Some Recent Advances in Subsampling and Active Learning
Open Access DepositedData efficiency is a key consideration in the application of predictive statistical methods. In this dissertation, we investigate this concern in two cases—big data subsampling and sequential data acquisition for expensive experiments. Big data, while offering unique opportunities, demands substantial computational power. Flexible predictive models can face scalability and convergence issues when challenged by large datasets. Subsampling is a promising solution to this problem. Running statistical models on a small yet informative portion of the data may provide resource-efficient predictions to complex systems without losing much accuracy. In the first project, we propose a new subsampling strategy, IES, for fitting nonparametric additive models with large dataset. Leveraging the minimax optimality of an orthogonal array (OA), the IES approach selects a subsample that approximates an OA to achieve the minimax optimality. We provide comprehensive uncertainty quantification for the method and prove its algorithmic convergence. The efficiency of IES is validated through simulations and a real-world data application. The second project addresses data efficiency of predictive models in the scarce data scenario. When obtaining an outcome from large experiments is costly, a viable alternative is to construct an accurate emulator for the outcome-input relation and use the predictions from the emulator in place of true outcomes. Active learning (AL) integrates sequential sampling with emulator updates and has demonstrated empirical success in reducing the number of inquiries needed for constructing the emulators. We propose a novel AL method titled active learning by subsample difference (ALSD) for Gaussian process (GP) emulators. ALSD samples in a two-stage manner, reflecting a exploitation and exploration trade-off. It exploits local feature of the outcome-input relation by testing the difference in predictions from subsample models and explores design region by optimizing fill distance. Numerical experiments show that ALSD achieves robust and competitive performance compared to the state-of-the-art.
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Some_Recent_Advances_in_Subsampling_and_Active_Learning.pdf | 2024-05-31 | Open Access |
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