# Scalable Bigraphical Lasso: Two-way Sparse Network Inference for Count Data

arXiv: https://arxiv.org/abs/2203.07912 · HTML: https://mlsanity.com/paper/2203.07912/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Covariance Estimation in High Dimensions via Kronecker Product Expansions](https://mlsanity.com/paper/1302.2686/) (2013)
- [Tensor Graphical Lasso (TeraLasso)](https://mlsanity.com/paper/1705.03983/) (2017)
- [Variational inference for sparse network reconstruction from count data](https://mlsanity.com/paper/1806.03120/) (2018)
- [Nonparametric graphical model for counts](https://mlsanity.com/paper/1901.00886/) (2019)
- [Graphical Models for Zero-Inflated Single Cell Gene Expression](https://mlsanity.com/paper/1610.05857/) (2016)
- [Two-way sparsity for time-varying networks, with applications in genomics](https://mlsanity.com/paper/1802.08114/) (2018)

## Built on by (most cited first, 3 of 3)

- [GmGM: a Fast Multi-Axis Gaussian Graphical Model](https://mlsanity.com/paper/2211.02920/) (2022)
- [Making Multi-Axis Gaussian Graphical Models Scalable to Millions of Cells](https://mlsanity.com/paper/2407.19892/) (2024)
- [Graphical Modelling without Independence Assumptions for Uncentered Data](https://mlsanity.com/paper/2408.02393/) (2024)

## Abstract (arXiv)

Classically, statistical datasets have a larger number of data points than features (n > p). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for n≈ p or p > n such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large p and n due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from O(n2p2) to O(n2 + p2). Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multi-way network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.