How can we attribute the behaviors of machine learning models to their training data? While the classic influence function sheds light on the impact of individual samples, it often fails to capture the more complex and pronounced collective influence of a set of samples. To tackle this challenge, we study the Most Influential Subset Selection (MISS) problem, which aims to identify a subset of training samples with the greatest collective influence. We conduct a comprehensive analysis of the prevailing approaches in MISS, elucidating their strengths and weaknesses. Our findings reveal that influence-based greedy heuristics, a dominant class of algorithms in MISS, can provably fail even in linear regression.

How can we attribute the behaviors of machine learning models to their training data? While the classic influence function sheds light on the impact of individual samples, it often fails to capture the more complex and pronounced collective influence of a set of samples. To tackle this challenge, we study the Most Influential Subset Selection (MISS) problem, which aims to identify a subset of training samples with the greatest collective influence. We conduct a comprehensive analysis of the prevailing approaches in MISS, elucidating their strengths and weaknesses. Our findings reveal that influence-based greedy heuristics, a dominant class of algorithms in MISS, can provably fail even in linear regression.

Pretrained language models have achieved remarkable success in various natural language processing tasks. However, pretraining has recently shifted toward larger models and larger data, and this has resulted in significant computational and energy costs. In this paper, we propose Influence Subset Selection (ISS) for language model, which explicitly utilizes end-task knowledge to select a tiny subset of the pretraining corpus. Specifically, the ISS selects the samples that will provide the most positive influence on the performance of the end-task. Furthermore, we design a gradient matching based influence estimation method, which can drastically reduce the computation time of influence. With only 0.45% of the data and a three-orders-of-magnitude lower computational cost, ISS outperformed pretrained models (e.g., RoBERTa) on eight datasets covering four domains.