The project pursued in this paper is to develop from first information-geometric principles a general method for learning the similarity between text documents. Each individual document is modeled as a memoryless information source. Based on a latent class decomposition of the term-document matrix, a lowdimensional (curved) multinomial subfamily is learned. From this model a canonical similarity function - known as the Fisher kernel - is derived. Our approach can be applied for unsupervised and supervised learning problems alike.

We first show how to represent sharp posterior probability distributions using real valued coefficients on broadly-tuned basis functions. Then we show how the precise times of spikes can be used to convey the real-valued coefficients on the basis functions quickly and accurately. Finally we describe a simple simulation in which spiking neurons learn to model an image sequence by fitting a dynamic generative model. 1 Population codes and energy landscapes A perceived object is represented in the brain by the activities of many neurons, but there is no general consensus on how the activities of individual neurons combine to represent the multiple properties of an object. We start by focussing on the case of a single object that has multiple instantiation parameters such as position, velocity, size and orientation. We assume that each neuron has an ideal stimulus in the space of instantiation parameters and that its activation rate or probability of activation falls off monotonically in all directions as the actual stimulus departs from this ideal.

Virtual reality (VR) provides immersive and controllable experimental environments. It expands the bounds of possible evoked potential (EP) experiments by providing complex, dynamic environments in order to study cognition without sacrificing environmental control.

Stochastic fluctuations of voltage-gated ion channels generate current and voltage noise in neuronal membranes. This noise may be a critical determinant of the efficacy of information processing within neural systems. Using Monte-Carlo simulations, we carry out a systematic investigation of the 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) also lead 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 with a neuron's ability to function as an integrator of its synaptic inputs and may limit the reliability and precision of neural information processing.

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 is consistent 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.

The nonnegative Boltzmann machine (NNBM) is a recurrent neural network model that can describe multimodal nonnegative data. Application of maximum likelihood estimation to this model gives a learning rule that is analogous to the binary Boltzmann machine. We examine the utility of the mean field approximation for the NNBM, and describe how Monte Carlo sampling techniques can be used to learn its parameters. Reflective slice sampling is particularly well-suited for this distribution, and can efficiently be implemented to sample the distribution. We illustrate learning of the NNBM on a transiationally invariant distribution, as well as on a generative model for images of human faces. Introduction The multivariate Gaussian is the most elementary distribution used to model generic data. It represents the maximum entropy distribution under the constraint that the mean and covariance matrix of the distribution match that of the data. For the case of binary data, the maximum entropy distribution that matches the first and second order statistics of the data is given by the Boltzmann machine [1].

A new method for multivariate density estimation is developed based on the Support Vector Method (SVM) solution of inverse ill-posed problems. The solution has the form of a mixture of densities. This method with Gaussian kernels compared favorably to both Parzen's method and the Gaussian Mixture Model method. For synthetic data we achieve more accurate estimates for densities of 2, 6, 12, and 40 dimensions. 1 Introduction The problem of multivariate density estimation is important for many applications, in particular, for speech recognition [1] [7]. When the unknown density belongs to a parametric set satisfying certain conditions one can estimate it using the maximum likelihood (ML) method. Often these conditions are too restrictive. Therefore, nonparametric methods were proposed. The most popular of these, Parzen's method [5], uses the following estimate given data

Transduction is an inference principle that takes a training sample and aims at estimating the values of a function at given points contained in the so-called working sample as opposed to the whole of input space for induction. Transduction provides a confidence measure on single predictions rather than classifiers - a feature particularly important for risk-sensitive applications. The possibly infinite number of functions is reduced to a finite number of equivalence classes on the working sample. A rigorous Bayesian analysis reveals that for standard classification loss we cannot benefit from considering more than one test point at a time. The probability of the label of a given test point is determined as the posterior measure of the corresponding subset of hypothesis space. We consider the PAC setting of binary classification by linear discriminant functions (perceptrons) in kernel space such that the probability of labels is determined by the volume ratio in version space. We suggest to sample this region by an ergodic billiard. Experimental results on real world data indicate that Bayesian Transduction compares favourably to the well-known Support Vector Machine, in particular if the posterior probability of labellings is used as a confidence measure to exclude test points of low confidence.

The psychophysical evidence for "selective attention" originates mainly from visual search experiments. In this work, we formulate a hierarchical system of interconnected modules consisting in populations of neurons for modeling the underlying mechanisms involved in selective visual attention. We demonstrate that our neural system for visual search works across the visual field in parallel but due to the different intrinsic dynamics can show the two experimentally observed modes of visual attention, namely: the serial and the parallel search mode. In other words, neither explicit model of a focus of attention nor saliencies maps are used. The focus of attention appears as an emergent property of the dynamic behavior of the system. The neural population dynamics are handled in the framework of the mean-field approximation. Consequently, the whole process can be expressed as a system of coupled differential equations.

In this article we study the effects of introducing structure in the input distribution of the data to be learnt by a simple perceptron. We determine the learning curves within the framework of Statistical Mechanics. Stepwise generalization occurs as a function of the number of examples when the distribution of patterns is highly anisotropic. Although extremely simple, the model seems to capture the relevant features of a class of Support Vector Machines which was recently shown to present this behavior.