Abstract

Abstract
A methodology for the synthesis of function free definite logic programs from incomplete specifications, background knowledge and programming knowledge is presented. The methodology is implemented as a system SKILit and sub-systems SKIL and MONIC. The specification consists of positive and negative examples of the predicate to synthesize, together with its input/output mode declaration.

Abstract
In this paper we present system Ltree for propositional supervised learning. Ltree is able to define decision surfaces both orthogonal and oblique to the axes defined by the attributes of the input space. This is done combining a decision tree with a linear discriminant by means of constructive induction. At each decision node Ltree defines a new instance space by insertion of new attributes that are projections of the examples that fall at this node over the hyper-planes given by a linear discriminant function. This new instance space is propagated down through the tree. Tests based on those new attributes are oblique with respect to the original input space. Ltree is a probabilistic tree in the sense that it outputs a class probability distribution for each query example. The class probability distribution is computed at learning time, taking into account the different class distributions on the path from the root to the actual node. We have carried out experiments on twenty one benchmark datasets and compared our system with other well known decision tree systems (orthogonal and oblique) like C4.5, OC1, LMDT, and CART. On these datasets we have observed that our system has advantages in what concerns accuracy and learning times at statistically significant confidence levels.

Abstract
Naive Bayes is a well known and studied algorithm both in statistics and machine learning. Bayesian learning algorithms represent each concept with a single probabilistic summary. In this paper we present an iterative approach to naive Bayes. The iterative Bayes begins with the distribution tables built by the naive Bayes. Those tables are iteratively updated in order to improve the probability class distribution associated with each training example. Experimental evaluation of Iterative Bayes on 25 benchmark datasets shows consistent gains in accuracy. An interesting side effect of our algorithm is that it shows to be robust to attribute dependencies.

Abstract

Abstract
In a previous work, we presented system Ltree, a multivariate tree that combines a decision tree with a linear discriminant by means of constructive induction. We have shown that it performs quite well, in terms of accuracy and learning times, in comparison with other multivariate systems like LMDT, OC1, and CART. In this work, we extend the previous work by using two new discriminant functions: a quadratic discriminant and a logistic discriminant. Using the same architecture as Ltree we obtain two new multivariate trees Qtree and LgTree. The three systems have been evaluate on 17 UCI datasets. From the empirical study, we argue that these systems can be shown as a composition of classifiers with low correlation error. From a bias-variance analysis of the error rate, the error reduction of all the systems in comparison to a univariate tree, is due to a reduction on both components.