# Hyperbolic Secant representation of the logistic function: Application to probabilistic Multiple Instance Learning for CT intracranial hemorrhage detection

arXiv: https://arxiv.org/abs/2403.14829 · HTML: https://mlsanity.com/paper/2403.14829/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Multiple Instance Learning: A Survey of Problem Characteristics and Applications](https://mlsanity.com/paper/1612.03365/) (2016)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Dependent Multinomial Models Made Easy: Stick Breaking with the P'olya-Gamma Augmentation](https://mlsanity.com/paper/1506.05843/) (2015)
- [Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation](https://mlsanity.com/paper/1802.06383/) (2018)
- [Conditionally conjugate mean-field variational Bayes for logistic models](https://mlsanity.com/paper/1711.06999/) (2017)
- [A Joint introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman filtering and other Kernel Smoothers](https://mlsanity.com/paper/2009.09217/) (2020)
- [A CNN-LSTM Architecture for Detection of Intracranial Hemorrhage on CT scans](https://mlsanity.com/paper/2005.10992/) (2020)
- [Extracting 2D weak labels from volume labels using multiple instance learning in CT hemorrhage detection](https://mlsanity.com/paper/1911.05650/) (2019)
- [Automated Augmented Conjugate Inference for Non-conjugate Gaussian Process Models](https://mlsanity.com/paper/2002.11451/) (2020)

## Built on by (most cited first, 1 of 1)

- [AI-Powered Intracranial Hemorrhage Detection: A Co-Scale Convolutional Attention Model with Uncertainty-Based Fuzzy Integral Operator and Feature Screening](https://mlsanity.com/paper/2412.14869/) (2024)

## Abstract (arXiv)

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 P'olya-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.