Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

10481 Abstracts Collection -- Computational Counting

From November 28 to December 3 2010, the Dagstuhl Seminar 10481 ``Computational Counting\u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries

Truncating the loop series expansion for Belief Propagation

Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms to the BP free energy, one for each "generalized loop" in the factor graph, the exact partition sum is obtained. However, the usually enormous number of generalized loops generally prohibits summation over all correction terms. In this article we introduce Truncated Loop Series BP (TLSBP), a particular way of truncating the loop series of M. Chertkov and V.Y. Chernyak by considering generalized loops as compositions of simple loops. We analyze the performance of TLSBP in different scenarios, including the Ising model, regular random graphs and on Promedas, a large probabilistic medical diagnostic system. We show that TLSBP often improves upon the accuracy of the BP solution, at the expense of increased computation time. We also show that the performance of TLSBP strongly depends on the degree of interaction between the variables. For weak interactions, truncating the series leads to significant improvements, whereas for strong interactions it can be ineffective, even if a high number of terms is considered.Comment: 31 pages, 12 figures, submitted to Journal of Machine Learning Researc

A Szintaktikai Lokalitás Minimalista Megközelítése: A szintaktikai lokalitási feltételekért felelős nyelvi alrendszerek munkamegosztásának vizsgálata = A Minimalist Approach to Syntactic Locality: A study of the division of labour of linguistic subsystems underlying syntactic locality effects

A projekt a szintaxis és az azzal érintkező grammatikai komponensek munkamegosztását vizsgálta a mozgatási és polaritás engedélyezési függőségekben jelentkező szintaktikai lokalitási hatások területén. A projektnek a generatív grammatika mai, Minimalista kutatási programjába illeszkedő radikális tézise szerint a természetes nyelvi szintaxis egyáltalán nem is tartalmaz külön lokalitási megszorítás(oka)t. Kimutattuk, hogy az általunk vizsgált, a szintaxisban jelentkező lokalitási hatások (i) a szintaktikai komputációs rendszer általános tulajdonságaiból, különösen a komputációs komplexitása minimalizálásának igényéből, valamint (ii) a szintaxis és a vele érintkező grammatikai alrendszerek munkamegosztásából fakadnak. A projekt olyan területeken vizsgálta a lokalitási hatások természetét, mint a főnévi kifejezések által képviselt szigetek, a szintaktikai fejmozgatás, a kvantorhatókör-értelmezés, a fókuszálás, a határozói módosítás, a mondatbeágyazás, a preszuppozíciós, a tagadó és a kérdő típusú gyenge szigetek, és egyes, a polaritásengedélyezésben szerepet játszó intervenciós hatások. A több nemzetközi együttműködést is kezdeményező kutatócsoport munkájának sikerességét a számos jelentős publikáció, köztük egy sor nemzetközi folyóiratcikk és nagy presztízsű nemzetközi kiadónál megjelenő könyvfejezet is jelzi. A kutatás keretében egy megvédett DSc értekezés és egy leadott PhD disszertáció is született, és egy további doktori disszertáció készül el még ebben az évben. | This project studied the division of labour between syntax and its interface subsystems in giving rise to some of the central syntactic locality properties of dependencies like movement and polarity licensing. Implementing the current Minimalist research program of transformational generative grammar, it explored the radical proposal that natural language syntax itself includes no special syntactic locality conditions per se. Instead, the locality effects under scrutiny are reduced to (i) the elementary properties of the syntactic computational system, including its quest to keep computational complexity to a minimum, which in turn subsumes its cyclic mapping to the interpretive systems of sound and meaning; and (ii) the division of labour between syntax and the interface subsystems, in particular, semantics and information structure. The topics investigated include the locality effects involved in noun phrase islands, syntactic head movement, quantifier scope interpretation, focusing, adverbial modification, clausal embedding, weak islands like presuppositional, negative, and wh-islands, and some apparent intervention effects in polarity licensing. The project established fruitful international co-operations, and its results have appeared in the form of a number of international journal and book chapter publications. The project has also yielded a completed PhD dissertation, a PhD thesis to be submitted later this year, and a DSc dissertation

Belief Propagation and Loop Series on Planar Graphs

We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation [3], to evaluating the partition function of the dimer matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn [4]. This allows to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed.Comment: Accepted for publication in Journal of Statistical Mechanics: theory and experimen

Modular Composition of Language Features through Extensions of Semantic Language Models

Today, programming or specification languages are often extended in order to customize them for a particular application domain or to refine the language definition. The extension of a semantic model is often at the centre of such an extension. We will present a framework for linking basic and extended models. The example which we are going to use is the RSL concurrency model. The RAISE specification language RSL is a formal wide-spectrum specification language which integrates different features, such as state-basedness, concurrency and modules. The concurrency features of RSL are based on a refinement of a classical denotational model for process algebras. A modification was necessary to integrate state-based features into the basic model in order to meet requirements in the design of RSL. We will investigate this integration, formalising the relationship between the basic model and the adapted version in a rigorous way. The result will be a modular composition of the basic process model and new language features, such as state-based features or input/output. We will show general mechanisms for integration of new features into a language by extending language models in a structured, modular way. In particular, we will concentrate on the preservation of properties of the basic model in these extensions