# Support Consistency of Direct Sparse-Change Learning in Markov Networks

arXiv: https://arxiv.org/abs/1407.0581 · HTML: https://mlsanity.com/paper/1407.0581/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2014.

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

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- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination](https://mlsanity.com/paper/2512.09266/) (2025)

## Abstract (arXiv)

We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for np = Omega(d2 log fracm2+m2) and nq = Omega(np2), with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to min(np, nq) = Omega(d2 log fracm2+m2) when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.