Spectral Inference Methods on Sparse Graphs: Theory and Applications

Understand

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects.

• One of the main challenges arising in the study of such networks is the inference of macroscopic, large-scale properties affecting a large number of objects, based solely on the microscopic interactions between their elementary constituents.
• Statistical physics, precisely created to recover the macroscopic laws of thermodynamics from an idealized model of interacting particles, provides significant insight to tackle such complex networks.
• In this dissertation, we use methods derived from the statistical physics of disordered systems to design and study new algorithms for inference on graphs.