Artificial intelligence(AI) systems based on deep neural networks (DNNs) and machine learning (ML) algorithms are increasingly used to solve critical problems in bioinformatics, biomedical informatics, and precision medicine. However, complex DNN or ML models that are unavoidably opaque and perceived as black-box methods, may not be able to explain why and how they make certain decisions. Such black-box models are difficult to comprehend not only for targeted users and decision-makers but also for AI developers. Besides, in sensitive areas like healthcare, explainability and accountability are not only desirable properties of AI but also legal requirements -- especially when AI may have significant impacts on human lives. Explainable artificial intelligence (XAI) is an emerging field that aims to mitigate the opaqueness of black-box models and make it possible to interpret how AI systems make their decisions with transparency. An interpretable ML model can explain how it makes predictions and which factors affect the model's outcomes. The majority of state-of-the-art interpretable ML methods have been developed in a domain-agnostic way and originate from computer vision, automated reasoning, or even statistics. Many of these methods cannot be directly applied to bioinformatics problems, without prior customization, extension, and domain adoption. In this paper, we discuss the importance of explainability with a focus on bioinformatics. We analyse and comprehensively overview of model-specific and model-agnostic interpretable ML methods and tools. Via several case studies covering bioimaging, cancer genomics, and biomedical text mining, we show how bioinformatics research could benefit from XAI methods and how they could help improve decision fairness.
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