Bernoulli水平集估计的前瞻捕获函数
Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation
摘要：
水平集估计（LSE）是识别未知函数取高于或低于指定阈值的值的区域的问题。有效LSE的主动采样策略主要在连续值函数中进行了研究。受人类心理物理学中常见的试验设计产生二进制响应的应用程序的启发，我们研究了LSE主动抽样与伯努利结果。对于高斯过程分类代理模型，最先进的连续输出方法所使用的前瞻模型后验是难以处理的。然而，我们推导出分析表达式的子级集成员资格的前瞻后验，并显示这些如何导致分析表达式的一类前瞻LSE采集功能，包括基于信息的方法。基准实验表明了考虑全局前瞻对整个后验的影响的重要性。我们证明了一个明显的好处，使用这类新的采集功能的基准问题，并在一个具有挑战性的现实世界的任务，估计一个高维的对比敏感度函数。
英文摘要：
Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued functions. Motivated by applications in human psychophysics where common experimental designs produce binary responses, we study LSE active sampling with Bernoulli outcomes. With Gaussian process classification surrogate models, the look-ahead model posteriors used by state-of-the-art continuous-output methods are intractable. However, we derive analytic expressions for look-ahead posteriors of sublevel set membership, and show how these lead to analytic expressions for a class of look-ahead LSE acquisition functions, including information-based methods. Benchmark experiments show the importance of considering the global look-ahead impact on the entire posterior. We demonstrate a clear benefit to using this new class of acquisition functions on benchmark problems, and on a challenging real-world task of estimating a high-dimensional contrast sensitivity function.
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