Agakov System Engineering Research Group Chair of Manufacturing Technology Universitiit Erlangen-Niirnberg 91058 Erlangen, Germany F.Agakov@lft·uni-erlangen.de Stephen N. Felderhof Division of Informatics University of Edinburgh Edinburgh EH1 2QL, UK stephenf@dai.ed.ac.uk Abstract Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. Below weconsider PoE models in which each expert is a Gaussian. Although the product of Gaussians is also a Gaussian, if each Gaussian hasa simple structure the product can have a richer structure. We examine (1) Products of Gaussian pancakes which give rise to probabilistic Minor Components Analysis, (2) products of I-factor PPCA models and (3) a products of experts construction for an AR(l) process. Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data.

We give an unified convergence analysis of ensemble learning methods includinge.g. AdaBoost, Logistic Regression and the Least-Square- Boost algorithm for regression. These methods have in common that they iteratively call a base learning algorithm which returns hypotheses that are then linearly combined. We show that these methods are related to the Gauss-Southwell method known from numerical optimization and state non-asymptotical convergence results for all these methods. Our analysis includes -norm regularized cost functions leading to a clean and general way to regularize ensemble learning.

Although these two approaches are the most obvious, Allwein et al. [Allwein et a1., 2000]

Recent work has shown impressive transform-invariant modeling and clustering for sets of images of objects with similar appearance. We seek to expand these capabilities to sets of images of an object class that show considerable variation across individual instances (e.g.

We present a model of binding of relationship information in a spatial domain (e.g., square above triangle) that uses low-order coarse-coded conjunctive representations instead of more popular temporal synchrony mechanisms. Supporters of temporal synchrony argue that conjunctive representations lack both efficiency (i.e., combinatorial numbers of units are required) and systematicity (i.e., the resulting representations are overly specific and thus do not support generalization to novel exemplars). Tocounter these claims, we show that our model: a) uses far fewer hidden units than the number of conjunctions represented, by using coarse-coded,distributed representations where each unit has a broad tuning curve through high-dimensional conjunction space, and b) is capable ofconsiderable generalization to novel inputs.

We present a new multiple-instance (MI) learning technique (EM DD) that combines EM with the diverse density (DD) algorithm. EM-DD is a general-purpose MI algorithm that can be applied with boolean or real-value labels and makes real-value predictions. On the boolean Musk benchmarks, the EM-DD algorithm without any tuning significantly outperforms all previous algorithms. EM-DD is relatively insensitive to the number of relevant attributes in the data set and scales up well to large bag sizes. Furthermore, EM DD provides a new framework for MI learning, in which the MI problem is converted to a single-instance setting by using EM to estimate the instance responsible for the label of the bag. 1 Introduction The multiple-instance (MI) learning model has received much attention.

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly,we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification anddensity estimation with Gaussian processes and on an independent componentanalysis problem.

Population codes often rely on the tuning of the mean responses to the stimulus parameters. However, this information can be greatly suppressed bylong range correlations. Here we study the efficiency of coding information in the second order statistics of the population responses. We show that the Fisher Information of this system grows linearly with the size of the system. We propose a bilinear readout model for extracting informationfrom correlation codes, and evaluate its performance in discrimination and estimation tasks. It is shown that the main source of information in this system is the stimulus dependence of the variances of the single neuron responses.

Animal data on delayed-reward conditioning experiments shows a striking property - the data for different time intervals collapses into a single curve when the data is scaled by the time interval. This is called the scalar property of interval timing. Here a simple model of a neural clock is presented and shown to give rise to the scalar property. The model is an accumulator consisting of noisy, linear spiking neurons. It is analytically tractable and contains only three parameters.

We derive an equivalence between AdaBoost and the dual of a convex optimization problem, showing that the only difference between minimizing theexponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized toform a conditional probability distribution over labels. In addition to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets support our theoretical analysis andgive additional insight into the relationship between boosting and logistic regression.