7,760 research outputs found
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
Abstract Learning Frameworks for Synthesis
We develop abstract learning frameworks (ALFs) for synthesis that embody the
principles of CEGIS (counter-example based inductive synthesis) strategies that
have become widely applicable in recent years. Our framework defines a general
abstract framework of iterative learning, based on a hypothesis space that
captures the synthesized objects, a sample space that forms the space on which
induction is performed, and a concept space that abstractly defines the
semantics of the learning process. We show that a variety of synthesis
algorithms in current literature can be embedded in this general framework.
While studying these embeddings, we also generalize some of the synthesis
problems these instances are of, resulting in new ways of looking at synthesis
problems using learning. We also investigate convergence issues for the general
framework, and exhibit three recipes for convergence in finite time. The first
two recipes generalize current techniques for convergence used by existing
synthesis engines. The third technique is a more involved technique of which we
know of no existing instantiation, and we instantiate it to concrete synthesis
problems
Inductive Logic Programming in Databases: from Datalog to DL+log
In this paper we address an issue that has been brought to the attention of
the database community with the advent of the Semantic Web, i.e. the issue of
how ontologies (and semantics conveyed by them) can help solving typical
database problems, through a better understanding of KR aspects related to
databases. In particular, we investigate this issue from the ILP perspective by
considering two database problems, (i) the definition of views and (ii) the
definition of constraints, for a database whose schema is represented also by
means of an ontology. Both can be reformulated as ILP problems and can benefit
from the expressive and deductive power of the KR framework DL+log. We
illustrate the application scenarios by means of examples. Keywords: Inductive
Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid
Knowledge Representation and Reasoning Systems. Note: To appear in Theory and
Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables
Off the Beaten Path: Let's Replace Term-Based Retrieval with k-NN Search
Retrieval pipelines commonly rely on a term-based search to obtain candidate
records, which are subsequently re-ranked. Some candidates are missed by this
approach, e.g., due to a vocabulary mismatch. We address this issue by
replacing the term-based search with a generic k-NN retrieval algorithm, where
a similarity function can take into account subtle term associations. While an
exact brute-force k-NN search using this similarity function is slow, we
demonstrate that an approximate algorithm can be nearly two orders of magnitude
faster at the expense of only a small loss in accuracy. A retrieval pipeline
using an approximate k-NN search can be more effective and efficient than the
term-based pipeline. This opens up new possibilities for designing effective
retrieval pipelines. Our software (including data-generating code) and
derivative data based on the Stack Overflow collection is available online
Efficient Regularized Least-Squares Algorithms for Conditional Ranking on Relational Data
In domains like bioinformatics, information retrieval and social network
analysis, one can find learning tasks where the goal consists of inferring a
ranking of objects, conditioned on a particular target object. We present a
general kernel framework for learning conditional rankings from various types
of relational data, where rankings can be conditioned on unseen data objects.
We propose efficient algorithms for conditional ranking by optimizing squared
regression and ranking loss functions. We show theoretically, that learning
with the ranking loss is likely to generalize better than with the regression
loss. Further, we prove that symmetry or reciprocity properties of relations
can be efficiently enforced in the learned models. Experiments on synthetic and
real-world data illustrate that the proposed methods deliver state-of-the-art
performance in terms of predictive power and computational efficiency.
Moreover, we also show empirically that incorporating symmetry or reciprocity
properties can improve the generalization performance
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