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    Area of Science:

    • Machine Learning
    • Signal Processing
    • Convex Analysis

    Background:

    • Online supervised multiregression tasks require adaptive models.
    • Reproducing Kernel Hilbert Spaces (RKHS) offer a powerful framework for nonlinear regression.
    • Traditional online RKHS methods face challenges with increasing memory requirements.

    Purpose of the Study:

    • Introduce a general framework for time-adaptive supervised multiregression.
    • Develop a computationally efficient algorithm for online multiregression in RKHS.
    • Address memory complexity issues in RKHS-based online learning.

    Main Methods:

    • Formulation of the problem in an infinite-dimensional RKHS.
    • Utilization of convex loss functions with analytic subgradients.
    • Implementation of a sparsification strategy for linear complexity.
    • Convergence analysis using convex analysis principles.

    Main Results:

    • A novel, time-adaptive multiregression framework is established.
    • The proposed sparsification strategy results in linear algorithmic complexity.
    • The method demonstrates effectiveness in multiaccess MIMO channel equalization with limited resources and no channel information.
    • Numerical results show competitive performance against advanced linear techniques.

    Conclusions:

    • The proposed framework offers an efficient and robust solution for online multiregression tasks.
    • The sparsification strategy effectively manages memory complexity in RKHS.
    • The method shows significant potential for applications in resource-constrained communication systems.