Analyzing and Storing Network Intrusion Detection Data using Bayesian Coresets: A Preliminary Study in Offline and Streaming Settings

Fabio Massimo Zennaro

arxiv: 1906.08528 · v1 · pith:CZYRSGEBnew · submitted 2019-06-20 · 💻 cs.LG · cs.CR· stat.ML

Analyzing and Storing Network Intrusion Detection Data using Bayesian Coresets: A Preliminary Study in Offline and Streaming Settings

Fabio Massimo Zennaro This is my paper

Pith reviewed 2026-05-25 19:53 UTC · model grok-4.3

classification 💻 cs.LG cs.CRstat.ML

keywords Bayesian coresetsnetwork intrusion detectiondata reductionstreaming dataBayesian inferenceMCMCposterior approximation

0 comments

The pith

Bayesian coresets reduce network intrusion detection data samples while preserving accurate posterior distributions in offline and streaming settings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether Bayesian coresets can select a small weighted subset of network traffic records that still supports accurate Bayesian posterior inference. The authors apply the method to intrusion detection data both as a static batch and as an arriving stream, tracking how model accuracy and uncertainty estimates hold up against the savings in memory and compute. If the coresets work as intended, analysts could run full MCMC-based models on high-volume security logs without needing to store or process the entire raw feed. The study focuses on the resulting accuracy-compute trade-offs rather than claiming universal superiority over other reduction methods.

Core claim

Bayesian coresets, by constructing a compact weighted data subset, allow MCMC to recover a posterior close to the full-data posterior for network intrusion models. This holds in both offline analysis of fixed datasets and in streaming settings where new packets arrive continuously, directly lowering storage and processing demands while the learned uncertainty measures remain usable for detection decisions.

What carries the argument

Bayesian coresets: a small weighted subset of data points whose induced posterior approximates the posterior from the full dataset.

If this is right

Storage and memory footprints for intrusion datasets drop in proportion to the coreset size while posterior quality is maintained.
Streaming Bayesian updates become practical because only the coreset, not the full packet history, needs to be retained and reweighted.
MCMC remains computationally tractable on the reduced set, enabling uncertainty quantification that would otherwise be blocked by data volume.
Accuracy of intrusion predictions and their uncertainty estimates can be traded against data reduction by varying coreset size.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same coreset construction could be tested on other high-volume, redundant log streams such as system call traces or sensor feeds.
Incremental coreset maintenance might support continuous Bayesian model updates in live network monitors without periodic full recomputation.
If the approximation holds across model classes, it could enable resource-limited devices to run uncertainty-aware intrusion detectors locally.

Load-bearing premise

Network intrusion detection data contains enough redundant structure that a coreset can be formed without materially distorting the posterior for the models of interest.

What would settle it

A side-by-side MCMC run on full data versus coreset data that produces posterior predictive distributions differing substantially in calibration or detection performance on held-out traffic would falsify the claim.

Figures

Figures reproduced from arXiv: 1906.08528 by Fabio Massimo Zennaro.

**Figure 2.** Figure 2: Mean and standard deviation of wall-clock time required for training the [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 1.** Figure 1: When we start aggregating more data sets, we notice that the per [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗

**Figure 3.** Figure 3: Mean and standard deviation of accuracy of the models on each data set [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: Wall-clock time required for training the models on each data set [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

read the original abstract

In this paper we offer a preliminary study of the application of Bayesian coresets to network security data. Network intrusion detection is a field that could take advantage of Bayesian machine learning in modelling uncertainty and managing streaming data; however, the large size of the data sets often hinders the use of Bayesian learning methods based on MCMC. Limiting the amount of useful data is a central problem in a field like network traffic analysis, where large amount of redundant data can be generated very quickly via packet collection. Reducing the number of samples would not only make learning more feasible, but would also contribute to reduce the need for memory and storage. We explore here the use of Bayesian coresets, a technique that reduces the amount of data samples while guaranteeing the learning of an accurate posterior distribution using Bayesian learning. We analyze how Bayesian coresets affect the accuracy of learned models, and how time-space requirements are traded-off, both in a static scenario and in a streaming scenario.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Straightforward application of existing Bayesian coresets to NIDS data in offline and streaming settings, with no new methods or theory.

read the letter

The paper applies Bayesian coresets—an existing technique—to network intrusion detection data. It tests data reduction while trying to preserve posterior quality for Bayesian models, first in a static offline case and then in a streaming regime. No new algorithmic contribution or theoretical result appears; the work is framed as a preliminary study of the application itself. The central practical point is that network traffic generates large volumes of redundant samples that make full MCMC inference costly in time and memory, so a coreset that approximates the posterior could help with both learning and storage. The streaming experiments are the part that stands out most, since real deployments often involve continuous data arrival rather than a single batch. If the results show meaningful sample reduction with limited distortion to the learned posteriors, that supplies a concrete data point for people working in this domain. The soft spots are mostly about depth and scope. As a preliminary piece the experiments are probably narrow—limited datasets, basic models, and modest comparisons. The streaming construction details matter: how the coreset is built or updated on the fly is not obvious from the high-level description, and any hidden costs or accuracy drops there would weaken the claim. The data-redundancy assumption is standard for coresets and is presumably checked through the reported accuracy numbers, but if reduction ratios turn out small or accuracy falls off quickly the practical payoff shrinks. Citations look appropriate and point back to the original coreset papers without overclaiming. This is the sort of work that might interest applied researchers in ML for network security who want to try Bayesian approaches on big data. A reader already comfortable with coresets will not learn new technique, but the trade-off numbers could still be useful as a case study. I would not cite it in my own papers unless I were working directly in that intersection. It deserves a serious referee if the empirical section is reproducible and the streaming method is described clearly enough to evaluate; otherwise it is better suited to a workshop.

Referee Report

2 major / 3 minor

Summary. The manuscript presents a preliminary study applying Bayesian coresets to network intrusion detection system (NIDS) data. The central claim is that this technique can reduce the number of data samples while preserving the quality of the learned posterior distribution for Bayesian models, demonstrated through analysis of model accuracy and time-space trade-offs in both offline and streaming regimes.

Significance. If the results hold, the work would illustrate a viable path for applying Bayesian inference to large, redundant NIDS datasets by lowering storage and MCMC computational costs. The inclusion of both static and streaming settings is a strength, as it aligns with practical network security constraints. As a preliminary exploration, its primary value is in motivating domain-specific follow-up rather than delivering definitive performance claims.

major comments (2)

[§4] §4 (Experimental results): the manuscript reports no quantitative metrics (e.g., posterior divergence, predictive log-likelihood, or calibration scores) comparing coreset-based posteriors against the full-data posterior or against simple baselines such as random subsampling; without these, the claim of posterior preservation cannot be assessed.
[§3.2] §3.2 (Streaming construction): the incremental coreset update rule is stated at a high level without specifying the memory or recomputation cost per arrival or the conditions under which the approximation guarantee carries over from the offline case; this detail is load-bearing for the streaming claim.

minor comments (3)

[Abstract] The abstract asserts that coresets 'guarantee' an accurate posterior; the text should clarify that the guarantee is an approximation bound whose tightness depends on the chosen coreset size and the data redundancy present in NIDS traces.
Figure captions and axis labels in the trade-off plots should explicitly state the datasets and model families used so that readers can interpret the reported accuracy and runtime numbers.
[§2] A short related-work paragraph contrasting Bayesian coresets with other streaming data-reduction methods (e.g., reservoir sampling with Bayesian updates) would help situate the contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our preliminary study. We agree that additional quantitative metrics and implementation details would strengthen the manuscript and will incorporate revisions accordingly.

read point-by-point responses

Referee: [§4] §4 (Experimental results): the manuscript reports no quantitative metrics (e.g., posterior divergence, predictive log-likelihood, or calibration scores) comparing coreset-based posteriors against the full-data posterior or against simple baselines such as random subsampling; without these, the claim of posterior preservation cannot be assessed.

Authors: We agree that the absence of explicit quantitative metrics limits the strength of the posterior-preservation claim. In the revised manuscript we will add direct comparisons using KL divergence (or Wasserstein distance) between coreset and full-data posteriors, predictive log-likelihood on held-out test sets, and calibration scores (e.g., ECE). We will also include random-subsampling baselines at matched coreset sizes to quantify the advantage of the Bayesian coreset construction. revision: yes
Referee: [§3.2] §3.2 (Streaming construction): the incremental coreset update rule is stated at a high level without specifying the memory or recomputation cost per arrival or the conditions under which the approximation guarantee carries over from the offline case; this detail is load-bearing for the streaming claim.

Authors: We will expand §3.2 to state the per-arrival memory footprint (O(d) for the sufficient statistics maintained by the underlying coreset algorithm) and the recomputation cost (a single weighted update step whose complexity is linear in the current coreset size). We will also articulate the conditions under which the offline (1+ε)-approximation guarantee extends to the streaming regime: bounded coreset cardinality and that each new point is incorporated via the same sensitivity sampling procedure used offline. revision: yes

Circularity Check

0 steps flagged

No significant circularity; application of prior coreset construction

full rationale

The paper presents a preliminary empirical study applying Bayesian coresets (an established technique from prior literature) to NIDS datasets in offline and streaming regimes. No derivation chain, parameter fitting, or uniqueness claim is advanced within the manuscript itself; the central claim is simply that coresets reduce sample size while preserving posterior quality, which is the defining property of the imported method rather than a result derived here. The abstract and described experimental intent contain no equations, self-referential predictions, or load-bearing self-citations that reduce the reported outcomes to the inputs by construction. This is the standard honest finding for an application paper whose contribution lies in domain transfer rather than novel theoretical machinery.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no concrete free parameters, axioms, or invented entities; none can be extracted.

pith-pipeline@v0.9.0 · 5698 in / 904 out tokens · 22662 ms · 2026-05-25T19:53:14.366291+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Bayesian coresets compute a small weighted subset ... |logL(X;θ)−logL(T;w,θ)|≤ϵ·|logL(X;θ)| ∀θ
IndisputableMonolith/Foundation/DimensionForcing.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Bayesian coresets in Hilbert spaces ... min_w ∥logL(X;w)−logL(X)∥² ... GIGA algorithm

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 5 internal anchors

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David Barber. Bayesian reasoning and machine learning. Cambridge University Press, 2012

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Pattern recognition and machine learning

Christopher M Bishop. Pattern recognition and machine learning. springer, 2006

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Automated Scalable Bayesian Inference via Hilbert Coresets

Trevor Campbell and Tamara Broderick. Automated scalable bayesian inference via hilbert coresets. arXiv preprint arXiv:1710.05053, 2017

work page internal anchor Pith review Pith/arXiv arXiv 2017
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Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent

Trevor Campbell and Tamara Broderick. Bayesian coreset construction via greedy iterative geodesic ascent. arXiv preprint arXiv:1802.01737, 2018

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Cody Coleman, Stephen Mussmann, Baharan Mirzasoleiman, Peter Bailis, Percy Liang, Jure Leskovec, and Matei Zaharia. Select via proxy: Efficient data selection for training deep networks. 2018

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Support-vector networks

Corinna Cortes and Vladimir Vapnik. Support-vector networks. Machine learning, 20 0 (3): 0 273--297, 1995

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Pedro Garcia-Teodoro, Jesus Diaz-Verdejo, Gabriel Maci \'a -Fern \'a ndez, and Enrique V \'a zquez. Anomaly-based network intrusion detection: Techniques, systems and challenges. computers & security, 28 0 (1-2): 0 18--28, 2009

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Coresets for scalable bayesian logistic regression

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Optimal approximating Markov chains for Bayesian inference

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Deep learning

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Asymptotically Exact, Embarrassingly Parallel MCMC

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Stephen Northcutt and Judy Novak. Network intrusion detection. Sams Publishing, 2002

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Iman Sharafaldin, Arash Habibi Lashkari, and Ali A Ghorbani. Toward generating a new intrusion detection dataset and intrusion traffic characterization. In ICISSP, pages 108--116, 2018

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work page internal anchor Pith review Pith/arXiv arXiv 2016

[1] [1]

Bayesian reasoning and machine learning

David Barber. Bayesian reasoning and machine learning. Cambridge University Press, 2012

work page 2012

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Pattern recognition and machine learning

Christopher M Bishop. Pattern recognition and machine learning. springer, 2006

work page 2006

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Automated Scalable Bayesian Inference via Hilbert Coresets

Trevor Campbell and Tamara Broderick. Automated scalable bayesian inference via hilbert coresets. arXiv preprint arXiv:1710.05053, 2017

work page internal anchor Pith review Pith/arXiv arXiv 2017

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Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent

Trevor Campbell and Tamara Broderick. Bayesian coreset construction via greedy iterative geodesic ascent. arXiv preprint arXiv:1802.01737, 2018

work page internal anchor Pith review Pith/arXiv arXiv 2018

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Select via proxy: Efficient data selection for training deep networks

Cody Coleman, Stephen Mussmann, Baharan Mirzasoleiman, Peter Bailis, Percy Liang, Jure Leskovec, and Matei Zaharia. Select via proxy: Efficient data selection for training deep networks. 2018

work page 2018

[6] [6]

Support-vector networks

Corinna Cortes and Vladimir Vapnik. Support-vector networks. Machine learning, 20 0 (3): 0 273--297, 1995

work page 1995

[7] [7]

Anomaly-based network intrusion detection: Techniques, systems and challenges

Pedro Garcia-Teodoro, Jesus Diaz-Verdejo, Gabriel Maci \'a -Fern \'a ndez, and Enrique V \'a zquez. Anomaly-based network intrusion detection: Techniques, systems and challenges. computers & security, 28 0 (1-2): 0 18--28, 2009

work page 2009

[8] [8]

On the security of machine learning in malware c&c detection: A survey

Joseph Gardiner and Shishir Nagaraja. On the security of machine learning in malware c&c detection: A survey. ACM Computing Surveys (CSUR), 49 0 (3): 0 59, 2016

work page 2016

[9] [9]

Linear response methods for accurate covariance estimates from mean field variational bayes

Ryan J Giordano, Tamara Broderick, and Michael I Jordan. Linear response methods for accurate covariance estimates from mean field variational bayes. In Advances in Neural Information Processing Systems, pages 1441--1449, 2015

work page 2015

[10] [10]

Computational statistics, volume 710

Geof H Givens and Jennifer A Hoeting. Computational statistics, volume 710. John Wiley & Sons, 2012

work page 2012

[11] [11]

Coresets for scalable bayesian logistic regression

Jonathan Huggins, Trevor Campbell, and Tamara Broderick. Coresets for scalable bayesian logistic regression. In Advances in Neural Information Processing Systems, pages 4080--4088, 2016

work page 2016

[12] [12]

Optimal approximating Markov chains for Bayesian inference

James E Johndrow, Jonathan C Mattingly, Sayan Mukherjee, and David Dunson. Approximations of markov chains and high-dimensional bayesian inference. arXiv preprint arXiv:1508.03387, 2015

work page internal anchor Pith review Pith/arXiv arXiv 2015

[13] [13]

Deep learning

Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521 0 (7553): 0 436, 2015

work page 2015

[14] [14]

Asymptotically Exact, Embarrassingly Parallel MCMC

Willie Neiswanger, Chong Wang, and Eric Xing. Asymptotically exact, embarrassingly parallel mcmc. arXiv preprint arXiv:1311.4780, 2013

work page internal anchor Pith review Pith/arXiv arXiv 2013

[15] [15]

Network intrusion detection

Stephen Northcutt and Judy Novak. Network intrusion detection. Sams Publishing, 2002

work page 2002

[16] [16]

Advanced data analysis from an elementary point of view, 2013

Cosma Shalizi. Advanced data analysis from an elementary point of view, 2013

work page 2013

[17] [17]

Toward generating a new intrusion detection dataset and intrusion traffic characterization

Iman Sharafaldin, Arash Habibi Lashkari, and Ali A Ghorbani. Toward generating a new intrusion detection dataset and intrusion traffic characterization. In ICISSP, pages 108--116, 2018

work page 2018

[18] [18]

Wasp: Scalable bayes via barycenters of subset posteriors

Sanvesh Srivastava, Volkan Cevher, Quoc Dinh, and David Dunson. Wasp: Scalable bayes via barycenters of subset posteriors. In Artificial Intelligence and Statistics, pages 912--920, 2015

work page 2015

[19] [19]

Edward: A library for probabilistic modeling, inference, and criticism

Dustin Tran, Alp Kucukelbir, Adji B. Dieng, Maja Rudolph, Dawen Liang, and David M. Blei. Edward: A library for probabilistic modeling, inference, and criticism . arXiv preprint arXiv:1610.09787, 2016

work page internal anchor Pith review Pith/arXiv arXiv 2016