Uncertain data management has become crucial in many sensing and scientific applications. As user-defined functions (UDFs) become widely used in these applications, an important task is to capture result uncertainty for queries that evaluate UDFs on uncertain data. In this work, we provide a general framework for supporting UDFs on uncertain data. Specifically, we propose a learning approach based on Gaussian processes (GPs) to compute approximate output distributions of a UDF when evaluated on uncertain input, with guaranteed error bounds. We also devise an online algorithm to compute such output distributions, which employs a suite of optimizations to improve accuracy and performance. Our evaluation using both real-world and synthetic functions shows that our proposed GP approach can outperform the state-of-the-art sampling approach with up to two orders of magnitude improvement for a variety of UDFs. 1
