It's an Alignment, Not a Trade-off: Revisiting Bias and Variance in Deep Models

• URL: http://arxiv.org/abs/2310.09250v1
• Date: Fri, 13 Oct 2023 17:06:34 GMT
• Title: It's an Alignment, Not a Trade-off: Revisiting Bias and Variance in Deep Models
• Authors: Lin Chen, Michal Lukasik, Wittawat Jitkrittum, Chong You, Sanjiv Kumar
• Abstract summary: We show that for an ensemble of deep learning based classification models, bias and variance are emphaligned at a sample level. We study this phenomenon from two theoretical perspectives: calibration and neural collapse.
• Score: 51.66015254740692
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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