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Décompositions tensorielles pour la complétion de bases de connaissance

Abstract : In this thesis, we focus on the problem of link prediction in binary tensors of order three and four containing positive observations only. Tensors of this type appear in web recommender systems, in bio-informatics for the completion of protein interaction databases, or more generally for the completion of knowledge bases. We benchmark our completion methods on knowledge bases which represent a variety of relationnal data and scales.Our approach is parallel to that of matrix completion. We optimize a non-convex regularised empirical risk objective over low-rank tensors. Our method is empirically validated on several databases, performing better than the state of the art.These performances however can only be reached for ranks that would not scale to full modern knowledge bases such as Wikidata. We focus on the Tucker decomposition which is more expressive than the Canonical decomposition but also harder to optimize. By fixing the adaptive algorithm Adagrad, we obtain a method to efficiently optimize Tucker decompositions with a fixed random core tensor. With these method, we obtain improved performances on several benchmarks for limited parameters per entities.Finally, we study the case of temporal knowledge bases, in which the predicates are only valid over certain time intervals. We propose a low-rank formulation and regularizer adapted to the temporal structure of the problem and obtain better performances than the state of the art.
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Submitted on : Tuesday, August 18, 2020 - 11:23:08 AM
Last modification on : Thursday, September 29, 2022 - 10:47:10 AM
Long-term archiving on: : Monday, November 30, 2020 - 9:06:04 PM


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  • HAL Id : tel-02916945, version 1


Timothée Lacroix. Décompositions tensorielles pour la complétion de bases de connaissance. Intelligence artificielle [cs.AI]. Université Paris-Est, 2020. Français. ⟨NNT : 2020PESC1002⟩. ⟨tel-02916945⟩



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