INTEGRATION OF EXACT STRUCTURAL-PROBABILISTIC ASSESSMENT AND SEQUENTIAL AGGREGATION OF SHORT RANDOM SEQUENCES
DOI:
https://doi.org/10.28925/2663-4023.2026.35.1436Keywords:
mathematical modeling, random sequences, structural analysis, joint distributions, streaming data, sequential aggregation, change detection, system monitoringAbstract
This paper investigates the integration of exact structural-probabilistic assessment of short random sequences with the sequential aggregation of local scores to characterize the evolution of structural changes in binary data streams. The need to account not only for symbol occurrence frequencies but also for their relative arrangement and the temporal ordering of local deviations is substantiated. The theoretical foundation of the proposed approach is provided by exact joint distributions of occurrence-count statistics for two- and three-symbol patterns, which account for dependencies and overlaps among structural configurations in short sequence fragments. These distributions are used to derive local structural atypicality scores relative to a baseline probabilistic model. A two-stage aggregation procedure is proposed, comprising structural aggregation of the scores within individual fragments, followed by sequential aggregation of their ordered trajectory. The resulting representation characterizes the level, trend, accumulation, current duration, and variability of structural deviations.
A reproducible computational experiment was conducted using a synthetic binary data stream with controlled changes in its generating regimes. The results demonstrate the response of local scores to changes in dependence between adjacent elements while the marginal symbol probabilities remain unchanged. Analysis of the sequential components revealed differences between increasing, persistent, and diminishing deviations that cannot be identified solely from the average level of local atypicality. The scientific significance of these findings lies in establishing the complementary nature of exact local structural characterization and the analysis of its sequential dynamics. The integrated representation provides a foundation for identifying potential early structural indicators of undesirable changes in diagnostic data streams. Future research will focus on validation using real-world data, evaluation of detection sensitivity and delay under a controlled false-alarm rate, and identification of the conditions under which the proposed approach can be effectively applied in practice.
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