Statistical mechanics and learning problems in neural networks

Luzi, Rachele (2019) Statistical mechanics and learning problems in neural networks, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica, 31 Ciclo. DOI 10.6092/unibo/amsdottorato/8730.
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My PhD thesis is based on Statistical Mechanics themes and their applications. In the second chapter I test the inverse problem method for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. I obtain the inversion by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion. In the third chapter I perform some analysis in order to characterize statistical properties of the observed mobility of drosophilas expressing different kinds of proteins. In the fourth chapter I give an overview of the already existing algorithm Replicated Belief Propagation (RBP) deeply analyzing the equations which define the model. In the fifth chapter I apply the RBP in order to predict the congestion formation in the framework of complex systems physics. Traffic is a complex system where vehicle interactions and finite volume effects produce different collective regimes and phase transition phenomena. Such prediction can be a difficult problem due to the heterogenous behavior of drivers when the vehicle density increases. We propose a novel pipeline to classify traffic slowdowns by analyzing the features extracted from the fundamental diagram of traffic. I train the RBP and we provide a forewarning time of prediction related to the training set size. Then I compare my results with those of the most common classifiers used in machine learning analysis.

Tipologia del documento
Tesi di dottorato
Luzi, Rachele
Dottorato di ricerca
Settore disciplinare
Settore concorsuale
Parole chiave
neural network, deep learning, mean-field models
Data di discussione
29 Marzo 2019

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