Mining frequent itemsets a perspective from operations research

Many papers on frequent itemsets have been published. Besides somecontests in this field were held. In the majority of the papers the focus ison speed. Ad hoc algorithms and datastructures were introduced. Inthis paper we put most of the algorithms in one framework, usingclassical Operations Research paradigms such as backtracking, depth-first andbreadth-first search, and branch-and-bound. Moreover we presentexperimental results where the different algorithms are implementedunder similar designs.data mining;operation research;Frequent itemsets

Mining frequent itemsets a perspective from operations research

Many papers on frequent itemsets have been published. Besides some contests in this field were held. In the majority of the papers the focus is on speed. Ad hoc algorithms and datastructures were introduced. In this paper we put most of the algorithms in one framework, using classical Operations Research paradigms such as backtracking, depth-first and breadth-first search, and branch-and-bound. Moreover we present experimental results where the different algorithms are implemented under similar designs

Implicit Hitting Set Algorithms for Constraint Optimization

Computationally hard optimization problems are commonplace not only in theory but also in practice in many real-world domains. Even determining whether a solution exists can be NP-complete or harder. Good, ideally globally optimal, solutions to instances of such problems can save money, time, or other resources. We focus on a particular generic framework for solving constraint optimization problems, the so-called implicit hitting set (IHS) approach. The approach is based on a theory of duality between solutions and sets of mutually conflicting constraints underlying a problem. Recent years have seen a number of new instantiations of the IHS approach for various problems and constraint languages. As the main contributions, we present novel instantiations of this generic algorithmic approach to four different NP-hard problem domains: maximum satisfiability (MaxSAT), learning optimal causal graphs, propositional abduction, and answer set programming (ASP). For MaxSAT, we build on an existing IHS algorithm with a fresh implementation and new methods for integrating preprocessing. We study a specific application of this IHS approach to MaxSAT for learning optimal causal graphs. In particular we develop a number of domain-specific search techniques to specialize the IHS algorithm for the problem. Furthermore, we consider two optimization settings where the corresponding decision problem is beyond NP, in these cases Σᴾ₂-hard. In the first, we compute optimal explanations for propositional abduction problems. In the second, we solve optimization problems expressed as answer set programs with disjunctive rules. For each problem domain, we empirically evaluate the resulting algorithm and contribute an open-source implementation. These implementations improve or complement the state of the art in their respective domains.Käytännön sovellutuksista kumpuavat optimointiongelmat ovat usein laskennallisesti haastavia. Deklaratiiviset menetelmät tarjoavat keskeisen tavan lähestyä erinäisiä laskennallisesti haastavia optimointiongelmia. Deklaratiivisissa lähestymistavoissa ratkaistavana oleva ongelma mallinnetaan yleisesti matemaattisina rajoitteina siten, että alkuperäisen ongelman instanssien rajoitekuvauksen rajoitteet voidaan toteuttaa jos ja vain jos ongelmainstanssille on olemassa ratkaisu. Ratkaisujen löytäminen rajoitekuvaukselle edellyttää yleisten algoritmisten ratkaisumenetelmien kehittämistä rajoitekuvauskielille. Tässä väitöskirjassa kehitetään uudentyyppisiä käytännöllisiä eksakteja deklaratiivisia ratkaisumenetelmiä jotka pohjautuvat ns. implicit hitting set (IHS) -optimointialgoritmiparadigmaan. Erityisesti työssä kehitetään ja toteutetaan IHS-pohjaisia menetelmiä neljälle laskennallisesti haastavalle, tekoälytutkimuksen näkökulmasta motivoidulle NP-kovalle optimointiongelmalle: lauselogiikan optimointilaajennukselle (MaxSAT), keskeiselle epämonotonisen päättelyn lähestymistavalle (answer set optimization, ASP), lauseloogiselle abduktiolle, sekä optimaalisten kausaaliverkkojen löytämisongelmalle. Työssä kehitetään sekä yleisiä että ongelmakohtaisia hakutekniikoita IHS-kontekstissa, kehitetään avoimen lähdekoodin implementaatioita, ja osoitetaan empiriisten evaluaatioiden kautta näiden olevan käytännössä varteenotettavia vaihtoehtoja kunkin ongelman tehokkaaseen ratkaisemiseen

Discovery of Unconventional Patterns for Sequence Analysis: Theory and Algorithms

The biology community is collecting a large amount of raw data, such as the genome sequences of organisms, microarray data, interaction data such as gene-protein interactions, protein-protein interactions, etc. This amount is rapidly increasing and the process of understanding the data is lagging behind the process of acquiring it. An inevitable first step towards making sense of the data is to study their regularities focusing on the non-random structures appearing surprisingly often in the input sequences: patterns. In this thesis we discuss three incarnations of the pattern discovery task, exploring three types of patterns that can model different regularities of the input dataset. While mask patterns have been designed to model short repeated biological sequences, showing a high conservation of their content at some specific positions, permutation patterns have been designed to detect repeated patterns whose parts maintain their physical adjacency but not their ordering in all the pattern occurrences. Transposons, instead, model mobile sequences in the input dataset, which can be discovered by comparing different copies of the same input string, detecting large insertions and deletions in their alignment