Related papers: Measuring sets by means
One of the main current challenges in itemset mining is to discover a small set of high-quality itemsets. In this paper we propose a new and general approach for measuring the quality of itemsets. The method is solidly founded in Bayesian…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…
Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…
We study from a statistical mechanics viewpoint some of the simplest mathematical objects, finite pure sets. Starting from the empty set, new generations are produced step by step, sets of the next generation being those whose elements are…
Metric search commonly involves finding objects similar to a given sample object. We explore a generalization, where the desired result is a fair tradeoff between multiple query objects. This builds on previous results on complex queries,…
Existing work on fairness typically focuses on making known machine learning algorithms fairer. Fair variants of classification, clustering, outlier detection and other styles of algorithms exist. However, an understudied area is the topic…
Consider the random set system of {1,2,...,n}, where each subset in the power set is chosen independently with probability p. A set H is said to be a hitting set if it intersects each chosen set. The second moment method is used to exhibit…
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…