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Learning time-dependent data with the signature transform

Abstract : Modern applications of artificial intelligence lead to high-dimensional multivariate temporal data that pose many challenges. Through a geometric approach to data flows, the notion of signature, a representation of a process as an infinite vector of its iterated integrals, is a promising tool. Its properties, developed in the context of rough path theory, make it a good candidate to play the role of features, then injected in learning algorithms. If the definition of the signature goes back to the work of Chen (1960), its use in machine learning is recent. Many theoretical and methodological questions remain to be explored. We are therefore interested in using the signature to develop generic and efficient algorithms for high-dimensional temporal data, with theoretical guarantees. This goal is mainly deployed in two directions: on the one hand, to develop new algorithms taking the signature of the data as input, and, on the other hand, to use the signature as a theoretical tool to study existing deep learning algorithms, via the recent notion of neural ordinary differential equation which makes the link between deep learning and differential equations.
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Submitted on : Monday, January 3, 2022 - 11:01:07 AM
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  • HAL Id : tel-03507274, version 1

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Adeline Fermanian. Learning time-dependent data with the signature transform. Statistics [math.ST]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS224⟩. ⟨tel-03507274⟩

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