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Multiresolution Analysis and Statistical Thresholding on Dynamic Networks
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Proposes ANIE, a multiresolution Haar-wavelet framework that estimates a low-rank subspace of node behavior from dynamic networks modeled as Poisson processes and uses thresholded empirical affinity coefficients to detect structural changes at multiple time scales.
Problem
Detecting structural change in dynamic networks requires choosing a fixed time-binning resolution, which trades temporal localization against statistical stability; fixed-resolution methods fail when changes occur at multiple time scales.
Approach
Model edge interactions as inhomogeneous Poisson processes under a low-rank COSIP model, estimate node subspace by truncated SVD of wavelet-projected counts (UASE-style), then compute empirical affinity coefficients per wavelet coefficient and apply z-score tests with Benjamini-Hochberg FDR control to denoise the intensity across scales.
Key results
- On synthetic ER-blocks and SBM networks, ANIE-Haar achieves lower intensity-estimation MISE than IPP-Hist and IPP-KDE, avoiding spurious oscillations in flat regions while localizing sharp changes.
- On the UCI Messages dataset, ANIE's multiscale scores identify the end-of-spring-term (day 60) and start-of-fall-term (day 150) structural changes, with the day-150 event not visible in raw message counts.
- Fitting time is reported as quadratic in number of nodes and exponential in the number of resolution levels J; experiments run on a MacBook Air M1 with 8GB RAM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ANIE-Haar instead of fixed-resolution IPP estimators | Synthetic ER-blocks · ER-blocks | MISE | Helped |
| Use ANIE instead of fixed-resolution IPP estimators | Synthetic SBM · SBM | intensity estimation error | Helped |
| Use multiresolution ANIE anomaly scores instead of fixed-resolution Tensorsplat scores | UCI Messages anomaly detection · UCI Messages | structural change detection | Helped |
| Apply statistical thresholding to the linear estimator (ablation) | ANIE · Simplified SBM | estimation error | Helped |
| Increase the number of Haar resolution levels J in the linear estimator (ablation) | ANIE linear estimator · Simplified SBM | estimation error | Hurt |
Surprising findings
- Tensorsplat's anomaly score largely tracks raw message volume, whereas ANIE detects a change not visible in message counts.
Limitations
- Variance estimation for z-scores is sensitive, especially at high resolutions.
- Fitting time grows exponentially with number of wavelet levels J.
- Only the Haar basis is explored in experiments; alternative bases and thresholding schemes are left for future work.
Experimental setup
Datasets: UCI Messages London Bike (TfL) 2017 trips
Benchmarks: UCI Messages
Metrics: MISE anomaly score time series comparison
Baselines: IPP-Hist IPP-KDE Laplacian Anomaly Detection (LAD) Tensorsplat
Builds on: COSIE UASE IPP
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