# Efficient Estimation for Longitudinal Networks via Adaptive Merging

arXiv: https://arxiv.org/abs/2211.07866 · HTML: https://mlsanity.com/paper/2211.07866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [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)
- [Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization](https://mlsanity.com/paper/2103.08895/) (2021)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Multiple Change-point Detection: a Selective Overview](https://mlsanity.com/paper/1512.04093/) (2015)
- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Community Detection in General Hypergraph via Graph Embedding](https://mlsanity.com/paper/2103.15035/) (2021)
- [A semiparametric extension of the stochastic block model for longitudinal networks](https://mlsanity.com/paper/1512.07075/) (2015)
- [Latent Space Models for Dynamic Networks with Weighted Edges](https://mlsanity.com/paper/2005.08261/) (2020)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Spectral clustering via adaptive layer aggregation for multi-layer networks](https://mlsanity.com/paper/2012.04646/) (2020)

## Abstract (arXiv)

Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.