# Topological regularization with information filtering networks

arXiv: https://arxiv.org/abs/2005.04692 · HTML: https://mlsanity.com/paper/2005.04692/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2020.

## Built on by (most cited first, 6 of 6)

- [HLOB -- Information Persistence and Structure in Limit Order Books](https://mlsanity.com/paper/2405.18938/) (2024)
- [Sparsification and Filtering for Spatial-temporal GNN in Multivariate Time-series](https://mlsanity.com/paper/2203.03991/) (2022)
- [Homological Neural Networks: A Sparse Architecture for Multivariate Complexity](https://mlsanity.com/paper/2306.15337/) (2023)
- [Homological Convolutional Neural Networks](https://mlsanity.com/paper/2308.13816/) (2023)
- [Topological Feature Selection](https://mlsanity.com/paper/2302.09543/) (2023)
- [Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications](https://mlsanity.com/paper/2505.03812/) (2025)

## Abstract (arXiv)

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 L0-norm regularized multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific L0-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.