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A Block EM Algorithm for Multivariate Skew Normal and Skew -Mixture Models.

Sharon X Lee, Kaleb L Leemaqz, Geoffrey J McLachlan

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    This study introduces a parallelized Expectation-Maximization (EM) algorithm for finite skew mixture models. The block implementation speeds up parameter estimation on multicore machines, benefiting users of R.

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    Area of Science:

    • Statistics
    • Computational Statistics

    Background:

    • Finite mixtures of skew distributions are valuable for modeling complex, asymmetric data.
    • The Expectation-Maximization (EM) algorithm, while effective, can be computationally intensive for parameter estimation.
    • Existing parallelization strategies for the EM algorithm primarily target distributed systems, limiting accessibility for users on standalone machines.

    Purpose of the Study:

    • To develop an efficient, parallelized Expectation-Maximization (EM) algorithm for finite skew mixture models tailored for multicore standalone machines.
    • To adapt the E- and M-steps of the EM algorithm for parallel computation using a block-based approach within the R programming environment.
    • To demonstrate the practical benefits and effectiveness of this new implementation for users of mixture models.

    Main Methods:

    • A block implementation of the Expectation-Maximization (EM) algorithm was developed.
    • The E- and M-steps were modified to allow data splitting into blocks for parallel processing across threads.
    • The focus was on fitting finite mixtures of multivariate skew normal and skew distributions.
    • The implementation was designed for the R programming environment on standalone multicore machines.

    Main Results:

    • The block implementation of the EM algorithm effectively parallelizes computations on multicore machines.
    • Both E- and M-steps were successfully modified to accommodate block-based data processing.
    • The approach demonstrated significant speedup in parameter estimation for skew mixture models.
    • Experiments on real data sets confirmed the practical effectiveness of the proposed method.

    Conclusions:

    • The developed block EM algorithm offers an efficient and accessible solution for fitting finite skew mixture models on multicore machines.
    • This parallelization strategy provides immediate performance benefits for R users working with complex asymmetric data.
    • The method is easily implementable and enhances the usability of mixture models in practical statistical analysis.