We present a probabilistic latent-variable framework for data visualisation, a key feature of which is its applicability to binary and categorical data types for which few established methods exist. A variational approximation to the likelihood is exploited to derive a fast algorithm for determining the model parameters. Illustrations of application to real and synthetic binary data sets are given.

We will also introduce a regularization strategy (analogous to weight decay) into boosting. This strategy uses slack variables to achieve a soft margin (section 4). Numerical experiments show the validity of our regularization approach in section 5 and finally a brief conclusion is given. 2 AdaBoost Algorithm Let {ht(x): t 1,...,T} be an ensemble of T hypotheses defined on input vector x and e

Even if the underlying phenomena are inherently deterministic, the complexity of these phenomena often makes a probabilistic formulation the only feasible approach from the computational point of view. Although quantities such as the mean, the variance, and possibly higher order moments of a random variable have often been sufficient to characterize a particular problem, the quest for higher modeling accuracy, and for more realistic assumptions drives us towards modeling the available random variables using their probability density. This of course leads us to the problem of density estimation (see [6]). The most common approach for density estimation is the nonparametric approach, where the density is determined according to a formula involving the data points available. The most common non parametric methods are the kernel density estimator, also known as the Parzen window estimator [4] and the k-nearest neighbor technique [1].

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

We present the CEM (Conditional Expectation Maximi::ation) algorithm as an extension of the EM (Expectation M aximi::ation) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to specifically optimize conditional likelihood instead of the usual joint likelihood. We apply the method to conditioned mixture models and use bounding techniques to derive the model's update rules. Monotonic convergence, computational efficiency and regression results superior to EM are demonstrated.

Dyadzc data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This type of data arises naturally in many application ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework of learning from dyadic data by statistical mixture models. Our approach covers different models with fiat and hierarchical latent class structures. We propose an annealed version of the standard EM algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains. 1 Introduction Over the past decade learning from data has become a highly active field of research distributed over many disciplines like pattern recognition, neural computation, statistics, machine learning, and data mining.

This paper reveals a previously ignored connection between two important fields: regularization and independent component analysis (ICA). We show that at least one representative of a broad class of algorithms (regularizers that reduce network complexity) extracts independent features as a byproduct. This algorithm is Flat Minimum Search (FMS), a recent general method for finding low-complexity networks with high generalization capability. FMS works by minimizing both training error and required weight precision. According to our theoretical analysis the hidden layer of an FMS-trained autoassociator attempts at coding each input by a sparse code with as few simple features as possible.

Cluster analysis is a fundamental principle in exploratory data analysis, providing the user with a description of the group structure of given data. A key problem in this context is the interpretation and visualization of clustering solutions in high-dimensional or abstract data spaces. In particular, probabilistic descriptions of the group structure, essential to capture inter-cluster relationships, are hardly assessable by simple inspection ofthe probabilistic assignment variables. VVe present a novel approach to the visualization of group structure. It is based on a statistical model of the object assignments which have been observed or estimated by a probabilistic clustering procedure. The objects or data points are embedded in a low dimensional Euclidean space by approximating the observed data statistics with a Gaussian mixture model. The algorithm provides a new approach to the visualization of the inherent structure for a broad variety of data types, e.g.

The Expectation-Maximization (EM) algorithm is an iterative procedure for maximum likelihood parameter estimation from data sets with missing or hidden variables [2]. It has been applied to system identification in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simultaneously [9]. We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The "expectation" step makes use of Extended Kalman Smoothing to estimate the state, while the "maximization" step re-estimates the parameters using these uncertain state estimates. In general, the nonlinear maximization step is difficult because it requires integrating out the uncertainty in the states.

We present a stochastic clustering algorithm based on pairwise similarity of datapoints. Our method extends existing deterministic methods, including agglomerative algorithms, min-cut graph algorithms, and connected components. Thus it provides a common framework for all these methods. Our graph-based method differs from existing stochastic methods which are based on analogy to physical systems. The stochastic nature of our method makes it more robust against noise, including accidental edges and small spurious clusters. We demonstrate the superiority of our algorithm using an example with 3 spiraling bands and a lot of noise. 1 Introduction Clustering algorithms can be divided into two categories: those that require a vectorial representation of the data, and those which use only pairwise representation. In the former case, every data item must be represented as a vector in a real normed space, while in the second case only pairwise relations of similarity or dissimilarity are used.