# Stacking Models for Nearly Optimal Link Prediction in Complex Networks

arXiv: https://arxiv.org/abs/1909.07578 · HTML: https://mlsanity.com/paper/1909.07578/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 30 of 35)

- [Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network](https://mlsanity.com/paper/2210.00881/) (2022)
- [Bayesian hierarchical stacking: Some models are (somewhere) useful](https://mlsanity.com/paper/2101.08954/) (2021)
- [Universal Link Predictor By In-Context Learning on Graphs](https://mlsanity.com/paper/2402.07738/) (2024)
- [Mixture of Link Predictors on Graphs](https://mlsanity.com/paper/2402.08583/) (2024)
- [Quantifying Spatial Homogeneity of Urban Road Networks via Graph Neural Networks](https://mlsanity.com/paper/2101.00307/) (2021)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [The Implications of the No-Free-Lunch Theorems for Meta-induction](https://mlsanity.com/paper/2103.11956/) (2021)
- [Diffusion Source Identification on Networks with Statistical Confidence](https://mlsanity.com/paper/2106.04800/) (2021)
- [Causal Lifting and Link Prediction](https://mlsanity.com/paper/2302.01198/) (2023)
- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [Link Prediction with Contextualized Self-Supervision](https://mlsanity.com/paper/2201.10069/) (2022)
- [Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths](https://mlsanity.com/paper/2112.00183/) (2021)
- [Social learning spontaneously emerges by searching optimal heuristics with deep reinforcement learning](https://mlsanity.com/paper/2204.12371/) (2022)
- [The maximum capability of a topological feature in link prediction](https://mlsanity.com/paper/2206.15101/) (2022)
- [Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection](https://mlsanity.com/paper/2210.09186/) (2022)
- [Variational Disentangled Graph Auto-Encoders for Link Prediction](https://mlsanity.com/paper/2306.11315/) (2023)
- [Entity Insertion in Multilingual Linked Corpora: The Case of Wikipedia](https://mlsanity.com/paper/2410.04254/) (2024)
- [Generating Human Understandable Explanations for Node Embeddings](https://mlsanity.com/paper/2406.07642/) (2024)
- [Systematic assessment of the quality of fit of the stochastic block model for empirical networks](https://mlsanity.com/paper/2201.01658/) (2022)
- [GRASP: Accelerating Shortest Path Attacks via Graph Attention](https://mlsanity.com/paper/2310.07980/) (2023)
- [Transfer Learning for Temporal Link Prediction](https://mlsanity.com/paper/2504.10925/) (2025)
- [Node metadata can produce predictability transitions in network inference problems](https://mlsanity.com/paper/2103.14424/) (2021)
- [Generalized Reciprocal Perspective](https://mlsanity.com/paper/2210.11616/) (2022)
- [Fitting Low-rank Models on Egocentrically Sampled Partial Networks](https://mlsanity.com/paper/2303.11230/) (2023)
- [Disentangling Node Attributes from Graph Topology for Improved Generalizability in Link Prediction](https://mlsanity.com/paper/2307.08877/) (2023)
- [A Review of Link Prediction Applications in Network Biology](https://mlsanity.com/paper/2312.01275/) (2023)
- [Towards understanding evolution of science through language model series](https://mlsanity.com/paper/2409.09636/) (2024)
- [A Transfer Learning Framework for Multilayer Networks via Model Averaging](https://mlsanity.com/paper/2506.12455/) (2025)
- [Directed Link Prediction using GNN with Local and Global Feature Fusion](https://mlsanity.com/paper/2506.20235/) (2025)
- [Meta-learning optimizes predictions of missing links in real-world networks](https://mlsanity.com/paper/2508.09069/) (2025)

## Abstract (arXiv)

Most real-world networks are incompletely observed. Algorithms that can accurately predict which links are missing can dramatically speedup the collection of network data and improve the validity of network models. Many algorithms now exist for predicting missing links, given a partially observed network, but it has remained unknown whether a single best predictor exists, how link predictability varies across methods and networks from different domains, and how close to optimality current methods are. We answer these questions by systematically evaluating 203 individual link predictor algorithms, representing three popular families of methods, applied to a large corpus of 548 structurally diverse networks from six scientific domains. We first show that individual algorithms exhibit a broad diversity of prediction errors, such that no one predictor or family is best, or worst, across all realistic inputs. We then exploit this diversity via meta-learning to construct a series of "stacked" models that combine predictors into a single algorithm. Applied to a broad range of synthetic networks, for which we may analytically calculate optimal performance, these stacked models achieve optimal or nearly optimal levels of accuracy. Applied to real-world networks, stacked models are also superior, but their accuracy varies strongly by domain, suggesting that link prediction may be fundamentally easier in social networks than in biological or technological networks. These results indicate that the state-of-the-art for link prediction comes from combining individual algorithms, which achieves nearly optimal predictions. We close with a brief discussion of limitations and opportunities for further improvement of these results.