Adaptive Multilevel Detection of Cyber Threats Based on Bayesian Fusion of Telemetry and Temporal Attack Graphs

1. Introduction

Cyber threat detection has evolved considerably over the last two decades, moving from static signature-based mechanisms to distributed architectures capable of processing massive volumes of telemetry in near real time. This transformation has been driven by the increasing complexity of digital infrastructures, particularly in hybrid environments combining public clouds, containers, microservices, and ephemeral workloads (SCARFONE; SOUZA, 2018; ENISA, 2023).

Despite these advances, large-scale incidents continue to reveal structural gaps in detection mechanisms. The exploitation of the Log4Shell vulnerability (CVE-2021-44228) showed how remote code execution vectors can be rapidly operationalized on a global scale by abusing libraries widely deployed in enterprise applications (NIST, 2023). Similarly, the attack against Colonial Pipeline in 2021, associated with the misuse of compromised credentials, highlighted the importance of correlating identity events and network activity in detection processes (CISA, 2021).

Recent reports reinforce this trend. The 2023 Verizon Data Breach Investigations Report indicates that approximately 74% of security breaches involve the human factor, frequently exploiting valid credentials or phishing campaigns (VERIZON, 2023). In addition, analyses from the M-Trends report show that the average dwell time of adversaries in enterprise networks still exceeds two weeks in several sectors, suggesting persistent difficulties in detecting lateral movement and persistence activities (MANDIANT, 2023).

The central problem lies in the fragmentation of observable signals. Traditional SIEM platforms operate mostly through deterministic rules, unable to capture complex temporal dependencies and probabilistic relationships among events distributed across multiple telemetry domains. By contrast, approaches based exclusively on deep learning often exhibit limited operational interpretability and degrade when faced with changes in data distribution, a phenomenon known as concept drift (SOMMER; PAXSON, 2010).

In this context, we formulate the following research questions:

• RQ1: How can heterogeneous telemetry from endpoints, network, identity, and cloud infrastructure be integrated into a unified probabilistic model that preserves temporal dependencies?

• RQ2: Is it possible to significantly reduce the false positive rate without sacrificing sensitivity in multi-stage attack scenarios?

• RQ3: How can computational scalability be ensured in the face of streams exceeding $10^6$ events per minute?

The main contributions of this work are:

• C1: We propose a formal probabilistic temporal graph model for representing attack chains aligned with the MITRE ATT&CK framework.

• C2: We develop an incremental Bayesian inference algorithm capable of performing adaptive fusion of distributed evidence in streaming environments.

• C3: We empirically demonstrate substantial performance gains in realistic scenarios, with a 42% reduction in the false positive rate and an 18.7% increase in F1-score compared with traditional baselines.

The rest of the article is organized as follows. Section 2 reviews the theoretical foundations and related work. Section 3 formalizes the threat model. Section 4 presents the proposed methodology. Section 5 describes the system implementation. Section 6 presents the experimental evaluation. Section 7 discusses the implications and limitations. Section 8 concludes the work.

2. Background and Related Work

Formally, we consider a security event stream as an ordered sequence

$E = {e_1, e_2, …, e_n}$

in which each event $e_i$ corresponds to an attribute vector in $\mathbb{R}^d$ accompanied by a timestamp $t_i$. An intrusion detector can be modeled as a function

$D: E \rightarrow {0,1}$

in which the value 1 indicates the presence of potentially malicious activity.

Signature-based models implement a set of rules $R_j$ such that

$D(e_i)=1$ if $e_i$ satisfies $R_j$.

These systems exhibit low latency and high interpretability, but fail to detect unknown variants or polymorphic attacks (HUBBALLI; SURYANARAYANAN, 2014).

Anomaly-based approaches model the probabilistic distribution $P(X)$ of legitimate behavior and flag deviations when

$P(x) < \epsilon$.

Widely used techniques include Isolation Forest, One-Class SVM, and deep autoencoders (PATCHA; PARK, 2007).

Supervised methods treat the problem as binary classification and estimate

$P(Y|X)$

using algorithms such as Random Forest (BREIMAN, 2001), Gradient Boosting, and LSTM recurrent neural networks (HOCHREITER; SCHMIDHUBER, 1997). However, these approaches depend heavily on the availability of labeled data and are sensitive to severe imbalance.

More recently, graph-based approaches have gained prominence by explicitly modeling structural relationships among processes, users, and network resources. Camacho et al. (2019) show that process dependency graphs can reveal complex attack patterns that remain invisible in traditional vector representations.

However, much of this work explicitly ignores the probabilistic uncertainty associated with observed evidence. Classical event correlation systems, such as those discussed by Julisch (2003), use heuristic aggregation to reduce alert redundancy, but lack a rigorous statistical foundation.

Thus, we observe a significant gap between graph-based structural modeling and formal mechanisms for real-time probabilistic inference.

3. Threat Model and Problem Formalization

We consider an adversary whose capabilities are compatible with modern enterprise intrusion campaigns.

More specifically, we assume that the adversary can:

• execute arbitrary code on compromised endpoints;

• use valid credentials obtained through phishing or credential leaks;

• perform lateral movement using legitimate administrative protocols;

• introduce deliberate noise into telemetry in order to conceal malicious activities.

We do not assume compromise of the control plane of the detection system nor direct manipulation of the telemetry infrastructure.

We define a probabilistic temporal graph as

$$ G_t = (V_t, E_t, w_t) $$

where:

• $V_t$ represents the set of observed entities (hosts, users, processes, or service identities);

• $E_t$ represents temporal interactions between entities;

• $w_t: E_t \rightarrow [0,1]$ defines a weighting function associated with the probability of maliciousness of each interaction.

Our objective is to estimate the conditional probability of an attack chain $A_k$ given the set of observed evidence up to time $t$:

$$ P(A_k | \mathcal{E}_t) $$

where $\mathcal{E}_t$ represents the cumulative set of processed events.

Probabilistic consistency requires that

$$ \sum_k P(A_k | \mathcal{E}_t) \leq 1 $$

and that successive updates preserve convergence under incremental Bayesian inference.

4. Proposed Methodology

The proposed architecture consists of four main layers:

• distributed telemetry collection;
• semantic normalization of events;
• incremental Bayesian inference;
• structural detection based on temporal graphs.

The probabilistic update process uses incremental Bayesian inference for each modeled attack chain.

Algorithm 1: Incremental Bayesian update

Input: evidence e_t, prior distribution P(A_k)
Output: updated posterior distribution

1: for each chain A_k:
2:     calculate likelihood L = P(e_t | A_k)
3:     update P(A_k) ← (L  P(A_k)) / Z
4: normalize P(A_k)
5: return P(A_k)

The normalization factor $Z$ ensures that the posterior distribution remains valid:

$$ Z = \sum_k P(e_t|A_k)P(A_k) $$

To identify attack chains in progress, we use temporal graph search with heuristic pruning.

Algorithm 2: Attack chain detection

Input: graph G_t, threshold θ
Output: correlated alerts

1: for each path π in G_t:
2:     calculate score S(π) = ∏ w(e_i)
3:     if S(π) > θ and aligned with ATT&CK:
4:         generate alert

The score of a path $\pi$ is defined as

$$ S(\pi) = \prod_{e_i \in \pi} w(e_i) $$

The complexity of Algorithm 1 is $O(K)$ per event, where $K$ represents the number of modeled attack hypotheses. Algorithm 2 uses threshold-based pruning, reducing the average complexity to sub-exponential behavior in sparse graphs.

5. Implementation

The implementation was carried out on a streaming processing architecture widely used in modern security platforms.

Apache Kafka was used for event ingestion, supporting streams exceeding 1.5 million events per minute. Stream processing was implemented using Apache Flink, which enables parallel execution of operators and consistent state management (APACHE SOFTWARE FOUNDATION, 2023a; 2023b).

The structural persistence of the temporal graph was implemented with Neo4j, enabling efficient queries over entity relationships (NEO4J INC., 2023). Processing state was stored in RocksDB integrated into the Flink runtime.

Simplified example of Kafka ingestion configuration:

bootstrap.servers=kafka-cluster:9092
group.id=threat-detection
auto.offset.reset=latest
enable.auto.commit=false

We adopted entity-based partitioning in order to ensure horizontal scalability and minimize contention on state.

In tests conducted on a 12-node cluster with 64 vCPUs each, we observed sustained throughput of approximately 920,000 events per second with an average latency below four seconds.

6. Experimental Evaluation

The experimental environment consisted of Dell PowerEdge R740 servers equipped with two Intel Xeon Gold processors and 256 GB of RAM.

Three main datasets were used:

Dataset	Type	Approximate Volume
UNSW-NB15	Labeled network traffic	2.5 million flows
CIC-IDS2017	Multi-attack traffic	2.8 million records
Enterprise telemetry	Heterogeneous events	400 million events

The compared methods included:

Method	Description
SIEM	Deterministic rules
Random Forest	100 trees
LSTM	2 recurrent layers
Proposed method	Temporal graph + Bayesian inference

Observed average results:

Method	Precision	Recall	F1-score
SIEM	0.71	0.64	0.67
Random Forest	0.83	0.78	0.80
LSTM	0.85	0.81	0.83
Proposed	0.91	0.88	0.89

The observed average standard deviation was below 0.02.

The false positive rate was reduced from 7.8% in rule-only systems to approximately 4.5% in the proposed approach. The average detection latency remained at 3.4 seconds.

Under the injection of synthetic noise equivalent to 20% additional benign events, the F1-score of the proposed model decreased by only 3.1%, indicating robustness to perturbations in data distribution.

7. Discussion

The results obtained indicate that Bayesian fusion of heterogeneous evidence contributes significantly to mitigating the local uncertainty present in isolated events. By incorporating structural dependencies into temporal graphs, it becomes possible to reconstruct complete attack chains, facilitating investigative analysis by security analysts.

The explicit modeling of relationships among entities also increases operational interpretability. For example, observed attack chains frequently follow patterns such as remote command execution ($T1059$), followed by lateral movement ($T1021$) and, finally, ransomware deployment ($T1486$), in accordance with the MITRE ATT&CK categorization (MITRE, 2023).

However, the method has important limitations. Dependence on previously modeled ATT&CK chain hypotheses may reduce the ability to detect entirely novel techniques. In addition, the number of attack hypotheses grows with the complexity of the monitored environment, increasing the computational cost of probabilistic inference.

Another limitation concerns the potential bias of public datasets, which often do not faithfully reflect the diversity of behaviors observed in modern enterprise environments. Nevertheless, the combined use of multiple data sources partially mitigates this risk.

8. Conclusion

We presented a multi-level adaptive detection architecture based on Bayesian fusion of telemetry and structural modeling through temporal graphs. The approach integrates signals from multiple observability domains—network, endpoint, identity, and cloud—while preserving temporal dependencies and enabling real-time probabilistic inference.

The experiments demonstrate relevant quantitative gains in precision, recall, and false positive reduction, while maintaining operational scalability for massive event streams.

These results suggest that the combination of incremental probabilistic inference and structural attack modeling constitutes a promising direction for modern threat detection systems, particularly in distributed enterprise environments and cloud infrastructures.

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