Theoretical Analysis of Momentum LMS Algorithm for Non-Stationary Data Streams
Researchers have developed theoretical guarantees for the Momentum Least Mean Squares (MLMS) algorithm operating on time-varying, nonstationary data streams. Classical adaptive filtering theory assumes data are independently and identically distributed, an assumption that breaks down in real-world streaming environments where system parameters drift over time. The work provides stability, tracking, and regret bounds for MLMS, offering a theoretically grounded tool for online learning in dynamic settings.
A new paper posted to arXiv formalizes the theoretical behavior of the Momentum Least Mean Squares (MLMS) algorithm when applied to nonstationary, time-varying stochastic linear systems. Standard LMS theory relies on i.i.d. data assumptions and characterizes stability through first-order random vector difference equations, but the addition of a momentum term introduces an extra dynamical state, elevating the analysis to second-order time-varying random vector difference equations involving products of random matrices. The authors derive tracking performance and regret bounds under several practical conditions, addressing a substantially harder mathematical problem than classical LMS stability analysis. Experiments on both synthetic and real-world data streams are reported to confirm rapid adaptation and robust tracking consistent with the theoretical predictions. The algorithm processes each sample in a single pass and maintains computational and memory complexity independent of stream length, making it suitable for large-scale online learning. The work positions MLMS as a promising adaptive identification tool for modern streaming applications where distribution shift and parameter drift are common.
What's missing
The real-world datasets used in experiments are not described in the abstract, making it difficult to assess the breadth of empirical validation. The paper does not appear to compare MLMS against other momentum-based or adaptive online learning algorithms beyond classical LMS, leaving open questions about relative performance. Conditions under which the derived bounds are tight or practically achievable are not detailed in the abstract.
What different sources said
- arXiv cs.LGCenter
Momentum LMS Theory beyond Stationarity: Stability, Tracking, and Regret
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