Neha Gupta, Jamie Smith, Ben Adlam, Zelda Mariet
Transactions on Machine Learning Research (TMLR)
Publication year: 2022

Ensembles are a straightforward, remarkably effective method for improving the accuracy, calibration, and robustness of neural networks on classification tasks. Yet, the reasons underlying their success remain an active area of research. Building upon (Pfau, 2013), we turn to the bias-variance decomposition of Bregman divergences in order to gain insight into the behavior of ensembles under classification losses. Introducing a dual reparameterization of the bias-variance decomposition, we first derive generalized laws of total expectation and variance, then discuss how bias and variance terms can be estimated empirically. Next, we show that the dual reparameterization naturally introduces a way of constructing ensembles which reduces the variance and leaves the bias unchanged. Conversely, we show that ensembles that directly average model outputs can arbitrarily increase or decrease the bias. Empirically, we see that such ensembles of neural networks may reduce the bias. We conclude with an empirical analysis of ensembles over neural network architecture hyperparameters, revealing that these techniques allow for more efficient bias reduction than standard ensembles.