2000
DOI: 10.1023/a:1007620705405 View full text |Buy / Rent full text
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Abstract: Abstract.One of the major limitations of relational learning is due to the complexity of verifying hypotheses on examples. In this paper we investigate this task in light of recent published results, which show that many hard problems exhibit a narrow "phase transition" with respect to some order parameter, coupled with a large increase in computational complexity. First we show that matching a class of artificially generated Horn clauses on ground instances presents a typical phase transition in solvability w… Show more

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“…In philosophy and pedagogy, one sometimes considers phase transitions in our understanding: The abstract transition from quantity to quality, as Hegel and his successors have discussed,[ 62 ] or the deeper understanding of a mathematical theorem gained once we have studied enough examples of its applications, or even in the study of chemistry the profound intuition acquired by the experimental chemist due to the many syntheses he or she has performed. Also in computer or machine learning, such transitions are observed,[ 63 ] e.g. during the teaching of a neural network, whose parameters are optimized by feeding it a multitude of teaching examples until the network is ready to correctly analyze and classify instances of input never presented before.…”
Section: Discussionmentioning
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“…In philosophy and pedagogy, one sometimes considers phase transitions in our understanding: The abstract transition from quantity to quality, as Hegel and his successors have discussed,[ 62 ] or the deeper understanding of a mathematical theorem gained once we have studied enough examples of its applications, or even in the study of chemistry the profound intuition acquired by the experimental chemist due to the many syntheses he or she has performed. Also in computer or machine learning, such transitions are observed,[ 63 ] e.g. during the teaching of a neural network, whose parameters are optimized by feeding it a multitude of teaching examples until the network is ready to correctly analyze and classify instances of input never presented before.…”
Section: Discussionmentioning
“…For that purpose, we use first-order logic to represent both data and background knowledge. In order to benefit from the tools of statistical learning and to avoid some of the weaknesses of pure inductive logic programming raised, for instance, in [27], we choose a Markov Logic network (MLN) [28,29] as the edge predictor. MLN allows to make predictions using a set of weighted first-order logic rules, thus providing interesting insights on decisions.…”
Section: Introductionmentioning