18,417 research outputs found
Estimating Maximally Probable Constrained Relations by Mathematical Programming
Estimating a constrained relation is a fundamental problem in machine
learning. Special cases are classification (the problem of estimating a map
from a set of to-be-classified elements to a set of labels), clustering (the
problem of estimating an equivalence relation on a set) and ranking (the
problem of estimating a linear order on a set). We contribute a family of
probability measures on the set of all relations between two finite, non-empty
sets, which offers a joint abstraction of multi-label classification,
correlation clustering and ranking by linear ordering. Estimating (learning) a
maximally probable measure, given (a training set of) related and unrelated
pairs, is a convex optimization problem. Estimating (inferring) a maximally
probable relation, given a measure, is a 01-linear program. It is solved in
linear time for maps. It is NP-hard for equivalence relations and linear
orders. Practical solutions for all three cases are shown in experiments with
real data. Finally, estimating a maximally probable measure and relation
jointly is posed as a mixed-integer nonlinear program. This formulation
suggests a mathematical programming approach to semi-supervised learning.Comment: 16 page
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Learning Tuple Probabilities
Learning the parameters of complex probabilistic-relational models from
labeled training data is a standard technique in machine learning, which has
been intensively studied in the subfield of Statistical Relational Learning
(SRL), but---so far---this is still an under-investigated topic in the context
of Probabilistic Databases (PDBs). In this paper, we focus on learning the
probability values of base tuples in a PDB from labeled lineage formulas. The
resulting learning problem can be viewed as the inverse problem to confidence
computations in PDBs: given a set of labeled query answers, learn the
probability values of the base tuples, such that the marginal probabilities of
the query answers again yield in the assigned probability labels. We analyze
the learning problem from a theoretical perspective, cast it into an
optimization problem, and provide an algorithm based on stochastic gradient
descent. Finally, we conclude by an experimental evaluation on three real-world
and one synthetic dataset, thus comparing our approach to various techniques
from SRL, reasoning in information extraction, and optimization
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