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Abstract:
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The problem of ordinary least squares (multiple linear regression) is a subtle, fundamental problem in data science, statistics, machine learning and other mathematical related fields. Its computation usually requires the inversion of the Gram matrix of the data samples and the resulting vector of estimates is considered a black box. Omitting or adding a covariates requires recomputing the inverse. We offer a novel closed form for the coefficients of least squares where each coefficient may be calculated separately or in iterative manner. Omitting or adding covariates to the model results in additive correction of the previous coefficients. We demonstrate how this closed form lends itself to more efficient practical implications of Ridge and LASSO regularization. We will demonstrate this work on relevant data examples.
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