Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory view

• URL: http://arxiv.org/abs/2406.09199v1
• Date: Thu, 13 Jun 2024 14:56:52 GMT
• Title: Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory view
• Authors: Mihailo Stojnic,
• Abstract summary: We show that emphRandom Duality Theory (RDT) can be utilized to obtain precise closed form characterizations of all estimators related optimizing quantities of interest.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider fully row/column-correlated linear regression models and study several classical estimators (including minimum norm interpolators (GLS), ordinary least squares (LS), and ridge regressors). We show that \emph{Random Duality Theory} (RDT) can be utilized to obtain precise closed form characterizations of all estimators related optimizing quantities of interest, including the \emph{prediction risk} (testing or generalization error). On a qualitative level out results recover the risk's well known non-monotonic (so-called double-descent) behavior as the number of features/sample size ratio increases. On a quantitative level, our closed form results show how the risk explicitly depends on all key model parameters, including the problem dimensions and covariance matrices. Moreover, a special case of our results, obtained when intra-sample (or time-series) correlations are not present, precisely match the corresponding ones obtained via spectral methods in [6,16,17,24].

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