# Meta Learning for High-dimensional Ising Model Selection Using ℓ1-regularized Logistic Regression

arXiv: https://arxiv.org/abs/2208.09539 · HTML: https://mlsanity.com/paper/2208.09539/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 19 Aug 2022.

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

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Meta Learning for Support Recovery in High-dimensional Precision Matrix Estimation](https://mlsanity.com/paper/2006.12598/) (2020)

## Abstract (arXiv)

In this paper, we consider the meta learning problem for estimating the graphs associated with high-dimensional Ising models, using the method of ℓ1-regularized logistic regression for neighborhood selection of each node. Our goal is to use the information learned from the auxiliary tasks in the learning of the novel task to reduce its sufficient sample complexity. To this end, we propose a novel generative model as well as an improper estimation method. In our setting, all the tasks are similar in their random model parameters and supports. By pooling all the samples from the auxiliary tasks to improperly estimate a single parameter vector, we can recover the true support union, assumed small in size, with a high probability with a sufficient sample complexity of Omega(1)  per task, for K = Omega(d3 log p )  tasks of Ising models with p nodes and a maximum neighborhood size d. Then, with the support for the novel task restricted to the estimated support union, we prove that consistent neighborhood selection for the novel task can be obtained with a reduced sufficient sample complexity of Omega(d3 log d).