Topological regularization with information filtering networks
This work addresses sparse modeling challenges in statistics and machine learning, particularly for multivariate distributions like Student-t, but appears incremental as it builds on existing regularization techniques.
The paper tackles the problem of sparse probabilistic modeling by introducing a topological regularization methodology using information filtering networks, which is applied to covariance selection and L0-norm regularized regression, with examples on stock price log-returns and artificial data showing its applicability and performance.
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.