We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as the multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of probability trees and random processes in the framework of Walley's theory. We indicate how our results can be used to reduce the computational complexity of dealing with imprecision in probability trees, and we prove an interesting and quite general version of the weak law of large numbers.

Most definitions of ontology, viewed as a "specification of a conceptualization", agree on the fact that if an ontology can take different forms, it necessarily includes a vocabulary of terms and some specification of their meaning in relation to the domain's conceptualization. And as domain knowledge is mainly conveyed through scientific and technical texts, we can hope to extract some useful information from them for building ontology. But is it as simple as this? In this article we shall see that the lexical structure, i.e. the network of words linked by linguistic relationships, does not necessarily match the domain conceptualization. We have to bear in mind that writing documents is the concern of textual linguistics, of which one of the principles is the incompleteness of text, whereas building ontology - viewed as task-independent knowledge - is concerned with conceptualization based on formal and not natural languages. Nevertheless, the famous Sapir and Whorf hypothesis, concerning the interdependence of thought and language, is also applicable to formal languages. This means that the way an ontology is built and a concept is defined depends directly on the formal language which is used; and the results will not be the same. The introduction of the notion of ontoterminology allows to take into account epistemological principles for formal ontology building.

Institut de Mathématiques, Université de Toulouse et CNRS (UMR 5219), 118 route de Narbonne, 31062 Toulouse cedex 9, France Abstract Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts. This work was partially supported by ANR Project "Graph-Comp". Preprint submitted to Neurocomputing 19 March 2018 1 Introduction Complex networks are large graphs with a non trivial organization. They arise naturally in numerous context [7], such as, to name a few, the World Wide Web (which gives a perfect example of how large and complex such a network may grow), metabolic pathways, citation networks between scientific articles or more general social networks that model interaction between individuals and/or organizations, etc. Complex networks share common properties that have allowed the emergence of mathematical descriptions such as small world graphs or power law graphs. The structure of these graphs often gives some keys to understand the complex network underlined. To study such a structure, one often begins with a metrology process applied to the graph that describes the degree distribution, the number of components, the density, etc. However, it should be noted that dealing with very large graphs (millions of vertices) is still an open question (see [9] for an example of an efficient algorithm to explore that kind of data sets). Several ways have been explored to cluster the vertices of the graph into communities [43] and some of them have in common the use of the Laplacian matrix. Indeed, there are important relationships between the spectrum of the Laplacian and the graph invariants that characterize its structure (see, e.g. These properties can be used for building, from the eigen-decomposition of the Laplacian, a similarity measure or a metric space such that the induced dissimilarities between vertices of the graph are related to its community structure (see [13], among others).

We propose a generic algorithm for computation of similarity measures for sequential data. The algorithm uses generalized suffix trees for efficient calculation of various kernel, distance and non-metric similarity functions. Its worst-case run-time is linear in the length of sequences and independent of the underlying embedding language, which can cover words, k-grams or all contained subsequences. Experiments with network intrusion detection, DNA analysis and text processing applications demonstrate the utility of distances and similarity coefficients for sequences as alternatives to classical kernel functions.

Multinomial logistic regression provides the standard penalised maximumlikelihood solution to multi-class pattern recognition problems. More recently, the development of sparse multinomial logistic regression models has found application in text processing and microarray classification, where explicit identification of the most informative features is of value. In this paper, we propose a sparse multinomial logistic regression method, in which the sparsity arises from the use of a Laplace prior, but where the usual regularisation parameter is integrated out analytically. Evaluation over a range of benchmark datasets reveals this approach results in similar generalisation performance to that obtained using cross-validation, but at greatly reduced computational expense.

Many recent studies analyze how data from different modalities can be combined. Often this is modeled as a system that optimally combines several sources of information about the same variable. However, it has long been realized that this information combining depends on the interpretation of the data. Two cues that are perceived by different modalities can have different causal relationships: (1) They can both have the same cause, in this case we should fully integrate both cues into a joint estimate.

Gaussian data is pervasive and many learning algorithms (e.g., k-means) model their inputs as a single sample drawn from a multivariate Gaussian. However, in many real-life settings, each input object is best described by multiple samples drawn from a multivariate Gaussian. Such data can arise, for example, in a movie review database where each movie is rated by several users, or in time-series domains such as sensor networks. Here, each input can be naturally described by both a mean vector and covariance matrix which parameterize the Gaussian distribution. In this paper, we consider the problem of clustering such input objects, each represented as a multivariate Gaussian. We formulate the problem using an information theoretic approach and draw several interesting theoretical connections to Bregman divergences and also Bregman matrix divergences. We evaluate our method across several domains, including synthetic data, sensor network data, and a statistical debugging application.

We present a method for binary online classification of triggered but temporally blurred events that are embedded in noisy time series in the context of online discrimination between left and right imaginary hand-movement. In particular the goal of the binary classification problem is to obtain the decision, as fast and as reliably as possible from the recorded EEG single trials. To provide a probabilistic decision at every time-point t the presented method gathers information from two distinct sequences of features across time. In order to incorporate decisions from prior time-points we suggest an appropriate weighting scheme, that emphasizes time instances, providing a higher discriminatory power between the instantaneous class distributions of each feature, where the discriminatory power is quantified in terms of the Bayes error of misclassification. The effectiveness of this procedure is verified by its successful application in the 3rd BCI competition. Disclosure of the data after the competition revealed this approach to be superior with single trial error rates as low as 10.7, 11.5 and 16.7% for the three different subjects under study.

The additive clustering model is widely used to infer the features of a set of stimuli from their similarities, on the assumption that similarity is a weighted linear function of common features. This paper develops a fully Bayesian formulation of the additive clustering model, using methods from nonparametric Bayesian statistics to allow the number of features to vary. We use this to explore several approaches to parameter estimation, showing that the nonparametric Bayesian approach provides a straightforward way to obtain estimates of both the number of features used in producing similarity judgments and their importance.