Multiple Instance Learning (MIL) is a weakly supervised paradigm that has been successfully applied to many different scientific areas and is particularly well suited to medical imaging. Probabilistic MIL methods, and more specifically Gaussian Processes (GPs), have achieved excellent results due to their high expressiveness and uncertainty quantification capabilities. One of the most successful GP-based MIL methods, VGPMIL, resorts to a variational bound to handle the intractability of the logistic function. Here, we formulate VGPMIL using Pólya-Gamma random variables. This approach yields the same variational posterior approximations as the original VGPMIL, which is a consequence of the two representations that the Hyperbolic Secant distribution admits. This leads us to propose a general GP-based MIL method that takes different forms by simply leveraging distributions other than the Hyperbolic Secant one. Using the Gamma distribution we arrive at a new approach that obtains competitive or superior predictive performance and efficiency. This is validated in a comprehensive experimental study including one synthetic MIL dataset, two well-known MIL benchmarks, and a real-world medical problem. We expect that this work provides useful ideas beyond MIL that can foster further research in the field.

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逻辑函数的双曲正割表示：应用于 CT 颅内出血检测的概率多实例学习

多实例学习 (MIL) 是一种弱监督范式，已成功应用于许多不同的科学领域，特别适合医学成像。概率 MIL 方法，更具体地说是高斯过程 (GP)，由于其高表达性和不确定性量化能力而取得了优异的结果。 VGPMIL 是最成功的基于 GP 的 MIL 方法之一，它采用变分界来处理逻辑函数的棘手问题。在这里，我们使用 Pólya-Gamma 随机变量制定 VGPMIL。这种方法产生与原始 VGPMIL 相同的变分后验近似，这是双曲正割分布允许的两种表示的结果。这促使我们提出一种基于 GP 的通用 MIL 方法，该方法通过简单地利用双曲正割分布以外的分布来采取不同的形式。使用伽玛分布，我们得出了一种新方法，可以获得有竞争力或卓越的预测性能和效率。这在一项综合实验研究中得到了验证，包括一个合成的 MIL 数据集、两个著名的 MIL 基准和一个现实世界的医疗问题。我们期望这项工作提供超越 MIL 的有用想法，从而促进该领域的进一步研究。