Interpretable Social Network Churn Prediction via Ergodic Markov Chains
Abstract
Predicting social network churn before it becomes visible in aggregate metrics remains an open challenge, particularly in enterprise settings where heterogeneous usage patterns, sparse data, and deployment constraints preclude standard supervised approaches. We formalize this problem as finite-step engagement projection over contributor-role Markov chains, with a stationary-distribution interpretation for ergodic chains in the long-run limit. For each engagement feature type within a network (e.g., Q&A, communities, articles, etc.), users are classified monthly into four behavioral states and a transition matrix is estimated from six months of history. Six-step propagation yields a label-free projection of the contributor mix; for ergodic chains, the Perron-Frobenius theorem establishes convergence under repeated propagation. Comparing projected future engagement to current engagement produces the Health Ratio, a single score requiring no trained model, no labels, and no infrastructure beyond SQL. Validated across seven rolling prediction windows on 11,500+ tenant-level networks, the Health Ratio achieves mean AUC 0.917 with a 156 times churn-rate gradient across risk tiers, outperforming all single-signal baselines and the growth-adjusted variant previously deployed in production. An ablation study shows that six-step propagation achieves similar churn discrimination to the eigenvector-based score. Deployed on Microsoft Engage since October 2025, the framework powers customer health monitoring and has enabled proactive intervention on at-risk networks before decline becomes visible in traditional metrics.
Related
- On the existence of a spectral gap for ergodic Markov chains
- On the Information Bottleneck for Ergodic Finite-State Markov Chains: Stationary Approximation and Asymptotic Optimality
- Ergodic and Metastable Behavior of Stochastic Popularity Dynamics in Social Networks
- Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction
- Asymptotics and finite sample bounds for prediction and smoothing in Wright-Fisher hidden Markov models
BibTeX
@misc{mcquistion2026interpretable,
title = {{Interpretable Social Network Churn Prediction via Ergodic Markov Chains}},
author = {Matthew McQuistion and Siddhartha Sharan and Afia Zaheer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05252},
eprint = {2611.05252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05252},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interpretable Social Network Churn Prediction via Ergodic Markov Chains
AU - Matthew McQuistion
AU - Siddhartha Sharan
AU - Afia Zaheer
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05252
UR - https://arxiv.org/abs/2611.05252
AB - Predicting social network churn before it becomes visible in aggregate metrics remains an open challenge, particularly in enterprise settings where heterogeneous usage patterns, sparse data, and deployment constraints preclude standard supervised approaches. We formalize this problem as finite-step engagement projection over contributor-role Markov chains, with a stationary-distribution interpretation for ergodic chains in the long-run limit. For each engagement feature type within a network (e.g., Q&A, communities, articles, etc.), users are classified monthly into four behavioral states and a transition matrix is estimated from six months of history. Six-step propagation yields a label-free projection of the contributor mix; for ergodic chains, the Perron-Frobenius theorem establishes convergence under repeated propagation. Comparing projected future engagement to current engagement produces the Health Ratio, a single score requiring no trained model, no labels, and no infrastructure beyond SQL. Validated across seven rolling prediction windows on 11,500+ tenant-level networks, the Health Ratio achieves mean AUC 0.917 with a 156 times churn-rate gradient across risk tiers, outperforming all single-signal baselines and the growth-adjusted variant previously deployed in production. An ablation study shows that six-step propagation achieves similar churn discrimination to the eigenvector-based score. Deployed on Microsoft Engage since October 2025, the framework powers customer health monitoring and has enabled proactive intervention on at-risk networks before decline becomes visible in traditional metrics.
ER -