Title: Multiresolution Analysis and Statistical Thresholding on Dynamic Networks
Venue: NeurIPS 2025
Accepted: yes
Keywords: Dynamic Networks

Multiresolution Analysis

Changepoint Detection
Abstract: 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 \emph{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 ($\textbf{A}$daptive $\textbf{N}$etwork $\textbf{I}$ntensity $\textbf{E}$stimation), 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 measure 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.
    An open-source implementation of the method is available at [https://github.com/aida-ugent/anie].


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel method for change detection in evolving graphs. The main goal of the approach is to provide the flexibility to be able to capture both highly localized changes, which might correspond to bursts in time, as well as broader changes. The authors introduce a time-continuous model that they call COSIP (Common Subspace Independent Processes), which is based on a shared subspace and a time-dependent affinity function, which captures the time-dependent changes. Given this theoretical model, detecting changes in the network structure can then be reduced to extracting the temporal features of the matrix-valued affinity function. The authors thus provide a practical algorithm for estimating the two components of their model from data, and provide theoretical consistency guarantees for their estimators. One nice feature of this model is that it is quite flexible and, for example, the basis can be chosen depending on the specific scenario. Finally, the authors also show experimental evidence that their model produces meaningful results in both synthetic and real-world scenarios, by comparing their resulting method against different baselines.\n\nSTRENGTHS AND WEAKNESSES:\nFirst, I should say that I am not an expert in this domain and therefore it is not easy for me to judge the novelty or scope of the contribution of this paper. From my perspective, the main strength of the method is the rigorous model behind the approach, which, as the authors highlight, combines robustness against high-frequency noise, together with the ability to meaningfully capture even rapid temporal changes. In addition, the flexibility of the model (with the ability to choose the basis) and the theoretical analysis, including consistency guarantees are all strengths of the proposed approach.\n\n1. The main weakness is probably the relatively weak experimental evaluation and inconsistent choice of baselines. This includes:\nThe key comparisons in Figure 2 seem to only be given in a qualitative manner. There is no quantitative evaluation against IPP-Hist and IPP-KDE which are the two closest baselines.\n2. The evaluation on real data (Section 5.2) is given against the Laplacian Anomaly Detection (LAD) baseline and not against IPP-Hist baselines. This is somewhat strange, since LAD is now over 15 years old, so comparing *only* against such a baseline is very limiting.\n\n\nI also have questions about the novelty and relation to prior work mentioned in the Questions section. Generally speaking, the lack of consistency of the baselines against which the method, and the exposition which (at least to a non-expert like myself) does not make it entirely clear which exact components are new and which ones are borrowed from existing works, be a limitation of the proposed approach.\n\nQUESTIONS:\n1. As a non-expert in this domain, I was surprised to see that, as the authors mentioned, “Note that, IPP-Hist is equivalent to Anie with Haar wavelet without thresholding”. I feel that this should have been mentioned earlier on, when describing the theoretical model, which is presented without any prior background. The authors do mention that the model extends the COSIE model [3] but do not reference IPP-Hist\n2. Since the model provided by the authors is an extension of the COSIE model, I would expect a comparison against that baseline in the experimental section. Why did the authors choose not to include such a comparison?\n3. I’m also wondering to what extent the assumption that the basis is shared (time-independent) in the model is realistic? I would imagine that in some datasets, there can be slow time-dependent changes that alter the entire global structure of the graph and those cannot be meaningfully captured by a universal basis, unless the size of the basis is very large. Have the authors witnessed such a scenario?\n\nLIMITATIONS:\nYes, the authors discuss the limitations of the proposed approach in Section 6 of the paper. They mention that one limitation is the method's reliance on variance estimation for Z-score computation, which may compromise thresholding robustness, especially at high resolutions. While this highlights one particular limitation, I am also wondering about the generality and applicability of the proposed theoretical model, which would be worth discussing as well.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a point-process based dynamic network modeling approach, which models the temporal network at the scale of nodes. Moreover, the wavelet signal decomposition is transferred to deal with the local changes in the intensity functions. The theoretical analysis is provided to demonstrate the consistentcy of subspace estimation and experiments as well as case studies are conducted to evluate the performance of the proposed method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The proposed method shows the adaptability to the time resolution of dynamic network and offers an subspace decomposition approach for low-rank computing.\n2. Wavelet is introduced to network dynamic analysis.\n3. The experiments on synthetic data and real data demonstrate the effectiveness of the proposed method, especially on precisely change-dynamics fitting.\n\nWeaknesses:\n1. The evaluation is limited to single change-point synthetic networks and one real-world networks. More datasets e.g., Enron email networks and Reddit that  include multiple change-points will improve the comprehensive performance evaluation of the proposed method.\n2. Quantitative measuring the success of hitting the change points and how much the method accurately identify the change points for multiple change-point case are required, besides the visualization of the results, e.g., Adjusted F1.\n3. Incorporating additional baseline methods will strengthen the comparative analysis, such as the representation learning/network comparsion based methods and time window base methods (as mentioned in the paper).\n\nQUESTIONS:\n1）Is  the proposed method capable of online change-point detection?\n2)  In implementing the comparison method LDA,  does you perform the optimal-parameter search?\n3)  It is hard to see the degree of agreement between the predicted change-point and the ground truth  in Fig.3(b).\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper proposes ANIE (Adaptive Network Intensity Estimation), a multi-resolution framework designed to detect changes in dynamic networks across multiple temporal resolutions, including both rapid and gradual changes. The method is tested on synthetic and real-world datasets and shows improved performance over selected baselines.

STRENGTHS AND WEAKNESSES:
Strength:
ANIE effectively captures network changes at multiple temporal scales and demonstrates good empirical performance across diverse datasets.

Weakness:
The method assumes a fixed cross-sectional structure $U$, which may limit its applicability in real scenarios, and lacks discussion of false alarm or miss detection probabilities under multiple testing.

QUESTIONS:
Can the method be extended to settings where the cross-sectional structure $U$ also evolves over time, such as dynamic community structures?

Are there any theoretical guarantees or approximation-based discussions for controlling false alarm or miss detection probabilities under the multiple testing framework?

In addition to the baseline LAD method used for comparison, there appear to be other change-detection approaches, such as the statistics used in Ref [43] and related works; comparison with these methods—both empirically and conceptually—would strengthen the paper from a change-detection perspective.

Line 240 typo: should be "conservative."

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nFor the problem of detecting structural changes in dynamic network data, the authors propose a multi-resolution framework called ANIE (Adaptive Network Intensity Estimation). Instead of binning over fixed time intervals and comparing changes in graph structure, ANIE models interactions as Poisson processes by estimating a low-dimension subspace for node behavior, and then quantifying change in node behavior using empirical affinity coefficients. This allows for detection of both rapid and gradual changes, without static time binning.\n\nThe first stage of ANIE uses truncated SVD over empirical coefficients to estimate a global subspace matrix Subsequently, these are denoised through statistical thresholding. The empirical affinity coefficient are computed by combining node pair coefficients weighted by latent factor affinity. \n\nThe authors conduct empirical analysis using synthetically constructed networks, following Erdos-Renyi approach and stochastic block models and on real world UCI messages data. The proposed approach effectively captures perturbations of underlying intensity across various temporal resolutions, demonstrating robustness to noise.\n\nSTRENGTHS AND WEAKNESSES:\nThe work is well written, the methodology is sound and the problem is well motivated. The experiments are conducted on a mix of synthetic and real world datasets and support the claims. The experiments are somewhat limited and could be made stronger with more network datasets.\n\nQUESTIONS:\n1. Elaborate in more detail on statistical thresholding for denosing.\n\n2. More empirical analysis on an expanded set of graph network datasets.\n\n3. The section on computational efficiency is relevant but short and vague. Please refine \"For a number of nodes below a few thousands, our method runs in a few seconds on a standard laptop.\" to provide more specific details of configurations and results.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}