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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
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    Area of Science:

    • Machine Learning
    • Big Data Analytics
    • Statistical Learning Theory

    Background:

    • Big data presents challenges due to noisy samples impacting algorithmic performance.
    • Distributed learning methods are crucial for handling large datasets efficiently.
    • Classical Support Vector Machines (cSVM) are powerful but sensitive to data quality.

    Purpose of the Study:

    • To introduce Markov sampling and weighted approaches for distributed cSVM.
    • To analyze the generalization error and convergence rates of weighted distributed cSVM.
    • To propose and evaluate a novel distributed cSVM algorithm (DM-cSVM) using Markov sampling.

    Main Methods:

    • Weighted distributed cSVM with uniformly ergodic Markov chain (u.e.M.c.) samples.
    • Estimation of generalization error and derivation of optimal convergence rates.
    • Application to strong mixing observations and independent and identically distributed (i.i.d.) samples.
    • Development of a novel distributed Markov sampling cSVM (DM-cSVM).

    Main Results:

    • Optimal convergence rate for weighted distributed cSVM with u.e.M.c. samples was obtained.
    • Generalization bounds were derived for strong mixing and i.i.d. samples.
    • Numerical studies demonstrated superior performance of DM-cSVM.
    • DM-cSVM showed reduced sampling and training time compared to other distributed algorithms.

    Conclusions:

    • Markov sampling and weighted strategies effectively enhance distributed cSVM performance.
    • The proposed DM-cSVM algorithm offers a robust and efficient solution for big data analysis.
    • The findings provide theoretical insights into generalization error and practical improvements in algorithm efficiency.