Estimating Normalized Graph Laplacians in Financial Markets

Gaussian Markov random fields, a class of graphical models, play an increasingly important role in real-world problems, where they are often applied to uncover conditional correlations between pairs of entities in a network. Motivated by recent applications of graphs in financial markets, we investigate the problem of learning undirected, weighted, normalized, graphical models. More precisely, we design an optimization algorithm to learn precision matrices that are modeled as normalized graph Laplacians. The proposed algorithm takes advantages of frameworks such as the alternating direction method of multipliers and projected gradient descent, which allows us to decompose the original problem into subproblems that can be solved efficiently. We demonstrate the empirical performance of the proposed algorithm, in comparison to state-of-the-art benchmark models, in a number of datasets involving financial time-series.