Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical Relational Artificial Intelligence with Relative
  Frequencies: A Contribution to Modelling and Transfer Learning across Domain
  Sizes   Dependencies on the relative frequency of a state in the domain are common
when modelling probabilistic dependencies on relational data. For instance, the
likelihood of a school closure during an epidemic might depend on the
proportion of infected pupils exceeding a threshold. Often, rather than
depending on discrete thresholds, dependencies are continuous: for instance,
the likelihood of any one mosquito bite transmitting an illness depends on the
proportion of carrier mosquitoes. Current approaches usually only consider
probabilities over possible worlds rather than over domain elements themselves.
We introduce two formalisms that explicitly incorporate relative frequencies
into statistical relational artificial intelligence. The first formalism,
Lifted Bayesian Networks for Conditional Probability Logic, expresses discrete
dependencies on probabilistic data. The second formalism, Functional Lifted
Bayesian Networks, expresses continuous dependencies. Incorporating relative
frequencies is not only beneficial to modelling; it also provides a more
rigorous approach to learning problems where training and test or application
domains have different sizes. To this end, we provide a representation of the
asymptotic probability distributions induced by the two formalisms on domains
of increasing sizes. Since that representation has well-understood scaling
behaviour across domain sizes, it can be used to estimate parameters for a
large domain consistently from randomly sampled subpopulations.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an