When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e.g., Clark & Matwin’s work with the CN2 rule learning algorithm). We show how...

This paper introduces modiication of two existing rule-inducing ML algorithms; they are now capable of processing continuous classes. The rst one is the CN4 algorithm, a large extension of the well-known CN2. It invokes its discretization procedure and also deals with continuous classes within the inductive process itself, i.e., 'on-line'. The other ML system, KEX (Knowledge EXplorer), treats n...

A conjecture of Erdős from 1967 asserts that any graph on n vertices which does not contain a fixed r-degenerate bipartite F has at most Cn2−1/r edges, where C is constant depending only F. We show this bound holds for large family graphs, including all blow-ups trees. Our results generalise many previously proven cases the conjecture, related Füredi and Alon, Krivelevich Sudakov. proof uses su...

BCT (Binary Classification Tree) is a system that learns from examples and represents learned concepts as a binary polythetic decision tree. Polythetic trees differ from monothetic decision trees in that a logical combination of multiple (versus a single) attribute values may label each tree arc. Statistical evaluations are used to recursively partition the concept space in two and expand the t...

One of the most important characteristics of empirical learning methods, such as AQ, ID3(CART), C4.5 and CN2, is that they find variables which are relevant to classification. In this paper, we define relevance in empirical classifier as relevance of each given attribute to apparent or predictive classification, and describe this type of relevance in terms of rough sets and matroid theory. The ...

Learning easily understandable decision rules from examples is one of the classic problems in machine learning. Most learning systems for this problem employ some variation of a greedy separate-and-conquer algorithm, which makes the rules order-dependent, and hence difficult to understand. In this paper, we describe a system called LERILS that learns highly accurate and comprehensible rules fro...

In this short note, we prove that for β < 1/5 every graph G with n vertices and n2−β edges contains a subgraph G′ with at least cn2−2β edges such that every pair of edges in G′ lie together on a cycle of length at most 8. Moreover edges in G′ which share a vertex lie together on a cycle of length at most 6. This result is best possible up to the constant factor and settles a conjecture of Duke,...

While recent research on rule learning has focussed largely on finding highly accurate hypotheses, we evaluate the degree to which these hypotheses are also simple, that is small. To realize this, we compare well-known rule learners, such as CN2, RIPPER, PART, FOIL and C5.0 rules, with the benchmark system SL2 that explicitly aims at computing small rule sets with few literals. The results show...

A set of n triangles sharing a common edge is called a book with n pages and is denoted by Bn. It is known that the Ramsey number r (Bn) satisfies r (Bn) = (4 + o (1))n. We show that every red-blue edge coloring of Kb(4−ε)nc with no monochromatic Bn exhibits quasi-random properties when ε tends to 0. This implies that there is a constant c > 0 such that for every red-blue edge coloring of Kr(Bn...