# Network Estimation by Mixing: Adaptivity and More

arXiv: https://arxiv.org/abs/2106.02803 · HTML: https://mlsanity.com/paper/2106.02803/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 97 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 26 of 26)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Concentration and regularization of random graphs](https://mlsanity.com/paper/1506.00669/) (2015)
- [Network Cross-Validation for Determining the Number of Communities in Network Data](https://mlsanity.com/paper/1411.1715/) (2014)
- [A goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/1412.4857/) (2014)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Hierarchical community detection by recursive partitioning](https://mlsanity.com/paper/1810.01509/) (2018)
- [Hypothesis Testing for Automated Community Detection in Networks](https://mlsanity.com/paper/1311.2694/) (2013)
- [Cross-Validation with Confidence](https://mlsanity.com/paper/1703.07904/) (2017)
- [Optimal hypothesis testing for stochastic block models with growing degrees](https://mlsanity.com/paper/1705.05305/) (2017)
- [Testing for Global Network Structure Using Small Subgraph Statistics](https://mlsanity.com/paper/1710.00862/) (2017)
- [Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections](https://mlsanity.com/paper/1304.1548/) (2013)
- [How Many Communities Are There?](https://mlsanity.com/paper/1412.1684/) (2014)
- [Optimal Adaptivity of Signed-Polygon Statistics for Network Testing](https://mlsanity.com/paper/1904.09532/) (2019)
- [Linear regression and its inference on noisy network-linked data](https://mlsanity.com/paper/2007.00803/) (2020)
- [Provable Estimation of the Number of Blocks in Block Models](https://mlsanity.com/paper/1705.08580/) (2017)
- [EM-Based Smooth Graphon Estimation Using Bayesian and Spline-Based Approaches](https://mlsanity.com/paper/1903.06936/) (2019)
- [Adjusted chi-square test for degree-corrected block models](https://mlsanity.com/paper/2012.15047/) (2020)
- [The blessing of transitivity in sparse and stochastic networks](https://mlsanity.com/paper/1307.2302/) (2013)
- [Sparse Popularity Adjusted Stochastic Block Model](https://mlsanity.com/paper/1910.01931/) (2019)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)

## Built on by (most cited first, 4 of 4)

- [Fitting Low-rank Models on Egocentrically Sampled Partial Networks](https://mlsanity.com/paper/2303.11230/) (2023)
- [A Transfer Learning Framework for Multilayer Networks via Model Averaging](https://mlsanity.com/paper/2506.12455/) (2025)
- [Simultaneous estimation of connectivity and dimensionality in samples of networks](https://mlsanity.com/paper/2508.12483/) (2025)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)

## Abstract (arXiv)

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suffers from model misspecification or relies on additional model selection procedures that are not well understood in theory and can potentially be unstable in practice. To address this difficulty, we propose a mixing strategy that leverages available arbitrary models to improve their individual performances. The proposed method is computationally efficient and almost tuning-free; thus, it can be used as an off-the-shelf method for network modeling. We show that the proposed method performs equally well as the oracle estimate when the true model is included as individual candidates. More importantly, the method remains robust and outperforms all current estimates even when the models are misspecified. Extensive simulation examples are used to verify the advantage of the proposed mixing method. Evaluation of link prediction performance on 385 real-world networks from six domains also demonstrates the universal competitiveness of the mixing method across multiple domains.