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58
Regularization networks and support vector machines
 Advances in Computational Mathematics
, 2000
"... Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization a ..."
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Cited by 266 (33 self)
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Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization and Support Vector Machines. We review both formulations in the context of Vapnik’s theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics. The emphasis is on regression: classification is treated as a special case.
Reinforcement learning for humanoid robotics
 Autonomous Robot
, 2003
"... Abstract. The complexity of the kinematic and dynamic structure of humanoid robots make conventional analytical approaches to control increasingly unsuitable for such systems. Learning techniques offer a possible way to aid controller design if insufficient analytical knowledge is available, and lea ..."
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Cited by 91 (20 self)
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Abstract. The complexity of the kinematic and dynamic structure of humanoid robots make conventional analytical approaches to control increasingly unsuitable for such systems. Learning techniques offer a possible way to aid controller design if insufficient analytical knowledge is available, and learning approaches seem mandatory when humanoid systems are supposed to become completely autonomous. While recent research in neural networks and statistical learning has focused mostly on learning from finite data sets without stringent constraints on computational efficiency, learning for humanoid robots requires a different setting, characterized by the need for realtime learning performance from an essentially infinite stream of incrementally arriving data. This paper demonstrates how even highdimensional learning problems of this kind can successfully be dealt with by techniques from nonparametric regression and locally weighted learning. As an example, we describe the application of one of the most advanced of such algorithms, Locally Weighted Projection Regression (LWPR), to the online learning of three problems in humanoid motor control: the learning of inverse dynamics models for modelbased control, the learning of inverse kinematics of redundant manipulators, and the learning of oculomotor reflexes. All these examples demonstrate fast, i.e., within seconds or minutes, learning convergence with highly accurate final peformance. We conclude that realtime learning for complex motor system like humanoid robots is possible with appropriately tailored algorithms, such that increasingly autonomous robots with massive learning abilities should be achievable in the near future. 1.
Learning from one example through shared densities on transforms
 In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
, 2000
"... We define a process called congealing in which elements of a dataset (images) are brought into correspondence with each other jointly, producing a datadefined model. It is based upon minimizing the summed componentwise (pixelwise) entropies over a continuous set of transforms on the data. One of t ..."
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Cited by 90 (7 self)
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We define a process called congealing in which elements of a dataset (images) are brought into correspondence with each other jointly, producing a datadefined model. It is based upon minimizing the summed componentwise (pixelwise) entropies over a continuous set of transforms on the data. One of the biproducts of this minimization is a set of transforms, one associated with each original training sample. We then demonstrate a procedure for effectively bringing test data into correspondence with the datadefined model produced in the congealing process. Subsequently, we develop a probability density over the set of transforms that arose from the congealing process. We suggest that this density over transforms may be shared by many classes, and demonstrate how using this density as “prior knowledge ” can be used to develop a classifier based on only a single training example for each class. 1
Functionally independent components of the late positive eventrelated potential during visual spatial attention
 J. NEUROSCI
, 1999
"... Human eventrelated potentials (ERPs) were recorded from 10 subjects presented with visual target and nontarget stimuli at five screen locations and responding to targets presented at one of the locations. The late positive response complexes of 25–75 ERP average waveforms from the two task conditio ..."
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Cited by 53 (19 self)
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Human eventrelated potentials (ERPs) were recorded from 10 subjects presented with visual target and nontarget stimuli at five screen locations and responding to targets presented at one of the locations. The late positive response complexes of 25–75 ERP average waveforms from the two task conditions were simultaneously analyzed with Independent Component Analysis, a new computational method for blindly separating linearly mixed signals. Three spatially fixed, temporally independent, behaviorally relevant, and physiologically plausible components were identified without reference to peaks in singlechannel waveforms. A novel frontoparietal component (P3f) began at �140 msec and peaked, in faster responders, at the onset of the motor command. The scalp distribution of P3f appeared consistent with brain regions activated during spatial orienting in functional imaging experiments. A longerlatency
Stability analysis of adaptive blind source separation
 NEURAL NETWORKS
, 1997
"... Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principles and approaches are different, most of them have very similar forms. Two important issues have remained to be elucidated further: the statistical efficiency and the sta ..."
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Cited by 42 (13 self)
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Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principles and approaches are different, most of them have very similar forms. Two important issues have remained to be elucidated further: the statistical efficiency and the stability of learning algorithms. The present letter analyzes a general form of statistically efficient algorithm and give a necessary and sufficient condition for the separating solution to be a stable equilibrium of a general learning algorithm. Moreover, when the separating solution is unstable, a simple method is given for stabilizing the separating solution by modifying the algorithm.
Electroencephalographic Brain Dynamics Following Manually Responded Visual Targets
 PLOS BIOLOGY
, 2004
"... Scalprecorded electroencephalographic (EEG) signals produced by partial synchronization of cortical field activity mix locally synchronous electrical activities of many cortical areas. Analysis of eventrelated EEG signals typically assumes that poststimulus potentials emerge out of a flat baseline ..."
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Cited by 42 (16 self)
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Scalprecorded electroencephalographic (EEG) signals produced by partial synchronization of cortical field activity mix locally synchronous electrical activities of many cortical areas. Analysis of eventrelated EEG signals typically assumes that poststimulus potentials emerge out of a flat baseline. Signals associated with a particular type of cognitive event are then assessed by averaging data from each scalp channel across trials, producing averaged eventrelated potentials (ERPs). ERP averaging, however, filters out much of the information about cortical dynamics available in the unaveraged data trials. Here, we studied the dynamics of cortical electrical activity while subjects detected and manually responded to visual targets, viewing signals retained in ERP averages not as responses of an otherwise silent system but as resulting from eventrelated alterations in ongoing EEG processes. We applied infomax independent component analysis to parse the dynamics of the unaveraged 31channel EEG signals into maximally independent processes, then clustered the resulting processes across subjects by similarities in their scalp maps and activity power spectra, identifying nine classes of EEG processes with distinct spatial distributions and eventrelated dynamics. Coupled twocycle postmotor theta bursts followed button presses in frontal midline and somatomotor clusters, while the broad postmotor "P300" positivity summed distinct contributions from several classes of frontal, parietal, and occipital processes. The observed eventrelated changes in local field activities, within and between cortical areas, may
Incremental Natural ActorCritic Algorithms
"... We present four new reinforcement learning algorithms based on actorcritic and naturalgradient ideas, and provide their convergence proofs. Actorcritic reinforcement learning methods are online approximations to policy iteration in which the valuefunction parameters are estimated using temporal ..."
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Cited by 41 (3 self)
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We present four new reinforcement learning algorithms based on actorcritic and naturalgradient ideas, and provide their convergence proofs. Actorcritic reinforcement learning methods are online approximations to policy iteration in which the valuefunction parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their compatibility with function approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further reduce variance in some cases. Our results extend prior twotimescale convergence results for actorcritic methods by Konda and Tsitsiklis by using temporal difference learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actorcritic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms. 1
O.: Regularizing flows for constrained matrixvalued images
 J. Math. Imaging Vision
, 2004
"... Abstract. Nonlinear diffusion equations are now widely used to restore and enhance images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a differentialgeometric framework to define PDEs acting on some manifol ..."
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Cited by 36 (11 self)
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Abstract. Nonlinear diffusion equations are now widely used to restore and enhance images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a differentialgeometric framework to define PDEs acting on some manifold constrained datasets. We consider the case of images taking value into matrix manifolds defined by orthogonal and spectral constraints. We directly incorporate the geometry and natural metric of the underlying configuration space (viewed as a Lie group or a homogeneous space) in the design of the corresponding flows. Our numerical implementation relies on structurepreserving integrators that respect intrinsically the constraints geometry. The efficiency and versatility of this approach are illustrated through the anisotropic smoothing of diffusion tensor volumes in medical imaging. Note: This is the draft
Learning from One Example in Machine Vision by Sharing Probability Densities
, 2002
"... Human beings exhibit rapid learning when presented with a small number of images of a new object. A person can identify an object under a wide variety of visual conditions after having seen only a single example of that object. This ability can be partly explained by the application of previously le ..."
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Cited by 13 (1 self)
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Human beings exhibit rapid learning when presented with a small number of images of a new object. A person can identify an object under a wide variety of visual conditions after having seen only a single example of that object. This ability can be partly explained by the application of previously learned statistical knowledge to a new setting. This thesis presents an approach to acquiring knowledge in one setting and using it in another. Specifically, we develop probability densities over common image changes. Given a single image of a new object and a model of change learned from a di#erent object, we form a model of the new object that can be used for synthesis, classification, and other visual tasks. We start by
A contribution to (neuromorphic) blind deconvolution by flexible approximated Bayesian estimation
 Signal Processing
, 2001
"... 'Bussgang' deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequenc defined on the basis of channel/equalizer cascade model which involves the definition of deconvolution noise. In this paper we consider four `Bussgang' blind deconvolution a ..."
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Cited by 11 (11 self)
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'Bussgang' deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequenc defined on the basis of channel/equalizer cascade model which involves the definition of deconvolution noise. In this paper we consider four `Bussgang' blind deconvolution algorithms for uniformly distributed source signals and investigate their numeric, performance as well as some of their analytic features. Particularlz, we show...