  A methodology to perform topological regularization via information filtering
network is introduced. This methodology can be directly applied to covariance
selection problem providing an instrument for sparse probabilistic modeling
with both linear and non-linear multivariate probability distributions such as
the elliptical and generalized hyperbolic families. It can also be directly
implemented for $L_0$-norm regularized multicollinear regression. In this
paper, I describe in detail an application to sparse modeling with multivariate
Student-t. A specific $L_0$-norm regularized expectation-maximization
likelihood maximization procedure is proposed for this sparse Student-t case.
Examples with real data from stock prices log-returns and from artificially
generated data demonstrate the applicability, performances, and potentials of
this methodology.
