Hyperbolic Secant Representation of the Logistic Function: Application to Probabilistic Multiple Instance Learning for CT Intracranial Hemorrhage Detection

作     者：Castro-Macías, Francisco M. Morales-Álvarez, Pablo Wu, Yunan Molina, Rafael Katsaggelos, Aggelos K. 

作者机构：Department of Computer Science and Artificial Intelligence University of Granada Spain Research Centre for Information and Communication Technologies University of Granada Spain Department of Statistics and Operations Research University of Granada Spain Department of Electrical and Computer Engineering Northwestern University United States Center for Computational Imaging and Signal Analytics in Medicine Northwestern University United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Medical imaging 

摘      要：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. © 2024, CC BY.