This thesis focuses on the development of advanced algorithmic techniques, primarily Markov Chain Monte Carlo (MCMC) methods, and message passing algorithms, to tackle high-dimensional optimization and inference problems. The algorithms used have a probabi ...
For Graph Neural Networks, oversmoothing denotes the homogenization of vertex embeddings as the number of layers increases. To better understand this phenomenon, we study community detection with a linearized Graph Convolutional Network on the Contextual S ...
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization solvers near global ...
Being able to reliably assess not only the accuracy but also the uncertainty of models' predictions is an important endeavor in modern machine learning. Even if the model generating the data and labels is known, computing the intrinsic uncertainty after le ...
