# Multiresolution Analysis and Statistical Thresholding on Dynamic Networks

arXiv: https://arxiv.org/abs/2506.01208 · HTML: https://mlsanity.com/paper/2506.01208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 22 of 22)

- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [The multilayer random dot product graph](https://mlsanity.com/paper/2007.10455/) (2020)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach](https://mlsanity.com/paper/1308.0723/) (2013)
- [Mutually exciting point process graphs for modelling dynamic networks](https://mlsanity.com/paper/2102.06527/) (2021)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs](https://mlsanity.com/paper/2302.01204/) (2023)
- [A tensor factorization model of multilayer network interdependence](https://mlsanity.com/paper/2206.01804/) (2022)
- [Optimal network online change point localisation](https://mlsanity.com/paper/2101.05477/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Tensorial and bipartite block models for link prediction in layered networks and temporal networks](https://mlsanity.com/paper/1803.01616/) (2018)
- [Multimodal urban mobility and multilayer transport networks](https://mlsanity.com/paper/2111.02152/) (2021)
- [Link prediction in dynamic networks using random dot product graphs](https://mlsanity.com/paper/1912.10419/) (2019)
- [Gaussian Embedding of Temporal Networks](https://mlsanity.com/paper/2405.17253/) (2024)
- [Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation](https://mlsanity.com/paper/1803.11202/) (2018)
- [PCA for Point Processes](https://mlsanity.com/paper/2404.19661/) (2024)
- [Online Bayesian changepoint detection for network Poisson processes with community structure](https://mlsanity.com/paper/2407.04138/) (2024)
- [Wavelet Spectra for Multivariate Point Processes](https://mlsanity.com/paper/1908.02634/) (2019)

## Built on by (most cited first, 1 of 1)

- [Non-Negative Matrix Factorization for Event Data](https://mlsanity.com/paper/2606.06205/) (2026)

## Abstract (arXiv)

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and the statistical stability of the extracted features. Despite this tradeoff, reminiscent of time-frequency tradeoffs in signal processing, most methods rely on a fixed temporal resolution. Choosing an appropriate resolution parameter is typically difficult and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales. We address this challenge by proposing ANIE (Adaptive Network Intensity Estimation), a multi-resolution framework designed to automatically identify the time scales at which network structure evolves, enabling the joint detection of both rapid and gradual changes. Modeling interactions as Poisson processes, our method proceeds in two steps: (1) estimating a low-dimensional subspace of node behavior, and (2) deriving a set of novel empirical affinity coefficients that quantify change in interaction intensity between latent factors and support statistical testing for structural change across time scales. We provide theoretical guarantees for subspace estimation and the asymptotic behavior of the affinity coefficients, enabling model-based change detection. Experiments on synthetic networks show that ANIE adapts to the appropriate time resolution and is able to capture sharp structural changes while remaining robust to noise. Furthermore, applications to real-world data showcase the practical benefits of ANIE's multiresolution approach to detecting structural change over fixed resolution methods.