Bayesian Networks in Cybersecurity: A Deep Dive into Prior-Knowledge-Informed AI

Introduction: Why Bayesian Networks for Cybersecurity?

Modern Intrusion Detection Systems (IDS) are often machine learning-based and require massive labeled datasets to detect threats. However, cybersecurity is highly dynamic, and zero-day attacks make traditional ML models ineffective.

So how do we detect threats without labeled training data?
The answer lies in Bayesian Networks (BNs)—a probabilistic approach that models uncertainty and learns dynamically.

In this deep dive, we’ll cover:

• Mathematical Foundations of Bayesian Networks
• Why BNs outperform ML-based methods for anomaly detection
• How to implement Bayesian AI for cybersecurity
• Benchmarking Bayesian AI vs. Traditional ML

The Problem with Traditional ML-Based IDS

Most cybersecurity AI models are supervised and trained on datasets like:

• CICIDS2018 (Canadian Institute for Cybersecurity Intrusion Dataset)
• UNSW-NB15 (University of New South Wales Intrusion Dataset)
• DARPA Intrusion Detection Evaluation Data

Problems with Supervised ML-Based IDS:

1. Requires Labeled Data: Needs thousands of attack and normal traffic samples.
2. Fails on Zero-Day Attacks: Cannot detect new threats not seen in training.
3. High False Positives: Struggles with adaptive adversaries and noisy traffic.
4. Retraining Overhead: Needs continuous retraining to stay effective.

Reference:

• A Survey of Machine Learning Techniques for Cybersecurity Intrusion Detection (ScienceDirect)

Bayesian Networks: The Future of AI in Cybersecurity

Unlike traditional ML models, Bayesian Networks (BNs) use probabilistic inference to classify and detect anomalies.

What is a Bayesian Network?

A Bayesian Network is a graphical model representing conditional dependencies between variables.

Mathematically, a BN consists of:

• Nodes (N): Representing events (e.g., “Malicious Traffic”, “Port Scan”).
• Edges (E): Conditional dependencies between events.
• Conditional Probability Tables (CPTs): Probability distributions of each node given its parents.

Example: Bayesian Network for Network Intrusion

• Event: “Unusual Packet Size” → “High Risk Anomaly” (depends on conditional probability)
• Event: “Source IP in Threat Intelligence Feed” → “Potential Malicious Activity”
• Event: “Port Scan Detected” → “Risk of Exploit”

This graphical representation allows probabilistic reasoning to determine if a traffic event is an attack.

Reference:

• Bayesian Networks in Cyber Threat Analysis (MDPI)

Mathematical Foundation: Bayesian Inference for Anomaly Detection

Bayesian AI uses Bayes’ Theorem to update probabilities dynamically:

[ P(A | B) = \frac{P(B | A) P(A)}{P(B)} ]

Where:

• **P(A

  B)** = Probability of Attack A given Evidence B

• **P(B

  A)** = Probability of Evidence B occurring in an Attack A

• P(A) = Prior probability of an attack occurring
• P(B) = Probability of observing Evidence B

Example: Detecting Malicious Traffic

If:

• ( P({Anomaly}) = 0.02 ) (2%)

• ( P({High Packet Size}

  {Anomaly}) = 0.85 )

• ( P({High Packet Size}) = 0.10 ) (10%)

Then:

[ P({Anomaly} | {High Packet Size}) = \frac{0.85 \times 0.02}{0.10} = 0.17 ]

Key Takeaway: If a packet has unusually high packet size, there is a 17% probability that it is part of anomalous/malicious traffic.

Reference:

• Probabilistic Reasoning in Intelligent Systems: Bayesian Networks and Beyond (Pearl, 1988)