# Nonparametric estimation of time-varying network connections by multi-stage smoothing

arXiv: https://arxiv.org/abs/2605.06862 · HTML: https://mlsanity.com/paper/2605.06862/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 20 of 20)

- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [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)
- [Dynamic stochastic blockmodels for time-evolving social networks](https://mlsanity.com/paper/1403.0921/) (2014)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Spectral clustering in the dynamic stochastic block model](https://mlsanity.com/paper/1705.01204/) (2017)
- [Change Point Estimation in a Dynamic Stochastic Block Model](https://mlsanity.com/paper/1812.03090/) (2018)
- [Sparse and Smooth: improved guarantees for Spectral Clustering in the Dynamic Stochastic Block Model](https://mlsanity.com/paper/2002.02892/) (2020)
- [Euclidean mirrors and dynamics in network time series](https://mlsanity.com/paper/2205.06877/) (2022)
- [Mixed-Effect Time-Varying Network Model and Application in Brain Connectivity Analysis](https://mlsanity.com/paper/1806.03829/) (2018)
- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [Two-way sparsity for time-varying networks, with applications in genomics](https://mlsanity.com/paper/1802.08114/) (2018)
- [Latent process models for functional network data](https://mlsanity.com/paper/2210.07491/) (2022)
- [Autoregressive Networks](https://mlsanity.com/paper/2010.04492/) (2020)
- [Penalized Network Cross-Validation for Nested Models by Edge-Sampling](https://mlsanity.com/paper/2506.14244/) (2025)
- [GRAND: Graph Release with Assured Node Differential Privacy](https://mlsanity.com/paper/2507.00402/) (2025)
- [Generalized Bayesian Inference for Dynamic Random Dot Product Graphs](https://mlsanity.com/paper/2509.19748/) (2025)

## Abstract (arXiv)

We consider the problem of estimating the underlying edge probabilities of a time-varying network observed at multiple time points. The probability structure is represented by a time-varying graphon that satisfies temporal H"older smoothness and piecewise Lipschitz conditions in the latent variables. We propose a multi-stage smoothing estimator that first applies temporal local smoothing to each edge and then performs node-domain smoothing using a data-driven neighborhood construction adapted from the method. An additional temporal smoothing step is introduced as an optional refinement when uniform accuracy over the entire time domain is required. Simulation studies demonstrate the benefits of combining temporal and node-domain smoothing under different generative models. We also apply the method to a real time-varying network dataset and show that it captures both smooth temporal evolution and structural patterns in the connectivity.