On Bias-Variance Alignment in Deep Models

Published: 16 Jan 2024, Last Modified: 16 Mar 2024ICLR 2024 spotlightEveryoneRevisionsBibTeX
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: bias-variance decomposition, ensemble, deep learning
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: Classical wisdom in machine learning holds that the generalization error can be decomposed into bias and variance, and these two terms exhibit a \emph{trade-off}. However, in this paper, we show that for an ensemble of deep learning based classification models, bias and variance are \emph{aligned} at a sample level, where squared bias is approximately \emph{equal} to variance for correctly classified sample points. We present empirical evidence confirming this phenomenon in a variety of deep learning models and datasets. Moreover, we study this phenomenon from two theoretical perspectives: calibration and neural collapse. We first show theoretically that under the assumption that the models are well calibrated, we can observe the bias-variance alignment. Second, starting from the picture provided by the neural collapse theory, we show an approximate correlation between bias and variance.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: general machine learning (i.e., none of the above)
Submission Number: 6759