Domain-Liftability of Relational Marginal Polytopes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00342407" target="_blank" >RIV/68407700:21230/20:00342407 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.mlr.press/v108/kuzelka20a.html" target="_blank" >http://proceedings.mlr.press/v108/kuzelka20a.html</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Domain-Liftability of Relational Marginal Polytopes

Popis výsledku v původním jazyce

We study computational aspects of "relational marginal polytopes" which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of first-order logic formulas, the relational marginal polytope is the set of all points that correspond to expected values of the relational marginal statistics that are realizable. In this paper we study the following two problems: (i) Do domain-liftability results for the partition functions of Markov logic networks (MLNs)carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexity-theoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domain-liftable whenever the computation of the partition function of the respective MLNs is domain-liftable (this result has not been rigorously proven before).

Název v anglickém jazyce

Domain-Liftability of Relational Marginal Polytopes

Popis výsledku anglicky

We study computational aspects of "relational marginal polytopes" which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of first-order logic formulas, the relational marginal polytope is the set of all points that correspond to expected values of the relational marginal statistics that are realizable. In this paper we study the following two problems: (i) Do domain-liftability results for the partition functions of Markov logic networks (MLNs)carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexity-theoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domain-liftable whenever the computation of the partition function of the respective MLNs is domain-liftable (this result has not been rigorously proven before).

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics

ISBN

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ISSN

2640-3498

e-ISSN

2640-3498

Počet stran výsledku

8

Strana od-do

2284-2291

Název nakladatele

Proceedings of Machine Learning Research

Místo vydání

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Místo konání akce

Palermo

Datum konání akce

3. 6. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000559931301090