A distribution shift between the training and test data can severely harm performance of machine learning models. Importance weighting addresses this issue by assigning different weights to data points during training. We argue that existing heuristics for determining the weights are suboptimal, as they neglect the increase of the variance of the estimated model due to the finite sample size of the training data. We interpret the optimal weights in terms of a bias-variance trade-off, and propose a bi-level optimization procedure in which the weights and model parameters are optimized simultaneously. We apply this optimization to existing importance weighting techniques for last-layer retraining of deep neural networks in the presence of sub-population shifts and show empirically that optimizing weights significantly improves generalization performance.

翻译：训练数据与测试数据之间的分布偏移会严重损害机器学习模型的性能。重要性加权通过为训练过程中的数据点分配不同权重来解决这一问题。我们认为，现有的权重确定启发式方法并非最优，因为它们忽略了由于训练数据有限样本量导致的模型估计方差增加。我们从偏差-方差权衡的角度阐释了最优权重，并提出了一种双层优化过程，其中权重与模型参数被同时优化。我们将此优化应用于现有重要性加权技术，针对深度神经网络在子群体偏移下的最后一层再训练，并通过实证表明优化权重能显著提升泛化性能。