Forgetting to Improve: Principled Data Removal in Active Learning

The uncertainty of a statistical model is most commonly factorized into an aleatoric and an epistemic part. This factorization changes how predictions are interpreted in downstream decision tasks. Importantly, except for the idealistic scenario with no model mismatch, the quantification is a characteristic of the model and not the data generating process. In this paper, we propose Forgetting to Improve a method that reduces this discrepancy by incorporating the task into the modeling framework. Our key insight is to acknowledge that in scenarios of model mismatch, data can have a detrimental effect on the modeling for a specific task. Based on this insight, we propose an influence function for Gaussian process models that allows for principled removal of detrimental data samples. We showcase the flexibility of this approach by demonstrating significant improvements across a range of tasks, including Bayesian optimization, model-based reinforcement learning, and transductive learning.