Statistical mechanics and learning problems in neural networks
Luzi, Rachele <1991>
Subject
MAT/07 Fisica matematica
Description
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.
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.