The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy conf...

The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy conf...

This paper presents an extension to Ant-Miner, named cAntMiner (Ant-Miner coping with continuous attributes), which incorporates an entropy-based discretization method in order to cope with continuous attributes during the rule construction process. By having the ability to create discrete intervals for continuous attributes “on-the-fly”, cAnt-Miner does not requires a discretization method in ...

We consider the model checking problem for interval Markov chains with open intervals. Interval Markov chains are generalizations of discrete time Markov chains where the transition probabilities are intervals, instead of constant values. We focus on the case where the intervals are open. At first sight, open intervals present technical challenges, as optimal (min, max) value for reachability m...

Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Latticetheoretical properties of decompositions are explored, ...

Most of the existing machine learning algorithms are able to extract knowledge from databases that store discrete attributes (features). If the attributes are continuous, the algorithms can be integrated with a discretization algorithm that transforms them into discrete attributes. The paper describes an algorithm, called CAIM (class-attribute interdependence maximization), for discretization o...