Recent years have witnessed increased demand for users to be able to interpret the results of data science pipelines, locate erroneous data items in the input, evaluate the importance of individual input data items, and acknowledge the contributions of data curators. Such applications often involve the use of the provenance at a fine-grained level, and require very fast response time. To address this issue, my goal is to expedite the use of fine-grained provenance in applications within both the database and machine learning domains, which are ubiquitous in contemporary data science pipelines. In applications from the database domain, I focus on the problem of data citation and provide two different types of solutions, Rewriting-based solutions and Provenance-based solutions, to generate fine-grained citations to database query results by implicitly or explicitly leveraging provenance information. In applications from the ML domain, the first considers the problem of incrementally updating ML models after the deletions of a small subset of training samples. This is critical for understanding the importance of individual training samples to ML models, especially in online pipelines. For this problem, I provide two solutions, PrIU and DeltaGrad, to incrementally update ML models constructed by SGD/GD methods, which utilize provenance information collected during the training phase on the full dataset before the deletion requests. The second application from the ML domain that I focus on is to explore how to clean label uncertainties located in the ML training dataset in a more efficient and cheaper manner. To address this problem, I proposed a solution, CHEF, to reduce the cost and the overhead at each phase of the label cleaning pipeline and maintain the overall model performance simultaneously. I also propose initial ideas for how to remove some assumptions used in these solutions to extend them to more general scenarios.