CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis

Survival analysis is a branch of statistics used for modeling the time until a specific event occurs and is widely used in medicine, engineering, finance, and many other fields. When choosing survival models, there is typically a trade-off between performance and interpretability, where the highest performance is achieved by black-box models based on deep learning. This is a major problem in fields such as medicine where practitioners are reluctant to blindly trust black-box models to make important patient decisions. Kolmogorov-Arnold Networks (KANs) were recently proposed as an interpretable and accurate alternative to multi-layer perceptrons (MLPs). We introduce CoxKAN, a Cox proportional hazards Kolmogorov-Arnold Network for interpretable, high-performance survival analysis. We evaluate the proposed CoxKAN on 4 synthetic datasets and 9 real medical datasets. The synthetic experiments demonstrate that CoxKAN accurately recovers interpretable symbolic formulae for the hazard function, and effectively performs automatic feature selection. Evaluation on the 9 real datasets show that CoxKAN consistently outperforms the Cox proportional hazards model and achieves performance that is superior or comparable to that of tuned MLPs. Furthermore, we find that CoxKAN identifies complex interactions between predictor variables that would be extremely difficult to recognise using existing survival methods, and automatically finds symbolic formulae which uncover the precise effect of important biomarkers on patient risk.

Calibrating Ensembles for Scalable Uncertainty Quantification in Deep Learning-based Medical Segmentation

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world problems. Scalable solutions often rely on classical techniques, such as dropout, during inference or training ensembles of identical models with different random seeds to obtain a posterior distribution. In this paper, we show that these approaches fail to approximate the classification probability. On the contrary, we propose a scalable and intuitive framework to calibrate ensembles of deep learning models to produce uncertainty quantification measurements that approximate the classification probability. On unseen test data, we demonstrate improved calibration, sensitivity (in two out of three cases) and precision when being compared with the standard approaches. We further motivate the usage of our method in active learning, creating pseudo-labels to learn from unlabeled images and human-machine collaboration.