Convex Clustering via Optimal Mass Transport

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations of a cardinality function which penalizes the size of the support set. We establish that a certain relaxation provides the tightest convex lower approximation to the cardinality penalty. We compare the performance of alternative relaxations on a numerical study on clustering.Comment: 12 pages, 12 figure

Set-related restrictions for semantic groupings

Semantic database models utilize several fundamental forms of groupings to increase their expressive power. In this paper we consider four of the most common of these constructs; basic set groupings, is-a related groupings, power set groupings, and Cartesian aggregation groupings. For each, we define a number of useful restrictions that control its structure and composition. This permits each grouping to capture more subtle distinctions of the concepts or situations in the application environment. The resulting set of restrictions forms a framework which increases the expressive power of semantic models and specifies various set-related integrity constraints

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Tractable Combinations of Global Constraints

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text overlap with arXiv:1307.179

Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

A Theory of Cheap Control in Embodied Systems

We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machineComment: 27 pages, 10 figure