# Lower Bounds on Active Learning for Graphical Model Selection

arXiv: https://arxiv.org/abs/1607.02413 · HTML: https://mlsanity.com/paper/1607.02413/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2016.

## Built on by (most cited first, 2 of 2)

- [Active Structure Learning of Bayesian Networks in an Observational Setting](https://mlsanity.com/paper/2103.13796/) (2021)
- [Active-LATHE: An Active Learning Algorithm for Boosting the Error Exponent for Learning Homogeneous Ising Trees](https://mlsanity.com/paper/2110.14341/) (2021)

## Abstract (arXiv)

We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting. Considering both Ising and Gaussian models, we provide algorithm-independent lower bounds for high-probability recovery within the class of degree-bounded graphs. Our main results are minimax lower bounds for the active setting that match the best known lower bounds for the passive setting, which in turn are known to be tight in several cases of interest. Our analysis is based on Fano's inequality, along with novel mutual information bounds for the active learning setting, and the application of restricted graph ensembles. While we consider ensembles that are similar or identical to those used in the passive setting, we require different analysis techniques, with a key challenge being bounding a mutual information quantity associated with observed subsets of nodes, as opposed to full observations.