Instance hardness measures for classification and regression problems


  • Gustavo P. Torquette Universidade Federal de São Paulo
  • Victor S. Nunes UNIFESP and Instituto Tecnológico de Aeronáutica
  • Pedro Y. A. Paiva Instituto Tecnológico de Aeronáutica
  • Ana C. Lorena Instituto Tecnológico de Aeronáutica



Data complexity, Instance Hardness, Hardness Measures, Machine Learning


While the most common approach in Machine Learning (ML) studies is to analyze the performance achieved on a dataset through summary statistics, a fine-grained analysis at the level of its individual instances can provide valuable information for the ML practitioner. For instance, one can inspect whether the instances which are hardest to have their labels predicted might have any quality issues that should be addressed beforehand; or one may identify the need for more powerful learning methods for addressing the challenge imposed by one or a set of instances. This paper formalizes and presents a set of meta-features for characterizing which instances of a dataset are the hardest to have their label predicted accurately and why they are so, aka instance hardness measures. While there are already measures able to characterize instance hardness in classification problems, there is a lack of work devoted to regression problems. Here we present and analyze instance hardness measures for both classification and regression problems according to different perspectives, taking into account the particularities of each of these problems. For validating our results, synthetic datasets with different sources and levels of complexity are built and analyzed, indicating what kind of difficulty each measure is able to better quantify. A Python package containing all implementations is also provided.


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How to Cite

P. Torquette, G., S. Nunes, V., Y. A. Paiva, P., & C. Lorena, A. (2024). Instance hardness measures for classification and regression problems. Journal of Information and Data Management, 15(1), 152–174.



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