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 Statistical Learning


Agnostic Classification of Markovian Sequences

Neural Information Processing Systems

Classification of finite sequences without explicit knowledge of their statistical nature is a fundamental problem with many important applications. We propose a new information theoretic approach to this problem which is based on the following ingredients: (i) sequences aresimilar when they are likely to be generated by the same source; (ii) cross entropies can be estimated via "universal compression"; (iii)Markovian sequences can be asymptotically-optimally merged. With these ingredients we design a method for the classification of discrete sequences whenever they can be compressed. We introduce the method and illustrate its application for hierarchical clustering of languages and for estimating similarities of protein sequences.



Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

Journal of Artificial Intelligence Research

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications.


Text-Based Information Retrieval Using Exponentiated Gradient Descent

Neural Information Processing Systems

The following investigates the use of single-neuron learning algorithms to improve the performance of text-retrieval systems that accept natural-language queries. A retrieval process is explained that transforms the natural-language query into the query syntax of a real retrieval system: the initial query is expanded using statistical and learning techniques and is then used for document ranking and binary classification. The results of experiments suggest that Kivinen and Warmuth's Exponentiated Gradient Descent learning algorithm works significantly better than previous approaches. 1 Introduction The following work explores two learning algorithms - Least Mean Squared (LMS) [1] and Exponentiated Gradient Descent (EG) [2] - in the context of text-based Information Retrieval (IR) systems. The experiments presented in [3] use connectionist to improve the retrieval of relevant documents from a largelearning models collection of text. Previous the area employs various techniques for improving retrieval [6, 7, 14].


One-unit Learning Rules for Independent Component Analysis

Neural Information Processing Systems

Neural one-unit learning rules for the problem of Independent Component Analysis (ICA) and blind source separation are introduced. In these new algorithms, every ICA neuron develops into a separator that finds one of the independent components. The learning rules use very simple constrained Hebbianjanti-Hebbian learning in which decorrelating feedback may be added. To speed up the convergence of these stochastic gradient descent rules, a novel computationally efficient fixed-point algorithm is introduced. 1 Introduction Independent Component Analysis (ICA) (Comon, 1994; Jutten and Herault, 1991) is a signal processing technique whose goal is to express a set of random variables as linear combinations of statistically independent component variables. The main applications of ICA are in blind source separation, feature extraction, and blind deconvolution.


Combinations of Weak Classifiers

Neural Information Processing Systems

To obtain classification systems with both good generalization performance and efficiency in space and time, we propose a learning method based on combinations of weak classifiers, where weak classifiers are linear classifiers (perceptrons) which can do a little better than making random guesses. A randomized algorithm is proposed to find the weak classifiers. Theyยท are then combined through a majority vote. As demonstrated through systematic experiments, the method developed is able to obtain combinations of weak classifiers with good generalization performance and a fast training time on a variety of test problems and real applications.


On a Modification to the Mean Field EM Algorithm in Factorial Learning

Neural Information Processing Systems

A modification is described to the use of mean field approximations in the E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. The modification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models.


Limitations of Self-organizing Maps for Vector Quantization and Multidimensional Scaling

Neural Information Processing Systems

SaM can be said to do clustering/vector quantization (VQ) and at the same time to preserve the spatial ordering of the input data reflected by an ordering of the code book vectors (cluster centroids) in a one or two dimensional output space, where the latter property is closely related to multidimensional scaling (MDS) in statistics. Although the level of activity and research around the SaM algorithm is quite large (a recent overview by [Kohonen 95] contains more than 1000 citations), only little comparison among the numerous existing variants of the basic approach and also to more traditional statistical techniques of the larger frameworks of VQ and MDS is available. Additionally, there is only little advice in the literature about how to properly use 446 A. Flexer SOM in order to get optimal results in terms of either vector quantization (VQ) or multidimensional scaling or maybe even both of them. To make the notion of SOM being a tool for "data visualization" more precise, the following question has to be answered: Should SOM be used for doing VQ, MDS, both at the same time or none of them? Two recent comprehensive studies comparing SOM either to traditional VQ or MDS techniques separately seem to indicate that SOM is not competitive when used for either VQ or MDS: [Balakrishnan et al. 94J compare SOM to K-means clustering on 108 multivariate normal clustering problems with known clustering solutions and show that SOM performs significantly worse in terms of data points misclassified


Learning Appearance Based Models: Mixtures of Second Moment Experts

Neural Information Processing Systems

This paper describes a new technique for object recognition based on learning appearance models. The image is decomposed into local regions which are described by a new texture representation called "Generalized Second Moments" that are derived from the output of multiscale, multiorientation filter banks. Class-characteristic local texture features and their global composition is learned by a hierarchical mixture of experts architecture (Jordan & Jacobs). The technique is applied to a vehicle database consisting of 5 general car categories (Sedan, Van with backdoors, Van without backdoors, old Sedan, and Volkswagen Bug). This is a difficult problem with considerable in-class variation.


A Constructive RBF Network for Writer Adaptation

Neural Information Processing Systems

This paper discusses a fairly general adaptation algorithm which augments a standard neural network to increase its recognition accuracy for a specific user. The basis for the algorithm is that the output of a neural network is characteristic of the input, even when the output is incorrect. We exploit this characteristic output by using an Output Adaptation Module (OAM) which maps this output into the correct user-dependent confidence vector. The OAM is a simplified Resource Allocating Network which constructs radial basis functions online. We applied the OAM to construct a writer-adaptive character recognition system for online handprinted characters.