We show that the recently proposed variant of the Support Vector machine (SVM) algorithm, known as v-SVM, can be interpreted as a maximal separation between subsets of the convex hulls of the data, which we call soft convex hulls. The soft convex hulls are controlled by choice of the parameter v. The proposed geometric interpretation of v-SVM also leads to necessary and sufficient conditions for the existence of a choice of v for which the v-SVM solution is nontrivial. 1 Introduction Recently, SchOlkopf et al. [I) introduced a new class of SVM algorithms, called v-SVM, for both regression estimation and pattern recognition. The basic idea is to remove the user-chosen error penalty factor C that appears in SVM algorithms by introducing a new variable p which, in the pattern recognition case, adds another degree of freedom to the margin. For a given normal to the separating hyperplane, the size of the margin increases linearly with p.

However, most models have simply ignored these data; the few that have attempted toaddress them have failed by at least an order of magnitude. We discuss key data on the speed of acquisition, and show how to account for them using a statistically sound model of learning, in which differential reliabilities of stimuli playa crucial role. 1 Introduction Conditioning experiments probe the ways that animals make predictions about rewards and punishments and how those predictions are used to their advantage. Substantial quantitative data are available as to how pigeons and rats acquire conditioned responsesduring autoshaping, which is one of the simplest paradigms of classical conditioning.

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributionsof feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hiddenclass labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihoodestimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting various objects inSAR images and target recognition in optical aerial images. 1 Introduction

We introduce a novel method of constructing language models, which avoids some of the problems associated with recurrent neural networks.The method of creating a Prediction Fractal Machine (PFM) [1] is briefly described and some experiments are presented which demonstrate the suitability of PFMs for language modeling. PFMs distinguish reliably between minimal pairs, and their behavior isconsistent with the hypothesis [4] that wellformedness is'graded' not absolute. A discussion of their potential to offer fresh insights into language acquisition and processing follows. 1 Introduction Cognitive linguistics has seen the development in recent years of two important, related trends.

In this paper we discuss the semiparametric statistical model for blind deconvolution. First we introduce a Lie Group to the manifold of noncausal FIRfilters. Then blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is derived for blind deconvolution. A natural gradient learning algorithmis developed for training noncausal filters. Stability of the natural gradient algorithm is also analyzed in this framework.

We describe an iterative algorithm for building vector machines used in classification tasks. The algorithm builds on ideas from support vector machines, boosting, and generalized additive models.

Imagine that you wish to classify data consisting of tens of thousands of examples residingin a twenty thousand dimensional space. How can one apply standard machine learning algorithms? We describe the Parallel Problems Server(PPServer) and MATLAB*P.

When a visual image consists of a figure against a background, V1 cells are physiologically observed to give higher responses to image regions corresponding to the figure relative to their responses to the background. The medial axis of the figure also induces relatively higherresponses compared to responses to other locations in the figure (except for the boundary between the figure and the background). Since the receptive fields of V1 cells are very small comparedwith the global scale of the figure-ground and medial axis effects, it has been suggested that these effects may be caused by feedback from higher visual areas. I show how these effects can be accounted for by V1 mechanisms when the size of the figure is small or is of a certain scale. They are a manifestation of the processes of pre-attentive segmentation which detect and highlight the boundaries between homogeneous image regions. 1 Introduction Segmenting figure from ground is one of the most important visual tasks.

Stochastic fluctuations of voltage-gated ion channels generate current and voltage noise in neuronal membranes. This noise may be a critical determinantof the efficacy of information processing within neural systems. Using Monte-Carlo simulations, we carry out a systematic investigation ofthe relationship between channel kinetics and the resulting membrane voltage noise using a stochastic Markov version of the Mainen-Sejnowski model of dendritic excitability in cortical neurons. Our simulations show that kinetic parameters which lead to an increase in membrane excitability (increasing channel densities, decreasing temperature) alsolead to an increase in the magnitude of the sub-threshold voltage noise. Noise also increases as the membrane is depolarized from rest towards threshold. This suggests that channel fluctuations may interfere witha neuron's ability to function as an integrator of its synaptic inputs and may limit the reliability and precision of neural information processing.

A novel learning approach for human face detection using a network of linear units is presented. The SNoW learning architecture is a sparse network of linear functions over a predefined or incrementally learnedfeature space and is specifically tailored for learning in the presence of a very large number of features. A wide range of face images in different poses, with different expressions and under different lighting conditions are used as a training set to capture the variations of human faces. Experimental results on commonly used benchmark data sets of a wide range of face images show that the SNoW-based approach outperforms methods that use neural networks, Bayesian methods, support vector machines and others. Furthermore,learning and evaluation using the SNoW-based method are significantly more efficient than with other methods. 1 Introduction Growing interest in intelligent human computer interactions has motivated a recent surge in research on problems such as face tracking, pose estimation, face expression and gesture recognition. Most methods, however, assume human faces in their input images have been detected and localized.