  We investigate the problem of learning undirected graphical models under
Laplacian structural constraints from the point of view of financial market
data. We show that Laplacian constraints have meaningful physical
interpretations related to the market index factor and to the conditional
correlations between stocks. Those interpretations lead to a set of guidelines
that users should be aware of when estimating graphs in financial markets. In
addition, we propose algorithms to learn undirected graphs that account for
stylized facts and tasks intrinsic to financial data such as non-stationarity
and stock clustering.
