  Graphs are fundamental mathematical structures used in various fields to
represent data, signals and processes. In this paper, we propose a novel
framework for learning/estimating graphs from data. The proposed framework
includes (i) formulation of various graph learning problems, (ii) their
probabilistic interpretations and (iii) associated algorithms. Specifically,
graph learning problems are posed as estimation of graph Laplacian matrices
from some observed data under given structural constraints (e.g., graph
connectivity and sparsity level). From a probabilistic perspective, the
problems of interest correspond to maximum a posteriori (MAP) parameter
estimation of Gaussian-Markov random field (GMRF) models, whose precision
(inverse covariance) is a graph Laplacian matrix. For the proposed graph
learning problems, specialized algorithms are developed by incorporating the
graph Laplacian and structural constraints. The experimental results
demonstrate that the proposed algorithms outperform the current
state-of-the-art methods in terms of accuracy and computational efficiency.

Machine Learning;Machine Learning