# Fitting networks with a cancellation trick

arXiv: https://arxiv.org/abs/2502.16728 · HTML: https://mlsanity.com/paper/2502.16728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 23 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Convexified Modularity Maximization for Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1512.08425/) (2015)
- [Influential Feature PCA for high dimensional clustering](https://mlsanity.com/paper/1407.5241/) (2014)
- [Using SVD for Topic Modeling](https://mlsanity.com/paper/1704.07016/) (2017)
- [Optimal Adaptivity of Signed-Polygon Statistics for Network Testing](https://mlsanity.com/paper/1904.09532/) (2019)
- [Improvements on SCORE, Especially for Weak Signals](https://mlsanity.com/paper/1811.05927/) (2018)
- [Recent Advances in Text Analysis](https://mlsanity.com/paper/2401.00775/) (2024)
- [A likelihood-ratio type test for stochastic block models with bounded degrees](https://mlsanity.com/paper/1807.04426/) (2018)

## Abstract (arXiv)

The degree-corrected block model (DCBM), latent space model (LSM), and β-model are all popular network models. We combine their modeling ideas and propose the logit-DCBM as a new model. Similar as the β-model and LSM, the logit-DCBM contains nonlinear factors, where fitting the parameters is a challenging open problem. We resolve this problem by introducing a cancellation trick. We also propose R-SCORE as a recursive community detection algorithm, where in each iteration, we first use the idea above to update our parameter estimation, and then use the results to remove the nonlinear factors in the logit-DCBM so the renormalized model approximately satisfies a low-rank model, just like the DCBM. Our numerical study suggests that R-SCORE significantly improves over existing spectral approaches in many cases. Also, theoretically, we show that the Hamming error rate of R-SCORE is faster than that of SCORE in a specific sparse region, and is at least as fast outside this region.