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This overview paper synthesizes foundational theories explaining how overparameterized models generalize well despite interpolating noisy data, effectively challenging traditional bias-variance tradeoff dogmas. By framing these insights through a statistical signal processing lens, it clarifies the double descent phenomenon and outlines key open frontiers in modern machine learning theory. The work is essential for researchers seeking to understand the theoretical underpinnings of deep learning's empirical success beyond standard generalization bounds.
A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning
arXiv:2109.02355v2 Announce Type: replace-cross Abstract: The last decade of progress in machine learning (ML), especially the deep learning era, has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles was the good empirical generalization of overparameterized models. Overparameterized models are highly complex with respect to the size of the training dataset, which enables them to perfectly fit (i.e., interpolate) even noisy training data. 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 been observed to generalize remarkably well on fresh test data. Indeed, the discovery of the double descent phenomenon has revealed that highly overparameterized models can improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime required new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in foundational analyses of overparameterized linear regression and related statistical learning tasks, mostly published between 2018 and 2022, which resulted in precise analytic characterizations of double descent. This paper provides an overview of the theory of overparameterized ML (henceforth abbreviated as TOPML) by focusing on explaining the most foundational 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 frontiers that remain.
Title:A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning
Abstract:The last decade of progress in machine learning (ML), especially the deep learning era, has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles was the good empirical generalization of overparameterized models. Overparameterized models are highly complex with respect to the size of the training dataset, which enables them to perfectly fit (i.e., interpolate) even noisy training data. 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 been observed to generalize remarkably well on fresh test data. Indeed, the discovery of the double descent phenomenon has revealed that highly overparameterized models can improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime required new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in foundational analyses of overparameterized linear regression and related statistical learning tasks, mostly published between 2018 and 2022, which resulted in precise analytic characterizations of double descent. This paper provides an overview of the theory of overparameterized ML (henceforth abbreviated as TOPML) by focusing on explaining the most foundational 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 frontiers that remain.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2109.02355 [stat.ML]
(or arXiv:2109.02355v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2109.02355 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 354 words
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