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Statistics > Machine Learning

arXiv:2109.02355 (stat)
[Submitted on 6 Sep 2021]

Title:A Farewell to the Bias-Variance Tradeoff? An Overview of the
Theory of Overparameterized Machine Learning

Authors:Yehuda Dar, Vidya Muthukumar, Richard G. Baraniuk
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    Abstract: The rapid recent progress in machine learning (ML) has
    raised a number of scientific questions that challenge the
    longstanding dogma of the field. One of the most important
    riddles is the good empirical generalization of overparameterized
    models. Overparameterized models are excessively complex with
    respect to the size of the training dataset, which results in
    them perfectly fitting (i.e., interpolating) the training data,
    which is usually noisy. Such interpolation of noisy data is
    traditionally associated with detrimental overfitting, and yet a
    wide range of interpolating models -- from simple linear models
    to deep neural networks -- have recently been observed to
    generalize extremely well on fresh test data. Indeed, the
    recently discovered double descent phenomenon has revealed that
    highly overparameterized models often improve over the best
    underparameterized model in test performance.
    Understanding learning in this overparameterized regime requires
    new theory and foundational empirical studies, even for the
    simplest case of the linear model. The underpinnings of this
    understanding have been laid in very recent analyses of
    overparameterized linear regression and related statistical
    learning tasks, which resulted in precise analytic
    characterizations of double descent. This paper provides a
    succinct overview of this emerging theory of overparameterized ML
    (henceforth abbreviated as TOPML) that explains these recent
    findings through a statistical signal processing perspective. We
    emphasize the unique aspects that define the TOPML research area
    as a subfield of modern ML theory and outline interesting open
    questions that remain.

Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as:  arXiv:2109.02355 [stat.ML]
          (or arXiv:2109.02355v1 [stat.ML] for this version)

Submission history

From: Yehuda Dar [view email]
[v1] Mon, 6 Sep 2021 10:48:40 UTC (3,149 KB)
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