Understanding Double Descent Requires a Fine-Grained Bias-Variance Decomposition

by   Ben Adlam, et al.

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high variance of the predictive function. However, such a simple trade-off does not adequately describe deep learning models that simultaneously attain low bias and variance in the heavily overparameterized regime. A primary obstacle in explaining this behavior is that deep learning algorithms typically involve multiple sources of randomness whose individual contributions are not visible in the total variance. To enable fine-grained analysis, we describe an interpretable, symmetric decomposition of the variance into terms associated with the randomness from sampling, initialization, and the labels. Moreover, we compute the high-dimensional asymptotic behavior of this decomposition for random feature kernel regression, and analyze the strikingly rich phenomenology that arises. We find that the bias decreases monotonically with the network width, but the variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise. The divergence is caused by the interaction between sampling and initialization and can therefore be eliminated by marginalizing over samples (i.e. bagging) or over the initial parameters (i.e. ensemble learning).



There are no comments yet.


page 14


Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime

Deep neural networks can achieve remarkable generalization performances ...

What causes the test error? Going beyond bias-variance via ANOVA

Modern machine learning methods are often overparametrized, allowing ada...

Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized models

The bias-variance trade-off is a central concept in supervised learning....

Kernel regression in high dimension: Refined analysis beyond double descent

In this paper, we provide a precise characterize of generalization prope...

Understanding Generalization in Adversarial Training via the Bias-Variance Decomposition

Adversarially trained models exhibit a large generalization gap: they ca...

Explaining Classification Models Built on High-Dimensional Sparse Data

Predictive modeling applications increasingly use data representing peop...

Bias-Variance Games

Firms engaged in electronic commerce increasingly rely on machine learni...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.