论文标题
部分可观测时空混沌系统的无模型预测
On how to avoid exacerbating spurious correlations when models are overparameterized
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Overparameterized models fail to generalize well in the presence of data imbalance even when combined with traditional techniques for mitigating imbalances. This paper focuses on imbalanced classification datasets, in which a small subset of the population -- a minority -- may contain features that correlate spuriously with the class label. For a parametric family of cross-entropy loss modifications and a representative Gaussian mixture model, we derive non-asymptotic generalization bounds on the worst-group error that shed light on the role of different hyper-parameters. Specifically, we prove that, when appropriately tuned, the recently proposed VS-loss learns a model that is fair towards minorities even when spurious features are strong. On the other hand, alternative heuristics, such as the weighted CE and the LA-loss, can fail dramatically. Compared to previous works, our bounds hold for more general models, they are non-asymptotic, and, they apply even at scenarios of extreme imbalance.
