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Spuriousness arises when there is an association between two or more variables in a dataset that are not causally related. In this work, we propose an explainability framework to preemptively disentangle the nature of such spurious associations in a dataset before model training. We leverage a body of work in information theory called Partial Information Decomposition (PID) to decompose the total information about the target into four nonnegative quantities, namely unique information (in core and spurious features, respectively), redundant information, and synergistic information. Our framework helps anticipate when the core or spurious feature is indispensable, when either suffices, and when both are jointly needed for an optimal classifier trained on the dataset. Next, we leverage this decomposition to propose a novel measure of the spuriousness of a dataset. We arrive at this measure systematically by examining several candidate measures, and demonstrating what they capture and miss through intuitive canonical examples and counterexamples. Our framework Spurious Disentangler consists of segmentation, dimensionality reduction, and estimation modules, with capabilities to specifically handle high-dimensional image data efficiently. Finally, we also perform empirical evaluation to demonstrate the trends of unique, redundant, and synergistic information, as well as our proposed spuriousness measure across 6 benchmark datasets under various experimental settings. We observe an agreement between our preemptive measure of dataset spuriousness and post-training model generalization metrics such as worst-group accuracy, further supporting our proposition. The code is available at https://github.com/Barproda/spuriousness-disentangler. 

Knowledge distillation deploys complex machine learning models in resource-constrained environments by training a smaller student model to emulate internal representations of a complex teacher model. However, the teacher’s representations can also encode nuisance or additional information not relevant to the downstream task. Distilling such irrelevant information can actually impede the performance of a capacity-limited student model. This observation motivates our primary question: What are the information-theoretic limits of knowledge distillation? To this end, we leverage Partial Information Decomposition to quantify and explain the transferred knowledge and knowledge left to distill for a downstream task. We theoretically demonstrate that the task-relevant transferred knowledge is succinctly captured by the measure of redundant information about the task between the teacher and student. We propose a novel multi-level optimization to incorporate redundant information as a regularizer, leading to our framework of Redundant Information Distillation (RID). RID leads to more resilient and effective distillation under nuisance teachers as it succinctly quantifies task-relevant knowledge rather than simply aligning student and teacher representations.