The problem that we address in this paper is how a mobile robot can plan in order to arrive at its goal with minimum uncertainty. Traditional motion planning algorithms often assume that a mobile robot can track its position reliably, however, in real world situations, reliable localization may not always be feasible. Partially Observable Markov Decision Processes (POMDPs) provide one way to maximize the certainty of reaching the goal state, but at the cost of computational intractability for large state spaces. The method we propose explicitly models the uncertainty of the robot's position as a state variable, and generates trajectories through the augmented pose-uncertainty space. By minimizing the positional uncertainty at the goal, the robot reduces the likelihood it becomes lost. We demonstrate experimentally that coastal navigation reduces the uncertainty at the goal, especially with degraded localization.

Gaussian mixtures (or so-called radial basis function networks) for density estimation provide a natural counterpart to sigmoidal neural networks for function fitting and approximation. In both cases, it is possible to give simple expressions for the iterative improvement of performance as components of the network are introduced one at a time. In particular, for mixture density estimation we show that a k-component mixture estimated by maximum likelihood (or by an iterative likelihood improvement that we introduce) achieves log-likelihood within order 1/k of the log-likelihood achievable by any convex combination. Consequences for approximation and estimation using Kullback-Leibler risk are also given. A Minimum Description Length principle selects the optimal number of components k that minimizes the risk bound. 1 Introduction In density estimation, Gaussian mixtures provide flexible-basis representations for densities that can be used to model heterogeneous data in high dimensions. Consider a parametric family G { pe(x), x E X C Rd': fJ E The main theme of the paper is to give approximation and estimation bounds of arbitrary densities by finite mixture densities.

The Karush-Kuhn-Tucker Theorem is used to derive conditions for determining whether or not a given working set is optimal. These conditions become the algorithm)s termination criteria) as an alternative to Osuna)s criteria (also used by Joachims without modification) which used conditions for individual points. The advantage of the new conditions is that knowledge of the hyperplane)s constant factor b) which in some cases is difficult to compute) is not required. Further investigation of the new termination conditions allows to form the strategy for selecting an optimal working set. The new algorithm is applicable to the pattern recognition SVM) and is provably equivalent to Joachims) algorithm. One can also interpret the new algorithm in the sense of the method of feasible directions. Experimental results presented in the last section demonstrate superior performance of the new method in comparison with traditional training of regression SVM. 2 General Principles of Regression SVM Decomposition The original decomposition algorithm proposed for the pattern recognition SVM in [2] has been extended to the regression SVM in [4]. For the sake of completeness I will repeat the main steps of this extension with the aim of providing terse and streamlined notation to lay the ground for working set selection.

In this paper we discuss the semi parametric statistical model for blind deconvolution. First we introduce a Lie Group to the manifold of noncausal FIR filters. 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 algorithm is developed for training noncausal filters. Stability of the natural gradient algorithm is also analyzed in this framework.

In hyperspectral imagery one pixel typically consists of a mixture of the reflectance spectra of several materials, where the mixture coefficients correspond to the abundances of the constituting materials. We assume linear combinations of reflectance spectra with some additive normal sensor noise and derive a probabilistic MAP framework for analyzing hyperspectral data. As the material reflectance characteristics are not know a priori, we face the problem of unsupervised linear unmixing.

We describe a method for learning an overcomplete set of basis functions for the purpose of modeling sparse structure in images. The sparsity of the basis function coefficients is modeled with a mixture-of-Gaussians distribution. One Gaussian captures nonactive coefficients with a small-variance distribution centered at zero, while one or more other Gaussians capture active coefficients with a large-variance distribution. We show that when the prior is in such a form, there exist efficient methods for learning the basis functions as well as the parameters of the prior. The performance of the algorithm is demonstrated on a number of test cases and also on natural images.

The neocortex is characterized by an extensive system of recurrent excitatory connections between neurons in a given area. The precise computational function of this massive recurrent excitation remains unknown. Previous modeling studies have suggested a role for excitatory feedback in amplifying feedforward inputs [1]. Recently, however, it has been shown that recurrent excitatory connections between cortical neurons are modified according to a temporally asymmetric Hebbian learning rule: synapses that are activated slightly before the cell fires are strengthened whereas those that are activated slightly after are weakened [2, 3]. Information regarding the postsynaptic activity of the cell is conveyed back to the dendritic locations of synapses by back-propagating action potentials from the soma.

We examine a psychophysical law that describes the influence of stimulus and context on perception. According to this law choice probability ratios factorize into components independently controlled by stimulus and context. It has been argued that this pattern of results is incompatible with feedback models of perception. In this paper we examine this claim using neural network models defined via stochastic differential equations. We show that the law is related to a condition named channel separability and has little to do with the existence of feedback connections. In essence, channels are separable if they converge into the response units without direct lateral connections to other channels and if their sensors are not directly contaminated by external inputs to the other channels. Implications of the analysis for cognitive and computational neurosicence are discussed.

Psychophysical and physiological evidence shows that sound localization of acoustic signals is strongly influenced by their synchrony with visual signals. This effect, known as ventriloquism, is at work when sound coming from the side of a TV set feels as if it were coming from the mouth of the actors. The ventriloquism effect suggests that there is important information about sound location encoded in the synchrony between the audio and video signals. In spite of this evidence, audiovisual synchrony is rarely used as a source of information in computer vision tasks. In this paper we explore the use of audio visual synchrony to locate sound sources. We developed a system that searches for regions of the visual landscape that correlate highly with the acoustic signals and tags them as likely to contain an acoustic source.

We propose a new and efficient technique for incorporating contextual information into object classification. Most of the current techniques face the problem of exponential computation cost. In this paper, we propose a new general framework that incorporates partial context at a linear cost. This technique is applied to microscopic urinalysis image recognition, resulting in a significant improvement of recognition rate over the context free approach. This gain would have been impossible using conventional context incorporation techniques.