns revealed that acoustically similar sounds have similar point patterns. To detect these similarities, we defined a novel dissimilarity function by considering these point patterns as 3-D point graphs and applied a graph matching algorithm, which assigns the points of one sound to the points of the other sound. This novel dissimilarity measure is used in combination with a kernel machine for the classification experiments, yielding an average accuracy of 95% in one versus one discrimination tasks.

The median and mean graph are basic building blocks for statistical graph analysis and unsupervised pattern recognition methods such as central clustering and graph quantization. This contribution provides sufficient conditions for consistent estimators of true but unknown central points of a distribution on graphs.

Pairwise clustering methods are able to handle relational data, in which a set of objects is described via a matrix of pairwise (dis)similarities. Here, we consider a cost function for pairwise clustering which maximizes model entropy under the constraint that the error for reconstructing objects from class information is fixed to a small value. Based on the analysis of structural transitions, we derive a new incremental pairwise clustering method which increases the number of clusters until a certain value of a Lagrange multiplier is reached. In addition, the calculation of phase transitions is used for speed-up. The incremental duplication of clusters helps to avoid local optima, and the stopping criterion automatically determines the number of clusters. The performance of the method is assessed on artificial and real-world data.

Bimal, a fast method for approximately solving the maximum contact map overlap (maxCMO) problem is introduced. The method is based on an approximate model of the maxCMO-problem using the generic bipartite graph matching framework, which is then optimally solved by double dynamic programming. The performance of Bimal has been evaluated in an empirical comparative study including clustering of protein structures according to the SCOP fold's level. Solving about 800 pairwise alignments of medium-sized proteins takes less than 1 min on a 1.7 GHz machine and yields good results for similar protein structures. Bimal accurately classified proteins in agreement with the SCOP classification. In particular, for similar proteins, Bimal provides a good tradeoff between computation speed and solution quality and is because of its high speed useful for solving large-scaled maxCMO applications.

We show that multiple structure alignment (MStA) using contact maps is equivalent to the problem of finding a sample mean of contact maps. From this result, we derive a subgradient method for solving the MStA method. Experiments show that the proposed algorithm is a flexible alignment method that provides an excellent tradeoff between accuracy and speed.

The linear correlation coefficient is typically used to characterize and analyze dependencies of neural spike counts. Here, we show that the correlation coefficient is in general insufficient to characterize these dependencies. We construct two neuron spike count models with Poisson-like marginals and vary their dependence structure using copulas. To this end, we construct a copula that allows to keep the spike counts uncorrelated while varying their dependence strength. Moreover, we employ a network of leaky integrate-and-fire neurons to investigate whether weakly correlated spike counts with strong dependencies are likely to occur in real networks. We find that the entropy of uncorrelated but dependent spike count distributions can deviate from the corresponding distribution with independent components by more than 25% and that weakly correlated but strongly dependent spike counts are very likely to occur in biological networks. Finally, we introduce a test for deciding whether the dependence structure of distributions with Poisson-like marginals is well characterized by the linear correlation coefficient and verify it for different copula-based models.

Simultaneous spike-counts of neural populations are typically modeled by a Gaussian distribution. On short time scales, however, this distribution is too restrictive to describe and analyze multivariate distributions of discrete spike-counts. We present an alternative that is based on copulas and can account for arbitrary marginal distributions, including Poisson and negative binomial distributions as well as second and higher-order interactions. We describe maximum likelihood-based procedures for fitting copula-based models to spike-count data, and we derive a so-called flashlight transformation which makes it possible to move the tail dependence of an arbitrary copula into an arbitrary orthant of the multivariate probability distribution. Mixtures of copulas that combine different dependence structures and thereby model different driving processes simultaneously are also introduced. First, we apply copula-based models to populations of integrate-and-fire neurons receiving partially correlated input and show that the best fitting copulas provide information about the functional connectivity of coupled neurons which can be extracted using the flashlight transformation. We then apply the new method to data which were recorded from macaque prefrontal cortex using a multi-tetrode array. We find that copula-based distributions with negative binomial marginals provide an appropriate stochastic model for the multivariate spike-count distributions rather than the multivariate Poisson latent variables distribution and the often used multivariate normal distribution. The dependence structure of these distributions provides evidence for common inhibitory input to all recorded stimulus encoding neurons. Finally, we show that copula-based models can be successfully used to evaluate neural codes, e.g., to characterize stimulus-dependent spike-count distributions with information measures. This demonstrates that copula-based models are not only a versatile class of models for multivariate distributions of spike-counts, but that those models can be exploited to understand functional dependencies.

The analysis of microarray data is a challenging task for statistical and machine learning methods, since the datasets usually contain a very large number of features (genes) and only a small number of examples (subjects). In this work, we describe a technique for gene selection and classification of microarray data based on the recently proposed potential support vector machine (P-SVM) for feature selection and a nu-SVM for classification. The P-SVM expands the decision function in terms of a sparse set of "support features". Based on this novel technique for feature selection, we suggest a fully automated method for gene selection, hyper-parameter optimization and microarray classification. Benchmark results are given for the two datasets provided by the ICMLA'08 Automated Micro-Array Classification Challenge.

In this work, a new learning paradigm called target selection is proposed, which can be used to test for associations between a single genetic variable and a multidimensional, quantitative phenotype. In target selection, the task of a learning machine is to chose one out of several nominal target variables, as well as a probabilistic classification function for the selected target. For this new paradigm, a cost function is derived from the concept of mutual information and a learning algorithm is suggested. The significance of the generalization performance of the model learned using target selection is tested using a label permutation test. Here, the proposed target selection paradigm is applied to a genomic imaging study.

We present an analytic and geometric view of the sample mean of graphs. The theoretical framework yields efficient subgradient methods for approximating a structural mean and a simple plug-in mechanism to extend existing central clustering algorithms to graphs. Experiments in clustering protein structures show the benefits of the proposed theory.

Correlations between spike counts are often used to analyze neural coding. The noise is typically assumed to be Gaussian. Yet, this assumption is often inappropriate, especially for low spike counts. In this study, we present copulas as an alternative approach. With copulas it is possible to use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for modeling noise distributions of spike counts. Furthermore, copulas place a wide range of dependence structures at the disposal and can be used to analyze higher order interactions. We develop a framework to analyze spike count data by means of copulas. Methods for parameter inference based on maximum likelihood estimates and for computation of Shannon entropy are provided. We apply the method to our data recorded from macaque prefrontal cortex. The data analysis leads to three significant findings: (1) copula-based distributions provide better fits than discretized multivariate normal distributions; (2) negative binomial margins fit the data better than Poisson margins; and (3) a dependence model that includes only pairwise interactions overestimates the information entropy by at least 19% compared to the model with higher order interactions.

One major role of primary visual cortex (V1) in vision is the encoding of the orientation of lines and contours. The role of the local recurrent network in these computations is, however, still a matter of debate. To address this issue, we analyze intracellular recording data of cat V1, which combine measuring the tuning of a range of neuronal properties with a precise localization of the recording sites in the orientation preference map. For the analysis, we consider a network model of Hodgkin-Huxley type neurons arranged according to a biologically plausible two-dimensional topographic orientation preference map. We then systematically vary the strength of the recurrent excitation and inhibition relative to the strength of the afferent input. Each parametrization gives rise to a different model instance for which the tuning of model neurons at different locations of the orientation map is compared to the experimentally measured orientation tuning of membrane potential, spike output, excitatory, and inhibitory conductances. A quantitative analysis shows that the data provides strong evidence for a network model in which the afferent input is dominated by strong, balanced contributions of recurrent excitation and inhibition. This recurrent regime is close to a regime of 'instability', where strong, self-sustained activity of the network occurs. The firing rate of neurons in the best-fitting network is particularly sensitive to small modulations of model parameters, which could be one of the functional benefits of a network operating in this particular regime.

We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An efficient selection procedure for Lagrange multipliers is given, and two heuristics for improving the SMO procedure are described: block optimization and annealing of the regularization parameter epsilon. A comparison of the variants shows that the dual SMO, including block optimization and annealing, performs efficiently in terms of computation time. In contrast to standard support vector machines (SVMs), the P-SVM is applicable to arbitrary dyadic data sets, but benchmarks are provided against libSVM's epsilon-SVR and C-SVC implementations for problems that are also solvable by standard SVM methods. For those problems, computation time of the P-SVM is comparable to or somewhat higher than the standard SVM. The number of support vectors found by the P-SVM is usually much smaller for the same generalization performance.

Sensory systems adapt their neural code to changes in the sensory environment, often on multiple time scales. Here, we report a new form of adaptation in a first-order auditory interneuron (AN2) of crickets. We characterize the response of the AN2 neuron to amplitude-modulated sound stimuli and find that adaptation shifts the stimulus-response curves toward higher stimulus intensities, with a time constant of 1.5 s for adaptation and recovery. The spike responses were thus reduced for low-intensity sounds. We then address the question whether adaptation leads to an improvement of the signal's representation and compare the experimental results with the predictions of two competing hypotheses: infomax, which predicts that information conveyed about the entire signal range should be maximized, and selective coding, which predicts that "foreground" signals should be enhanced while "background" signals should be selectively suppressed. We test how adaptation changes the input-response curve when presenting signals with two or three peaks in their amplitude distributions, for which selective coding and infomax predict conflicting changes. By means of Bayesian data analysis, we quantify the shifts of the measured response curves and also find a slight reduction of their slopes. These decreases in slopes are smaller, and the absolute response thresholds are higher than those predicted by infomax. Most remarkably, and in contrast to the infomax principle, adaptation actually reduces the amount of encoded information when considering the whole range of input signals. The response curve changes are also not consistent with the selective coding hypothesis, because the amount of information conveyed about the loudest part of the signal does not increase as predicted but remains nearly constant. Less information is transmitted about signals with lower intensity.

In this analytical study we compare the risk of the Monte Carlo (MC) and the least-squares TD (LSTD) estimator. We prove that for the case of acyclic Markov Reward Processes (MRPs) LSTD has minimal risk for any convex loss function in the class of unbiased estimators. When comparing the Monte Carlo estimator, which does not assume a Markov structure, and LSTD, we find that the Monte Carlo estimator is equivalent to LSTD if both estimators have the same amount of information. Theoretical results are supported by an empirical evaluation of the estimators.

Feedback on past queries is a valuable resource for improving retrieval performance on new queries. We introduce a modular approach to incorporating feedback information into given retrieval architectures. We propose to fusion the original ranking with those returned by rerankers, each of which trained on feedback given for a distinct, single query. Here, we examine the basic case of improving a query's original ranking qtest by only using one reranker: the one trained on feedback on the "closest" query qtrain. We examine the use of various distance measures between queries to first identify qtrain and then determine the best linear combination of the original and the reranker's ratings, that is: to find out which feedback to learn from, and how strongly to use it. We show the cosine distance between the term vectors of the two queries, each enriched by representations of the top N originally returned documents, to reliably answer both questions. The fusion performs equally well or better than a) always using only the original ranker or the reranker, b) selecting a hard distance threshold to decide between the two, or c) fusioning results with a ratio that is globally optimized, but fixed across all tested queries.

MOTIVATION: As more genomes are sequenced, the demand for fast gene classification techniques is increasing. To analyze a newly sequenced genome, first the genes are identified and translated into amino acid sequences which are then classified into structural or functional classes. The best-performing protein classification methods are based on protein homology detection using sequence alignment methods. Alignment methods have recently been enhanced by discriminative methods like support vector machines (SVMs) as well as by position-specific scoring matrices (PSSM) as obtained from PSI-BLAST. However, alignment methods are time consuming if a new sequence must be compared to many known sequences-the same holds for SVMs. Even more time consuming is to construct a PSSM for the new sequence. The best-performing methods would take about 25 days on present-day computers to classify the sequences of a new genome (20,000 genes) as belonging to just one specific class--however, there are hundreds of classes. Another shortcoming of alignment algorithms is that they do not build a model of the positive class but measure the mutual distance between sequences or profiles. Only multiple alignments and hidden Markov models are popular classification methods which build a model of the positive class but they show low classification performance. The advantage of a model is that it can be analyzed for chemical properties common to the class members to obtain new insights into protein function and structure. We propose a fast model-based recurrent neural network for protein homology detection, the 'Long Short-Term Memory' (LSTM). LSTM automatically extracts indicative patterns for the positive class, but in contrast to profile methods it also extracts negative patterns and uses correlations between all detected patterns for classification. LSTM is capable to automatically extract useful local and global sequence statistics like hydrophobicity, polarity, volume, polarizability and combine them with a pattern. These properties make LSTM complementary to alignment-based approaches as it does not use predefined similarity measures like BLOSUM or PAM matrices. RESULTS: We have applied LSTM to a well known benchmark for remote protein homology detection, where a protein must be classified as belonging to a SCOP superfamily. LSTM reaches state-of-the-art classification performance but is considerably faster for classification than other approaches with comparable classification performance. LSTM is five orders of magnitude faster than methods which perform slightly better in classification and two orders of magnitude faster than the fastest SVM-based approaches (which, however, have lower classification performance than LSTM). Only PSI-BLAST and HMM-based methods show comparable time complexity as LSTM, but they cannot compete with LSTM in classification performance. To test the modeling capabilities of LSTM, we applied LSTM to PROSITE classes and interpreted the extracted patterns. In 8 out of 15 classes, LSTM automatically extracted the PROSITE motif. In the remaining 7 cases alternative motifs are generated which give better classification results on average than the PROSITE motifs. AVAILABILITY: The LSTM algorithm is available from http://www.bioinf.jku.at/software/LSTM_protein/.

The joint analysis of genetic and brain imaging data is the key to understand the genetic underpinnings of brain dysfunctions in several psychiatric diseases known to have a strong genetic component. The goal is to identify associations between genetic and functional or morphometric brain measurements. We here suggest a machine learning method to solve this task, which is based on the recently proposed Potential Support Vector Machine (P-SVM) for variable selection, a subsequent k-NN classification and an estimation of the effect of `correlations by chance'. We apply it to the detection of associations between candidate single nucleotide polymorphisms (SNPs) and volumetric MRI measurements in alcohol dependent patients and healthy controls.

We propose a new annealing method for the hyperparameters of several recent Learning Vector Quantization algorithms. We first analyze the relationship between values assigned to the hyperparameters, the on-line learning process, and the structure of the resulting classifier. Motivated by the results we then suggest an annealing method, where each hyperparameter is initially set to a large value and is then slowly decreased during learning. We apply the annealing method to the LVQ 2.1, SLVQ-LR, and RSLVQ methods, and we compare the generalization performance achieved with the new annealing method and with a standard hyperparameter selection using 10-fold cross validation. Benchmark results are provided for the datasets letter and pendigits from the UCI Machine Learning Repository. The new selection method provides equally good or - for some data sets - even superior results when compared to standard selection methods. More importantly, however, the number of learning trials for different values of the hyperparameters is drastically reduced. The results are insensitive to the form and parameters of the annealing schedule.

We present a new optimization procedure which is particularly suited for the solution of second-order kernel methods like e.g. Kernel-PCA. Common to these methods is that there is a cost function to be optimized, under a positive definite quadratic constraint, which bounds the solution. For example, in kernel-PCA the constraint provides unit length and orthogonal (in feature space) principal components. The cost function is often quadratic which allows to solve the problem as a generalized eigenvalue problem. However, in contrast to support vector machines, which employ box constraints, quadratic constraints usually do not lead to sparse solutions. Here we give up the structure of the generalized eigenvalue problem in favor of a non-quadratic regularization term added to the cost function, which enforces sparse solutions. To optimize this more 'complicated' cost function, we introduce a modified conjugate gradient descent method. Starting from an admissible point, all iterations are carried out inside the subspace of admissible solutions, which is defined by the hyper-ellipsoidal constraint surface.

MOTIVATION: We propose a new model-based technique for summarizing high-density oligonucleotide array data at probe level for Affymetrix GeneChips. The new summarization method is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. Thereafter, the RNA concentration is estimated from the model. In contrast to previous methods our new method called 'Factor Analysis for Robust Microarray Summarization (FARMS)' supplies both P-values indicating interesting information and signal intensity values. RESULTS: We compare FARMS on Affymetrix's spike-in and Gene Logic's dilution data to established algorithms like Affymetrix Microarray Suite (MAS) 5.0, Model Based Expression Index (MBEI), Robust Multi-array Average (RMA). Further, we compared FARMS with 43 other methods via the 'Affycomp II' competition. The experimental results show that FARMS with default parameters outperforms previous methods if both sensitivity and specificity are simultaneously considered by the area under the receiver operating curve (AUC). We measured two quantities through the AUC: correctly detected expression changes versus wrongly detected (fold change) and correctly detected significantly different expressed genes in two sets of arrays versus wrongly detected (P-value). Furthermore FARMS is computationally less expensive then RMA, MAS and MBEI. AVAILABILITY: The FARMS R package is available from http://www.bioinf.jku.at/software/farms/farms.html. SUPPLEMENTARY INFORMATION: http://www.bioinf.jku.at/publications/papers/farms/supplementary.ps

We describe a new technique for the analysis of dyadic data, where two sets of objects (row and column objects) are characterized by a matrix of numerical values that describe their mutual relationships. The new technique, called potential support vector machine (P-SVM), is a large-margin method for the construction of classifiers and regression functions for the column objects. Contrary to standard support vector machine approaches, the P-SVM minimizes a scale-invariant capacity measure and requires a new set of constraints. As a result, the P-SVM method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square. We then describe two complementary regularization schemes. The first scheme improves generalization performance for classification and regression tasks; the second scheme leads to the selection of a small, informative set of row support objects and can be applied to feature selection. Benchmarks for classification, regression, and feature selection tasks are performed with toy data as well as with several real-world data sets. The results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets. In addition, a theoretical justification is provided for the new approach.

Optimal linear filters are well known as a useful technique for processing extracellular recordings of neural activity. They can be tuned to respond only to a corresponding waveform template, while minimizing the energy of all other templates, and can be used to resolve spikes that are overlapping. The derivation of optimal linear multichannel filters goes back to , but the computation is usually carried out in the frequency domain. This procedure, however, may introduce artefacts, because it assumes a cyclic cross correlation as the filtering operation, which is not applicable for filtering long signals. The only way to avoid the problems of cyclic operations is zero padding, at the expense of longer filters and, hence, higher filtering costs. In this letter, we propose to derive the optimal linear multichannel filters in the time domain, using the correct noncyclic operations. This leads to a quadratic optimization problem with linear constraints and allows us to formulate the filters as a function of the waveform templates in closed form. We compare the quality of the time-domain derived filters to those derived in the frequency domain in terms of their responses to waveform templates, which we extracted from real tetrode recordings. It turns out that the time-domain filters never perform worse than the frequency-domain filters but can be significantly shorter with the same or better performance.

Angiography plays a major role in analyzing brain activity (fMRI), tumor development, and ischemia. Exact knowledge of spatial distributions of arteries and veins is necessary. Unfortunately, commonly used non invasive MR approaches are biased by incomplete representations of vascular components in a single dataset. Therefore, we developed specialized algorithms, allowing generation of firstly more complete and secondly undistorted geometric models of the vascular system by fusing information from separate scans of the same specimen. Hereby each scan stresses different aspects of the vascular system like enhancing veins by use of contrast agents. The processing consists of a snake-based vessel reconstruction and a multiscale topological alignment of vessel parts. Our results show, that using contrast agents, not only putative veins appear, but some vessels (arteries as well as veins) also vanish. The latter could be due to complete saturation of the exited (inflowing) blood with contrast agent, which would result in total signal loss.

We introduce a novel "importance weight" method (IW) to speed up learning of "difficult" data sets including unbalanced data, highly non-linear data, or long-term dependencies in sequences. An importance weight is assigned to every training data point and controls its contribution to the total weight update. The importance weights are obtained by solving a quadratic optimization problem and determines the learning informativeness of a data point. For linear classifiers we show, that IW is equivalent to standard support vector learning. We apply IW to feedforward multi-layer perceptrons and to recurrent neural networks (LSTM). Benchmarks with QuickProp and standard gradient descent methods show that IW is usually much faster in terms of epochs as well as in terms of absolute CPU time, and that it provides equal or better prediction results. IW improved gradient descent results on "real world" protein datasets. In the "latching benchmark" for sequence prediction, IW was able to extract dependencies between sites which are 1,000,000 sequence elements apart - a new record.

We investigate the optimal kernel for sample-based model selection in unsupervised learning if maximum likelihood approaches are intractable. Given a set of training data and a set of data generated by the model, two kernel density estimators are constructed. A model is selected through gradient descent w.r.t. the model parameters on the integrated squared difference between the density estimators. Firstly we prove that convergence is optimal, i.e. that the cost function has only one global minimum w.r.t. the locations of the model samples, if and only if the kernel in the reparametrized cost function is a Coulomb kernel. As a consequence, Gaussian kernels commonly used for density estimators are suboptimal. Secondly we show that the absolute value of the difference between model and reference density converges at least with 1/t. Finally, we apply the new methods to distribution free ICA and to nonlinear ICA.

Recent experimental studies of hetero-synaptic interactions in various systems have shown the role of signaling in the plasticity, challenging the conventional understanding of Hebb's rule. It has also been found that activity plays a major role in plasticity, with neurotrophins acting as molecular signals translating activity into structural changes. Furthermore, role of synaptic efficacy in biasing the outcome of competition has also been revealed recently. Motivated by these experimental findings we present a model for the development of simple cell receptive field structure based on the competitive hetero-synaptic interactions for neurotrophins combined with cooperative hetero-synaptic interactions in the spatial domain. We find that with proper balance in competition and cooperation, the inputs from two populations (ON/OFF) of LGN cells segregate starting from the homogeneous state. We obtain segregated ON and OFF regions in simple cell receptive field. Our modeling study supports the experimental findings, suggesting the role of synaptic efficacy and the role of spatial signaling. We find that using this model we obtain simple cell RF, even for positively correlated activity of ON/OFF cells. We also compare different mechanism of finding the response of cortical cell and study their possible role in the sharpening of orientation selectivity. We find that degree of selectivity improvement in individual cells varies from case to case depending upon the structure of RF field and type of sharpening mechanism.

The standard approach to the classification of objects is to consider the examples as independent and identically distributed (iid). In many real world settings, however, this assumption is not valid, because a topo- graphical relationship exists between the objects. In this contribution we consider the special case of image segmentation, where the objects are pixels and where the underlying topography is a 2D regular rectangular grid. We introduce a classification method which not only uses measured vectorial feature information but also the label configuration within a to- pographic neighborhood. Due to the resulting dependence between the labels of neighboring pixels, a collective classification of a set of pixels becomes necessary. We propose a new method called 'Topographic Sup- port Vector Machine' (TSVM), which is based on a topographic kernel and a self-consistent solution to the label assignment shown to be equiv- alent to a recurrent neural network. The performance of the algorithm is compared to a conventional SVM on a cell image segmentation task.

Speech processing using multichannel microphone systems is often based on slowly adapting, linear filters. These systems are able to extract a single source from a mixture (and suppress the others)-if the speech radiation can be described by a linear and time-invariant transfer function. Here, we test this assumption using a two-channel microphone array and a human talker as the speech source. We measure correlations between the signals received by the two microphones for individual phonemes using the magnitude squared coherence. Stationarity is addressed by comparing optimal filters between different phoneme pairs using the system distance. We find that, in particular for fricatives, the coherence of the speech signals radiated to different directions is very low. We also find, that the transfer functions from the mouth to the microphones differ significantly between vowels, depending on the locations of the two microphones. These measurements show that the general mixing model does not hold for speech for arbitrary microphone setups, and that multichannel microphone systems have to be carefully designed.

The authors present a new method for the segmentation of autoradiographic brain image stacks, as well as the automatic extraction and 3D visualization of functional information encoded in the image gray values. The difficulty in the evaluation of these so-called "2 1/2 D" data sets is that they do not inherently represent a continuous 3D data volume (as MRI or CT), but consist of a series of consecutive, strongly distorted gray value images of single tissue slices, while the exact position and direction of the original slices varies among different data sets. This complicates the comparison of different experiments. In this work, in addition to providing an enhanced active contour based segmentation algorithm, the concept of "map space" is introduced, which allows the automatic functional evaluation using a shape adaptive, rectangular, normalized, parametric representation of the cortex. Results are presented for a rat brain under acoustical stimulation.

Nonlinear (cid:12)ltering can solve very complex problems, but typically involve very time consuming calculations. Here we show that for (cid:12)lters that are constructed as a RBF network with Gaussian basis functions, a decomposition into linear (cid:12)lters exists, which can be computed e(cid:14)ciently in the frequency domain, yielding dramatic improvement in speed. We present an application of this idea to image processing. In electron micrograph images of photoreceptor terminals of the fruit (cid:13)y, Drosophila, synaptic vesicles containing neurotransmitter should be detected and labeled automatically. We use hand labels, provided by human experts, to learn a RBF (cid:12)lter using Support Vector Regression with Gaussian kernels. We will show that the resulting nonlinear (cid:12)lter solves the task to a degree of accuracy, which is close to what can be achieved by human experts. This allows the very time consuming task of data evaluation to be done e(cid:14)ciently.

Learning vector quantization (LVQ) is a popular class of adaptive nearest prototype classifiers for multiclass classification, but learning algorithms from this family have so far been proposed on heuristic grounds. Here, we take a more principled approach and derive two variants of LVQ using a gaussian mixture ansatz. We propose an objective function based on a likelihood ratio and derive a learning rule using gradient descent. The new approach provides a way to extend the algorithms of the LVQ family to different distance measure and allows for the design of "soft" LVQ algorithms. Benchmark results show that the new methods lead to better classification performance than LVQ 2.1. An additional benefit of the new method is that model assumptions are made explicit, so that the method can be adapted more easily to different kinds of problems.

We propose a new method for the construction of nearest prototype classifiers which is based on a Gaussian mixture ansatz and which can be interpreted as an annealed version of learning vector quantization (LVQ). The algorithm performs a gradient descent on a cost-function minimizing the classification error on the training set. We investigate the properties of the algorithm and assess its performance for several toy data sets and for an optical letter classification task. Results show 1) that annealing in the dispersion parameter of the Gaussian kernels improves classification accuracy; 2) that classification results are better than those obtained with standard learning vector quantization (LVQ 2.1, LVQ 3) for equal numbers of prototypes; and 3) that annealing of the width parameter improved the classification capability. Additionally, the principled approach provides an explanation of a number of features of the (heuristic) LVQ methods.

We introduce a family of classiflers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classiflers, includes the two best-known support-vector machines (SVMs), the ”{SVM and the C{SVM. In the electrostat- ics analogy, a training example corresponds to a charged conductor at a given location in space, the classiflcation function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algo- rithms and their interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-deflnite kernels, regularization techniques that allow for the construction of an optimal classifler in Minkowski space. Based on the framework, we propose novel SVMs and per- form simulation studies to show that they are comparable or su- perior to standard SVMs. The experiments include classiflcation tasks on data which are represented in terms of their pairwise prox- imities, where a Coulomb Classifler outperformed standard SVMs.

We investigate the problem of learning a classiflcation task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column ob- jects may belong to difierent sets, and the entries in the matrix express the relationships between them. We interpret the matrix el- ements as being produced by an unknown kernel which operates on object pairs and we show that - under mild assumptions - these ker- nels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classi- fler which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not pos- itive deflnite, and not even symmetric or square. We then consider the case that row objects are interpreted as features. We suggest an additional constraint, which imposes sparseness on the row objects and show, that the method can then be used for feature selection. Finally, we apply this method to data obtained from DNA microar- rays, where \column" objects correspond to samples, \row" objects correspond to genes and matrix elements correspond to expression levels. Benchmarks are conducted using standard one-gene classifl- cation and support vector machines and K-nearest neighbors after standard feature selection. Our new method extracts a sparse set of genes and provides superior classiflcation results.

In this work, we focus on methods for the preprocessing of neurons from three-dimensional (3-D) confocal microscopy images, which are needed for a subsequent detailed morphologic analysis. Due to the specific image properties of confocal microscopy scans, we had to include several heuristic approaches which are based on multiscale edges to guarantee meaningful results: (1) a reliable segmentation of objects of different sizes independent of image contrast, and, based on it, (2) the computation of skeleton points along the branch central axes, and (3) the reliable detection of branching points and of problematic regions. These are preprocessing steps to gather information which is needed by the subsequent construction of a graph representing the geometry of the neuron and a final surface reconstruction.

The accurate comparison of inter-individual 3D image datasets of brains requires warping techniques to reduce geometric variations. In this study we use a point-based method of warping with weighted sums of displacement vectors, which is extended by an optimization process. To improve the practicability of 3D warping, we investigate 3D operators as landmark detectors for the applicability to our image datasets. The combined approach was tested on 3D autoradiographs of brains of Mongolian gerbils. The warping function is distance-weighted with landmark-specific weighting factors. These weighting factors are optimized by a computational evolution strategy. Within this optimization process the quality of warping is quantified by the sum of spatial differences of manually predefined registration points (registration error). The described approach combines a highly suitable procedure to detect landmarks in brain images and a point-based warping technique, which optimizes local weighting factors.

In this paper we propose a very simple but highly effective algorithm for single channel noise reduction of speech signals. One of the main objectives is to find a balanced tradeoff between noise reduction and speech distortion in the processed signal. This is accomplished by a system based on spectral minimum detection and diffusive gain factors. Our approach to speech enhancement is capable of distinguishing between speech and noise interference in the microphone signal, even when they are located in the same frequency band.

We present a new method for the blind separation of sources, which do not fulfill the independence assumption. In contrast to standard methods we consider groups of neighboring samples ("patches") within the observed mixtures. First we extract independent features from the observed patches. It turns out that the average dependencies between these features in different sources is in general lower than the dependencies be(cid:173) tween the amplitudes of different sources. We show that it might be the case that most of the dependencies is carried by only a small number of features. Is this case - provided these features can be identified by some heuristic - we project all patches into the subspace which is orthogonal to the subspace spanned by the "correlated" features. Standard ICA is then performed on the elements of the transformed patches (for which the independence assumption holds) and ro(cid:173) bustly yields a good estimate of the mixing matrix.

Cortical neurons might be considered as threshold elements inte(cid:173) grating in parallel many excitatory and inhibitory inputs. Due to the apparent variability of cortical spike trains this yields a strongly fluctuating membrane potential, such that threshold crossings are highly irregular. Here we study how a neuron could maximize its sensitivity w.r.t. a relatively small subset of excitatory input. Weak signals embedded in fluctuations is the natural realm of stochastic resonance. The neuron's response is described in a hazard-function approximation applied to an Ornstein-Uhlenbeck process. We an(cid:173) alytically derive an optimality criterium and give a learning rule for the adjustment of the membrane fluctuations, such that the sensitivity is maximal exploiting stochastic resonance. We show that adaptation depends only on quantities that could easily be estimated locally (in space and time) by the neuron. The main results are compared with simulations of a biophysically more re(cid:173) alistic neuron model.

Cq-profiles are 12-dimensional vectors, each component referring to a pitch class. They can be employed to represent keys. Cq-profiles are calculated with the constant Q filter bank. They have the following advantages: 1) they correspond to probe tone ratings; 2) calculation is possible in real-time; 3) stability is obtained with respect to sound quality; and 4) they are transposable. By using the cq-profile technique as a simple auditory model in combination with the SOM, an arrangement of keys emerges, that resembles results from psychological experiments and from the music theory. Cq-profiles are reliably applied to modulation tracking by introducing a special distance measure.

We start from the observation that sensory coding is not a static mapping but a process and focus on this temporal aspect. We propose that first extracting the salient features of a stimulus and then the details is an efficient coding strategy in terms of information processing when the network bandwidth increases with time. The authors: (i) show by using a simple transfer function that modulating the coding strategy from an initially highly competitive to a less competitive mapping is efficient for information encoding in time; and (ii) present simulation results of a detailed computational model of a cortical hypercolumn in order to demonstrate that this strategy could be implemented in the primary visual cortex. They propose a dynamic cortical amplifier model and suggest fast depressing synapses at the excitatory lateral connections as a possible mechanism to modulate the level competition on a short timescale.

We consider active data selection and test point rejection strategies for Gaussian process regression based on the variance of the posterior over target values. Gaussian process regression is viewed as transductive regression that provides target distributions for given points rather than selecting an explicit regression function. Since not only the posterior mean but also the posterior variance are easily calculated we use this additional information to two ends: active data selection is performed by either querying at points of high estimated posterior variance or at points that minimize the estimated posterior variance averaged over the input distribution of interest or (in a transductive manner) averaged over the test set. Test point rejection is performed using the estimated posterior variance as a confidence measure. We find that, for both a two-dimensional toy problem and a real-world benchmark problem, the variance is a reasonable criterion for both active data selection and test point rejection.

We investigate how structured information processing within a neural net can emerge as a result of unsupervised learning from data. Our model consists of input neurons and hidden neurons which are recurrently connected and which represent the thalamus and the cortex, respectively. On the basis of a maximum likelihood framework the task is to generate given input data using the code of the hidden units. Hidden neurons are fully connected allowing for different roles to play within the unfolding time-dynamics of this data generation process. One parameter which is related to the sparsity of neuronal activation varies across the hidden neurons. As a result of training the net captures the structure of the data generation process. The results imply that the division of the cortex into laterally and hierarchically organized areas can evolve to a certain degree as an adaptation to the environment.

We report an analysis of orientation and ocular dominance maps that were recorded optically from area 17 of cats and ferrets. Similar to a recent study performed in primates (Obermayer & Blasdel, 1997), we find that 80% (for cats and ferrets) of orientation singularities that are nearest neighbors have opposite sign and that the spatial distribution of singularities deviates from a random distribution of points, because the average distances between nearest neighbors are significantly larger than expected for a random distribution. Orientation maps of normally raised cats and ferrets show approximately the same typical wavelength; however, the density of singularities is higher in ferrets than in cats. Also, we find the well-known overrepresentation of cardinal versus oblique orientations in young ferrets (Chapman & Bonhoeffer, 1998; Coppola, White, Fitzpatrick, & Purves, 1998) but only a weak, not quite significant overrepresentation of cardinal orientations in cats, as has been reported previously (Bonhoeffer & Grinvald, 1993). Orientation and ocular dominance slabs in cats exhibit a tendency of being orthogonal to each other (Hubener, Shoham, Grinvald, & Bonhoeffer, 1997), albeit less pronounced, as has been reported for primates (Obermayer & Blasdel, 1993). In chronic recordings from single animals, a decrease of the singularity density and an increase of the ocular dominance wavelength with age but no change of the orientation wavelengths were found. Orientation maps are compared with two pattern models for orientation preference maps: bandpass-filtered white noise and the field analogy model. Bandpass-filtered white noise predicts sign correlations between orientation singularities, but the correlations are significantly stronger (87% opposite sign pairs) than what we have found in the data. Also, bandpass-filtered noise predicts a deviation of the spatial distribution of singularities from a random dot pattern. The field analogy model can account for the structure of certain local patches but not for the whole orientation map. Differences between the predictions of the field analogy model and experimental data are smaller than what has been reported for primates (Obermayer & Blasdel, 1997), which can be explained by the smaller size of the imaged areas in cats and ferrets.

We derive an efficient algorithm for topographic mapping of proximity data (TMP), which can be seen as an extension of Kohonen's self-organizing map to arbitrary distance measures. The TMP cost function is derived in a Baysian framework of folded Markov chains for the description of autoencoders. It incorporates the data by a dissimilarity matrix D and the topographic neighborhood by a matrix H of transition probabilities. From the principle of maximum entropy, a nonfactorizing Gibbs distribution is obtained, which is approximated in a mean-field fashion. This allows for maximum likelihood estimation using an expectation-maximization algorithm. In analogy to the transition from topographic vector quantization to the self-organizing map, we suggest an approximation to TMP that is computationally more efficient. In order to prevent convergence to local minima, an annealing scheme in the temperature parameter is introduced, for which the critical temperature of the first phase transition is calculated in terms of D and H. Numerical results demonstrate the working of the algorithm and confirm the analytical results. Finally, the algorithm is used to generate a connection map of areas of the cat's cerebral cortex.

We report the results of an analysis of orientation maps in primate striate cortex with focus on singularities and their distribution. Data were obtained from squirrel monkeys and macaque monkeys of different ages. We find the approximately 80% of singularities that are nearest neighbors have the opposite sign and that the spatial distribution of singularities differs significantly from a random distribution of points. We do not find evidence for consistent geometric patterns that singularities may form across the cortex. Except for a different overall alignment of orientation bands and different periods of repetition, maps obtained from different animals and different ages are found similar with respect to the measures used. Orientation maps are then compared with two different pattern models that are currently discussed in the literature: bandpass-filtered white noise, which accounts very well for the overall map structure, and the field analogy model, which specifies the orientation map by the location of singularities and their properties. The bandpass-filtered noise approach to orientation patterns correctly predicts the sign correlations between singularities and accounts for the deviations in the spatial distribution of singularities away from a random dot pattern. The field analogy model can account for the structure of certain local patches of the orientation map but not for the whole map. Neither of the models is completely satisfactory, and the structure of the orientation map remains to be fully explained.

Correlation-based learning (CBL) has been suggested as the mechanism that underlies the development of simple-cell receptive fields in the primary visual cortex of cats, including orientation preference (OR) and ocular dominance (OD) (Linsker, 1986; Miller, Keller, & Stryker, 1989). CBL has been applied successfully to the development of OR and OD individually (Miller, Keller, & Stryker, 1989; Miller, 1994; Miyashita & Tanaka, 1991; Erwin, Obermayer, & Schulten, 1995), but the conditions for their joint development have not been studied (but see Erwin & Miller, 1995, for independent work on the same question) in contrast to competitive Hebbian models (Obermayer, Blasdel, & Schulten, 1992). In this article, we provide insight into why this has been the case: OR and OD decouple in symmetric CBL models, and a joint development of OR and OD is possible only in a parameter regime that depends on nonlinear mechanisms.

Orientation and ocular dominance maps in the primary visual cortex of mammals are among the most thoroughly investigated of the patterns in the cerebral cortex. A considerable amount of work has been dedicated to unraveling both their detailed structure and the neural mechanisms that underlie their formation and development. Many schemes have been proposed, some of which are in competition. Some models focus on development of receptive fields while others focus on the structure of cortical maps, i.e., the arrangement of receptive field properties across the cortex. Each model used different means to determine its success at reproducing experimental map patterns, often relying principally on visual comparison. Experimental data are becoming available that allow a more careful evaluation of models. In this contribution more than 10 of the most prominent models of cortical map formation and structure are critically evaluated and compared with the most recent experimental findings from macaque striate cortex. Comparisons are based on properties of the predicted or measured cortical map patterns. We introduce several new measures for comparing experimental and model map data that reveal important differences between models. We expect that the use of these measures will improve current models by helping determine parameters to match model maps to experimental data now becoming available from a variety of species. Our study reveals that (1) despite apparent differences, many models are based on similar principles and consequently make similar predictions, (2) several models produce orientation map patterns that are not consistent with the experimental data from macaques, regardless of the plausibility of the models' suggested physiological implementations, and (3) no models have yet fully accounted for both the local and the global relationships between orientation and ocular dominance map patterns.

More than ten of the most prominent models for the structure and for the activity dependent formation of orientation and ocu(cid:173) lar dominance columns in the striate cort(>x have been evaluated. We implemented those models on parallel machines, we extensively explored parameter space, and we quantitatively compared model predictions with experimental data which were recorded optically from macaque striate cortex. In our contribution we present a summary of our results to date. Briefly, we find that (i) despite apparent differences, many models are based on similar principles and, consequently, make similar pre(cid:173) dictions, (ii) certain "pattern models" as well as the developmental "correlation-based learning" models disagree with the experimen(cid:173) tal data, and (iii) of the models we have investigated, "competitive Hebbian" models and the recent model of Swindale provide the best match with experimental data. 1 Models and Data The models for the formation and structure of orientation and ocular dominance columns which we have investigated are summarized in table 1. Models fall into two categories: "Pattern models" whose aim is to achieve a concise description of the observed patterns and "developmental models" which are focussed on the pro- 94 E. Erwin, K. Obermayer, K. Schulten Class Pattern Models Models

A discussion is presented of the properties of the model in the high-dimensional limit. The authors present results from a Monte Carlo simulation indicating a facilitation of the map-ordering process if the dimensionality of the input space is increased, and they provide a mathematical analysis of the development of localized receptive fields via the input-selection mechanism. The analytical results are compared with data from large-scale simulations using a Connection Machine CM-2, and very good agreement is found