Véronique Ventos

Towards Learning in CARIN-ALN

In this paper we investigate a new language for learning, which combines two well-known representation formalisms, Description Logics and Horn Clause Logics. Our goal is to study the feasability of learning in such a hybrid description - horn clause language, namely CARIN-ALN [LR98b], in the presence of hybrid background knowledge, including a Horn clause and a terminological component. After setting our learning framework, we present algorithms for testing example coverage and subsumption between two hypotheses, based on the existential entailment algorithm studied in[LR98b]. While the hybrid language is more expressive than horn clause logics alone, the complexity of these two steps for CARIN-ALN remains bounded by their respective complexity in horn clause logics.

ZooM: a nested Galois lattices-based system for conceptual clustering

This paper deals with the representation of multi-valued data by clustering them in a small number of classes organized in a hierarchy and described at an appropriate level of abstraction. The contribution of this paper is three fold. First, we investigate a partial order, namely nesting, relating Galois lattices. A nested Galois lattice is obtained by reducing (through projections) the original lattice. As a consequence it makes coarser the equivalence relations defined on extents and intents. Second we investigate the intensional and extensional aspects of the languages used in our system ZooM. In particular we discuss the notion of α-extension of terms of a class language £. We also present our most expressive language £3, close to a description logic, and which expresses optionality or/and multi-valuation of attributes. Finally, the nesting order between the Galois lattices corresponding to various languages and extensions is exploited in the interactive system ZooM. Typically a ZooM session starts from a propositional language £2 and a coarse view of the data (through α-extension). Then the user selects two ordered nodes in the lattice and ZooM constructs a fine-grained lattice between the antecedents of these nodes. So the general purpose of ZooM is to give a general view of concepts addressing a large data set, then focussing on part of this coarse taxonomy.

Alpha galois lattices: an overview

What we propose here is to reduce the size of Galois lattices still conserving their formal structure and exhaustivity. For that purpose we use a preliminary partition of the instance set, representing the association of a “type” to each instance. By redefining the notion of extent of a term in order to cope, to a certain degree (denoted as α), with this partition, we define a particular family of Galois lattices denoted as Alpha Galois lattices. We also discuss the related implication rules defined as inclusion of such α-extents and show that Iceberg concept lattices are Alpha Galois lattices where the partition is reduced to one single class.

Abstract concept lattices

We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties.

Incremental construction of alpha lattices and association rules

In this paper we discuss Alpha Galois lattices (Alpha lattices for short) and the corresponding association rules. An alpha lattice is coarser than the related concept lattice and so contains fewer nodes, so fewer closed patterns, and a smaller basis of association rules. Coarseness depends on a a priori classification, i.e. a cover C of the powerset of the instance set I, and on a granularity parameter α. In this paper, we define and experiment a Merge operator that when applied to two Alpha lattices G(C1, α) and G(C2, α) generates the Alpha lattice G(C1∪C2, α), so leading to a class-incremental construction of Alpha lattices. We then briefly discuss the implementation of the incremental process and describe the min-max bases of association rules extracted from Alpha lattices.

Bijections between affine hyperplane arrangements and valued graphs

We show new bijective proofs of previously known formulas for the number of regions of some deformations of the braid arrangement, by means of a bijection between the no-broken-circuit sets of the corresponding integral gain graphs and some kinds of labelled binary trees. This leads to new bijective proofs for the Shi, Catalan, and similar hyperplane arrangements.

Automatic Construction and Refinement of a Class Hierarchy over Multi-valued Data

In many applications, it becomes crucial to help users to access to a huge amount of data by clustering them in a small number of classes described at an appropriate level of abstraction. In this paper, we present an approach based on the use of two languages of description of classes for the automatic clustering of multi-valued data. The first language of classes has a high power of abstraction and guides the construction of a lattice of classes covering the whole set of the data. The second language, more expressive and more precise, is the basis for the refinement of a part of the lattice that the user wants to focus on.

Concept Learning from (Very) Ambiguous Examples

We investigate here concept learning from incomplete examples, denoted here as ambiguous . We start from the learning from interpretations setting introduced by L. De Raedt and then follow the informal ideas presented by H. Hirsh to extend the Version space paradigm to incomplete data: a hypothesis has to be compatible with all pieces of information provided regarding the examples. We propose and experiment an algorithm that given a set of ambiguous examples, learn a concept as an existential monotone DNF. We show that 1) boolean concepts can be learned, even with very high incompleteness level as long as enough information is provided, and 2) monotone, non monotone DNF (i.e. including negative literals), and attribute-value hypotheses can be learned that way, using an appropriate background knowledge. We also show that a clever implementation, based on a multi-table representation is necessary to apply the method with high levels of incompleteness.

Les treillis de Galois Alpha

Our basic representation of the data is a Galois lattice, i.e. a lattice in which the terms of a representation language are partitioned into equivalence classes w.r.t. their extent (the extent of a term is the part of the instance set that satisfies the term). We propose here to simplify our view of the data, still conserving the Galois lattice formal structure. For that purpose we use a preliminary partition of the instance set, representing the association of a type to each instance. By redefining the notion of extent of a term in order to cope, to a certain degree (denoted as a), with this partition, we define a particular family of Galois lattices denoted as Alpha Galois lattices.

The Game of Bridge: A Challenge for ILP.

Designs of champion-level systems dedicated to a game have been considered as milestones for Artificial Intelligence. Such a success has not yet happened for the game of Bridge because (i) Bridge is a partially observable game (ii) a Bridge player must be able to explain at some point the meaning of his actions to his opponents. This paper presents a simple supervised learning problem in Bridge: given a ‘limit hand’, should a player bid or not, only considering his hand and the context of his decision. We describe this problem and some of its candidate modelisations. We then experiment state of the art propositional machine learning and ILP systems on this problem. Results of these preliminary experiments show that ILP systems are competitive or even outperform propositional Machine Learning systems. ILP systems are moreover able to build explicit models that have been validated by expert Bridge players.