论文标题

部分可观测时空混沌系统的无模型预测

CEREAL: Few-Sample Clustering Evaluation

论文作者

Nayak, Nihal V., Elenberg, Ethan R., Rosenbaum, Clemens

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。

Evaluating clustering quality with reliable evaluation metrics like normalized mutual information (NMI) requires labeled data that can be expensive to annotate. We focus on the underexplored problem of estimating clustering quality with limited labels. We adapt existing approaches from the few-sample model evaluation literature to actively sub-sample, with a learned surrogate model, the most informative data points for annotation to estimate the evaluation metric. However, we find that their estimation can be biased and only relies on the labeled data. To that end, we introduce CEREAL, a comprehensive framework for few-sample clustering evaluation that extends active sampling approaches in three key ways. First, we propose novel NMI-based acquisition functions that account for the distinctive properties of clustering and uncertainties from a learned surrogate model. Next, we use ideas from semi-supervised learning and train the surrogate model with both the labeled and unlabeled data. Finally, we pseudo-label the unlabeled data with the surrogate model. We run experiments to estimate NMI in an active sampling pipeline on three datasets across vision and language. Our results show that CEREAL reduces the area under the absolute error curve by up to 57% compared to the best sampling baseline. We perform an extensive ablation study to show that our framework is agnostic to the choice of clustering algorithm and evaluation metric. We also extend CEREAL from clusterwise annotations to pairwise annotations. Overall, CEREAL can efficiently evaluate clustering with limited human annotations.

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