# Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation

arXiv: https://arxiv.org/abs/1304.6803 · HTML: https://mlsanity.com/paper/1304.6803/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2013.

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

- [Learning High-Dimensional Differential Graphs From Multi-Attribute Data](https://mlsanity.com/paper/2312.03761/) (2023)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination](https://mlsanity.com/paper/2512.09266/) (2025)

## Abstract (arXiv)

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we directly learn the network structure change by estimating the ratio of Markov network models. This density-ratio formulation naturally allows us to introduce sparsity in the network structure change, which highly contributes to enhancing interpretability. Furthermore, computation of the normalization term, which is a critical bottleneck of the naive approach, can be remarkably mitigated. We also give the dual formulation of the optimization problem, which further reduces the computation cost for large-scale Markov networks. Through experiments, we demonstrate the usefulness of our method.