TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: Marginal MAP inference involves making MAP predictions in systems defined<lb>with latent variables or missing information. It is significantly more difficult than<lb>pure marginalization and MAP tasks, for which a large class of efficient and con-<lb>vergent variational algorithms, such as dual decomposition, exist. In this work, we<lb>generalize dual decomposition to a generic power sum inference task, which in-<lb>cludes marginal MAP, along with pure marginalization and MAP, as special cases.<lb>Our method is based on a block coordinate descent algorithm on a new convex<lb>decomposition bound, that is guaranteed to converge monotonically, and can be<lb>parallelized efficiently. We demonstrate our approach on marginal MAP queries<lb>defined on real-world problems from the UAI approximate inference challenge,<lb>showing that our framework is faster and more reliable than previous methods.

SOLUTION: Decomposition Bounds for Marginal MAP

PROBLEM: This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.

SOLUTION: Minkowski Operations of Sets with Application to Robot Localization

PROBLEM: We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph — in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing PF was a visiting professor at KU Leuven and FC a postdoctoral fellow at KU Leuven while this work was initiated ∗Corresponding author Email addresses: p-f@dsi.unifi.it (Paolo Frasconi), costa@informatik.uni-freiburg.de (Fabrizio Costa), Luc.DeRaedt@cs.kuleuven.be (Luc De Raedt), Kurt.DeGrave@cs.kuleuven.be (Kurt De Grave) Preprint submitted to Artificial Intelligence July 29, 2014 ar X iv :1 20 5. 39 81 v5 [ cs .A I] 2 8 Ju l 2 01 4 that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials.

SOLUTION:
kLog: A Language for Logical and Relational Learning with Kernels