This appendix is organized as follows. In Section A.1, we provide complete proofs for the results We develop a generalization of TCSR that considers multi-hop transitions in Section A.2. Finally, in Section A.3, we revisit connections with RL and sketch For convenience, we briefly recall each result before presenting a complete proof. Proposition 2. If A1-A2 are satisfied, then, for any initial row-stochastic matrix (k 1) Proposition 3. Algorithm 1 is equivalent the fixed-point iteration The last equality establishes the equivalence between (5) and Line 8 in Algorithm 1.A.2 TCSR( λ) We identify two cases of special interest. TCSR(0) is equivalent to Algorithm 1 presented in the main text. The survival function is closely related to fundamental objects in dynamic programming and reinforcement learning. The code is structured as follows.

This appendix is organized as follows. In Section A.1, we provide complete proofs for the results We develop a generalization of TCSR that considers multi-hop transitions in Section A.2. Finally, in Section A.3, we revisit connections with RL and sketch For convenience, we briefly recall each result before presenting a complete proof. Proposition 2. If A1-A2 are satisfied, then, for any initial row-stochastic matrix (k 1) Proposition 3. Algorithm 1 is equivalent the fixed-point iteration The last equality establishes the equivalence between (5) and Line 8 in Algorithm 1.A.2 TCSR( λ) We identify two cases of special interest. TCSR(0) is equivalent to Algorithm 1 presented in the main text. The survival function is closely related to fundamental objects in dynamic programming and reinforcement learning. The code is structured as follows.

This paper proposes a novel, node-splitting support vector machine (SVM) for creating survival trees. This approach is capable of non-linearly partitioning survival data which includes continuous, right-censored outcomes. Our method improves on an existing non-parametric method, which uses at most oblique splits to induce survival regression trees. In the prior work, these oblique splits were created via a non-SVM approach, by minimizing a piece-wise linear objective, called a dipole splitting criterion, constructed from pairs of covariates and their associated survival information. We extend this method by enabling splits from a general class of non-linear surfaces. We achieve this by ridge regularizing the dipole-splitting criterion to enable application of kernel methods in a manner analogous to classical SVMs. The ridge regularization provides robustness and can be tuned. Using various kernels, we induce both linear and non-linear survival trees to compare their sizes and predictive powers on real and simulated data sets. We compare traditional univariate log-rank splits, oblique splits using the original dipole-splitting criterion and a variety of non-linear splits enabled by our method. In these tests, trees created by non-linear splits, using polynomial and Gaussian kernels show similar predictive power while often being of smaller sizes compared to trees created by univariate and oblique splits. This approach provides a novel and flexible array of survival trees that can be applied to diverse survival data sets.

Federated Learning (FL) holds great promise for digital health by enabling collaborative model training without compromising patient data privacy. However, heterogeneity across institutions, lack of sustained reputation, and unreliable contributions remain major challenges. In this paper, we propose a robust, peer-driven reputation mechanism for federated healthcare that employs a hybrid communication model to integrate decentralized peer feedback with clustering-based noise handling to enhance model aggregation. Crucially, our approach decouples the federated aggregation and reputation mechanisms by applying differential privacy to client-side model updates before sharing them for peer evaluation. This ensures sensitive information remains protected during reputation computation, while unaltered updates are sent to the server for global model training. Using the Cox Proportional Hazards model for survival analysis across multiple federated nodes, our framework addresses both data heterogeneity and reputation deficit by dynamically adjusting trust scores based on local performance improvements measured via the concordance index. Experimental evaluations on both synthetic datasets and the SEER dataset demonstrate that our method consistently achieves high and stable C-index values, effectively down-weighing noisy client updates and outperforming FL methods that lack a reputation system.

Unsupervised learning of disease subtypes from multi-omics data presents a significant opportunity for advancing personalized medicine. We introduce OmicsCL, a modular contrastive learning framework that jointly embeds heterogeneous omics modalities-such as gene expression, DNA methylation, and miRNA expression-into a unified latent space. Our method incorporates a survival-aware contrastive loss that encourages the model to learn representations aligned with survival-related patterns, without relying on labeled outcomes. Evaluated on the TCGA BRCA dataset, OmicsCL uncovers clinically meaningful clusters and achieves strong unsupervised concordance with patient survival. The framework demonstrates robustness across hyperparameter configurations and can be tuned to prioritize either subtype coherence or survival stratification. Ablation studies confirm that integrating survival-aware loss significantly enhances the predictive power of learned embeddings. These results highlight the promise of contrastive objectives for biological insight discovery in high-dimensional, heterogeneous omics data.

Survival analysis, a foundational tool for modeling time-to-event data, has seen growing integration with machine learning (ML) approaches to handle the complexities of censored data and time-varying risks. Despite these advances, leveraging state-of-the-art survival models remains a challenge due to the fragmented nature of existing implementations, which lack standardized interfaces and require extensive preprocessing. We introduce SurvHive, a Python-based framework designed to unify survival analysis methods within a coherent and extensible interface modeled on scikit-learn. SurvHive integrates classical statistical models with cutting-edge deep learning approaches, including transformer-based architectures and parametric survival models. Using a consistent API, SurvHive simplifies model training, evaluation, and optimization, significantly reducing the barrier to entry for ML practitioners exploring survival analysis. The package includes enhanced support for hyper-parameter tuning, time-dependent risk evaluation metrics, and cross-validation strategies tailored to censored data. With its extensibility and focus on usability, SurvHive provides a bridge between survival analysis and the broader ML community, facilitating advancements in time-to-event modeling across domains. The SurvHive code and documentation are available freely at https://github.com/compbiomed-unito/survhive.

In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression. A central idea in our method is temporal consistency, a hypothesis that past and future outcomes in the data evolve smoothly over time. Our framework uniquely incorporates temporal consistency into large datasets by providing a stable training signal that captures long-term temporal relationships and ensures reliable updates. Additionally, the method supports arbitrarily complex architectures, enabling the modeling of intricate temporal dependencies, and allows for end-to-end training. Through numerous experiments we provide empirical evidence demonstrating our framework's ability to exploit temporal consistency across datasets of varying sizes. Moreover, our algorithm outperforms benchmarks on datasets with long sequences, demonstrating its ability to capture long-term patterns. Finally, ablation studies show how our method enhances training stability.

Question answering (QA) tasks have been extensively studied in the field of natural language processing (NLP). Answers to open-ended questions are highly diverse and difficult to quantify, and cannot be simply evaluated as correct or incorrect, unlike close-ended questions with definitive answers. While large language models (LLMs) have demonstrated strong capabilities across various tasks, they exhibit relatively weaker performance in evaluating answers to open-ended questions. In this study, we propose a method that leverages LLMs and the analytic hierarchy process (AHP) to assess answers to open-ended questions. We utilized LLMs to generate multiple evaluation criteria for a question. Subsequently, answers were subjected to pairwise comparisons under each criterion with LLMs, and scores for each answer were calculated in the AHP. We conducted experiments on four datasets using both ChatGPT-3.5-turbo and GPT-4. Our results indicate that our approach more closely aligns with human judgment compared to the four baselines. Additionally, we explored the impact of the number of criteria, variations in models, and differences in datasets on the results.

Deep learning has enabled breakthroughs in automated diagnosis from medical imaging, with many successful applications in ophthalmology. However, standard medical image classification approaches only assess disease presence at the time of acquisition, neglecting the common clinical setting of longitudinal imaging. For slow, progressive eye diseases like age-related macular degeneration (AMD) and primary open-angle glaucoma (POAG), patients undergo repeated imaging over time to track disease progression and forecasting the future risk of developing disease is critical to properly plan treatment. Our proposed Longitudinal Transformer for Survival Analysis (LTSA) enables dynamic disease prognosis from longitudinal medical imaging, modeling the time to disease from sequences of fundus photography images captured over long, irregular time periods. Using longitudinal imaging data from the Age-Related Eye Disease Study (AREDS) and Ocular Hypertension Treatment Study (OHTS), LTSA significantly outperformed a single-image baseline in 19/20 head-to-head comparisons on late AMD prognosis and 18/20 comparisons on POAG prognosis. A temporal attention analysis also suggested that, while the most recent image is typically the most influential, prior imaging still provides additional prognostic value.

TodevelopanovelUncertaintyQuantification (UQ) framework to estimate the uncertainty of patient survival models in the absence of ground truth, we developed and evaluated our approach based on a dataset of 1383 patients treated with stereotactic radiosurgery (SRS) for brain metastases between January 2015 and December 2020. Our motivating hypothesis is that a time-to-event prediction of a test patient on inference is more certain given a higher feature-space-similarity to patients in the training set. Therefore, the uncertainty for a particular patient-of-interest is represented by the concordance index between a patient similarity rank and a prediction similarity rank. Model uncertainty was defined as the increased percentage of the max uncertainty-constrained-AUC compared to the model AUC. We evaluated our method on multiple clinically-relevant endpoints, including time to intracranial progression (ICP), progression-free survival (PFS) after SRS, overall survival (OS), and time to ICP and/or death (ICPD), on a variety of both statistical and non-statistical models, including CoxPH, conditional survival forest (CSF), and neural multi-task linear regression (NMTLR). Our results show that all models had the lowest uncertainty on ICP (2.21%) and the highest uncertainty (17.28%) on ICPD. OS models demonstrated high variation in uncertainty performance, where NMTLR had the lowest uncertainty(1.96%)and CSF had the highest uncertainty (14.29%). In conclusion, our method can estimate the uncertainty of individual patient survival modeling results. As expected, our data empirically demonstrate that as model uncertainty measured via our technique increases, the similarity between a feature-space and its predicted outcome decreases.