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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-05202021-022351


Tipo di tesi
Tesi di dottorato di ricerca
Autore
CASTELLANA, DANIELE
URN
etd-05202021-022351
Titolo
A Tensor Framework for Learning in Structured Domains
Settore scientifico disciplinare
INF/01
Corso di studi
INFORMATICA
Relatori
tutor Prof. Bacciu, Davide
Parole chiave
  • Bayesian Non-Parametric
  • Hidden Markov Model
  • Machine Learning
  • Recursive Neural Model
  • Structured Data
  • Tensors
Data inizio appello
24/05/2021
Consultabilità
Completa
Riassunto
The aim of this thesis is to build a bridge between tensors and adaptive structured data processing, providing a general framework for learning in structured domains which has tensor theory at its backbone. To this end, we show that tensors arise naturally in model parameters from the formulation of learning problems in structured domains. We propose to approximate such parametrisations leveraging tensor decompositions whose hyper-parameters regulate the trade-off between expressiveness and compression ability. Moreover, we show that each decomposition introduces a specific inductive bias to the model. Another contribution of the thesis is the application of these new approximations to unbounded structures, where tensor decompositions needs combining with weight sharing constraints to control model complexity. The last contribution of our work is the development of two Bayesian non-parametric models for structures which learn to adapt their complexity directly from data.
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