Abstract

Conventional monitoring and alerting frameworks in distributed systems often rely on threshold-based metrics, which can produce excessive false positives and fail to capture complex dependencies between signals. This paper proposes an applied framework for using information-theoretic measures—specifically mutual information and the broader notion of entropy covariance—to detect anomalies and support governance in event-driven infrastructure.

The approach shifts focus from isolated metrics to the relationships between uncertainties: when two signals that normally exhibit dependency diverge, the system can treat this as an indicator of instability. Leveraging existing mathematical foundations from information theory, this work evaluates the operational value of dependency-aware monitoring on real event streams (e.g., Kafka topics, MongoDB change data capture). Rolling measures of mutual information and covariance are integrated into monitoring pipelines, and their effectiveness is compared against conventional thresholds.

Preliminary results suggest that dependency-based monitoring can reduce false positives, identify anomalies earlier, and provide interpretable signals for governance. The contribution is not the introduction of new mathematical constructs, but rather the translation and operationalization of established information-theoretic tools into the domain of infrastructure reliability. This applied perspective points toward a broader research agenda: embedding relational measures of uncertainty as a governance layer for automated systems.

Formal Background

  • Entropy (Shannon, 1948):
    $$ H(X) = - \sum_x p(x) \log p(x) $$ Measures the uncertainty of a random variable.

  • Covariance:
    $$ \mathrm{Cov}(X, Y) = \mathbb{E}[(X - \mu_X)(Y - \mu_Y)] $$ Measures the linear relationship between two random variables.

  • Mutual Information:
    $$ I(X;Y) = H(X) + H(Y) - H(X,Y) $$ Quantifies the reduction in uncertainty about one variable given knowledge of the other.

  • Transfer Entropy (Schreiber, 2000):
    A directional measure capturing how the past of one process reduces uncertainty about the future of another.

These measures provide a well-established mathematical toolkit for quantifying relationships between signals.

  • Mutual Information in Anomaly Detection
    Mutual information matrices combined with deep learning have been shown to improve anomaly detection in monitoring data (ScienceDirect, 2023).

  • Graph-Based Models
    Graph embeddings with edges defined by mutual information enable anomaly detection across multivariate systems (MDPI Electronics, 2024).

  • Mutual Information Matrices (PMIM)
    Rényi entropy–based mutual information matrices provide interpretable fault detection with low false alarm rates (arXiv, 2020).

  • Covariance-Based Approaches
    High-dimensional covariance estimation and Mahalanobis-distance methods remain effective in multivariate anomaly detection (Scholar’s Mine; ResearchGate, 2023).

Relation to Existing Principles

Although the terminology of entropy covariance is uncommon, the underlying intent resonates with several established concepts:

  • Mutual Information (Shannon, 1948): dependency measure between random variables.
  • Granger Causality and Transfer Entropy: directional influence in time series.
  • Multivariate Anomaly Detection: fault detection via dependency modeling.
  • Ashby’s Law of Requisite Variety (1950s): effective governance requires the regulator to match the variety of the system being regulated.

Distinctive Intent

The novel contribution lies not in new mathematics but in application and framing. While prior work applies dependency measures for detection, the intent here is governance: embedding the monitoring of relational uncertainty directly into feedback loops of automated infrastructure. This perspective suggests a potential paradigm for self-regulating systems, where protective bias is operationalized through information-theoretic dependencies.