Vicent Estruch

Minimal Distance-Based Generalisation Operators for First-Order Objects

Distance-based methods have been a successful family of machine learning techniques since the inception of the discipline. Basically, the classification or clustering of a new individual is determined by the distance to one or more prototypes. From a comprehensibility point of view, this is not especially problematic in propositional learning where prototypes can be regarded as a good generalisation (pattern) of a group of elements. However, for scenarios with structured data, this is no longer the case. In recent work, we developed a framework to determine whether a pattern computed by a generalisation operator is consistent w.r.t. a distance. In this way, we can determine which patterns can provide a good representation of a group of individuals belonging to a metric space. In this work, we apply this framework to analyse and define minimal distance-based generalisation operators (mgoperators) for first-order data. We show that Plotkins lggis a mgoperator for atoms under the distance introduced by J. Ramon, M. Bruynooghe and W. Van Laer. We also show that this is not the case for clauses with the distance introduced by J. Ramon and M. Bruynooghe. Consequently, we introduce a new mgoperator for clauses, which could be used as a base to adapt existing bottom-up methods in ILP.

Bagging Decision Multi-Trees ⋆

Ensemble methods improve accuracy by combining the predictions of a set of different hypotheses. A well-known method for generating hypothesis ensembles is Bagging. One of the main drawbacks of ensemble methods in general, and Bagging in particular, is the huge amount of computational resources required to learn, store, and apply the set of models. Another problem is that even using the bootstrap technique, many simple models are similar, so limiting the ensemble diversity. In this work, we investigate an optimization technique based on sharing the common parts of the models from an ensemble formed by decision trees in order to minimize both problems. Concretely, we employ a structure called decision multi-tree which can contain simultaneously a set of decision trees and hence consider just once the ”repeated” parts. A thorough experimental evaluation is included to show that the proposed optimisation technique pays off in practice.

A Memoizing Semantics for Functional Logic Languages

Declarative multi-paradigm languages combine the main features of functional and logic programming, like laziness, logic variables and non-determinism. The operational semantics of these languages is based on a combination of narrowing and residuation. In this article, we introduce a non-standard memoizing semantics for multi-paradigm declarative programs and prove its equivalence with the standard operational semantics. Both pure functional and pure logic programming have for long time taken advantage of tabling or memoizing schemes [15,19,7], which motivates the interest in the adapation of this technique to the integrated paradigm.

An integrated distance for atoms

In this work, we introduce a new distance function for data representations based on first-order logic (atoms, to be more precise) which integrates the main advantages of the distances that have been previously presented in the literature. Basically, our distance simultaneously takes into account some relevant aspects, concerning atom-based presentations, such as the position where the differences between two atoms occur (context sensitivity), their complexity (size of these differences) and how many times each difference occur (the number of repetitions). Although the distance is defined for first-order atoms, it is valid for any programming language with the underlying notion of unification. Consequently, many functional and logic programming languages can also use this distance.