An Explainable Multi-Task Similarity Measure: Integrating Accumulated Local Effects and Weighted Fr'echet Distance

In many machine learning contexts, tasks are often treated as interconnected components with the goal of leveraging knowledge transfer between them, which is the central aim of Multi-Task Learning (MTL). Consequently, this multi-task scenario requires addressing critical questions: which tasks are similar, and how and why do they exhibit similarity? In this work, we propose a multi-task similarity measure based on Explainable Artificial Intelligence (XAI) techniques, specifically Accumulated Local Effects (ALE) curves. ALE curves are compared using the Fr'echet distance, weighted by the data distribution, and the resulting similarity measure incorporates the importance of each feature. The measure is applicable in both single-task learning scenarios, where each task is trained separately, and multi-task learning scenarios, where all tasks are learned simultaneously. The measure is model-agnostic, allowing the use of different machine learning models across tasks. A scaling factor is introduced to account for differences in predictive performance across tasks, and several recommendations are provided for applying the measure in complex scenarios. We validate this measure using four datasets, one synthetic dataset and three real-world datasets. The real-world datasets include a well-known Parkinson's dataset and a bike-sharing usage dataset -- both structured in tabular format -- as well as the CelebA dataset, which is used to evaluate the application of concept bottleneck encoders in a multitask learning setting. The results demonstrate that the measure aligns with intuitive expectations of task similarity across both tabular and non-tabular data, making it a valuable tool for exploring relationships between tasks and supporting informed decision-making.