Previous deep learning approaches for survival analysis have primarily relied on ranking losses to improve discrimination performance, which often comes at the expense of calibration performance. To address such an issue, we propose a novel contrastive learning approach specifically designed to enhance discrimination without sacrificing calibration.

When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated . A survival model's calibration can be measured using, for instance, distributional calibration (

The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis as a principled way of extending the proportional hazard assumption, at the same time being able to leverage the strong approximation power of neural architectures for handling nonlinear covariate dependence.

Survival analysis has become a standard approach for modelling time to default by time-varying covariates in credit risk. Unlike most existing methods that implicitly assume a stationary data-generating process, in practise, mortgage portfolios are exposed to various forms of data drift caused by changing borrower behaviour, macroeconomic conditions, policy regimes and so on. This study investigates the impact of data drift on survival-based credit risk models and proposes a dynamic joint modelling framework to improve robustness under non-stationary environments. The proposed model integrates a longitudinal behavioural marker derived from balance dynamics with a discrete-time hazard formulation, combined with landmark one-hot encoding and isotonic calibration. Three types of data drift (sudden, incremental and recurring) are simulated and analysed on mortgage loan datasets from Freddie Mac. Experiments and corresponding evidence show that the proposed landmark-based joint model consistently outperforms classical survival models, tree-based drift-adaptive learners and gradient boosting methods in terms of discrimination and calibration across all drift scenarios, which confirms the superiority of our model design.

We study survival analysis in the dynamic setting: We seek to model the time to an event of interest given sequences of states. Taking inspiration from temporal-difference learning, a central idea in reinforcement learning, we develop algorithms that estimate a discrete-time survival model by exploiting a temporal-consistency condition. Intuitively, this condition captures the fact that the survival distribution at consecutive states should be similar, accounting for the delay between states. Our method can be combined with any parametric survival model and naturally accommodates right-censored observations. We demonstrate empirically that it achieves better sample-efficiency and predictive performance compared to approaches that directly regress the observed survival outcome.

Survival analysis relies fundamentally on the semi-parametric Cox Proportional Hazards (CoxPH) model and the parametric Accelerated Failure Time (AFT) model. CoxPH assumes constant hazard ratios, often failing to capture real-world dynamics, while traditional AFT models are limited by rigid distributional assumptions. Although deep learning models like DeepAFT address these constraints by improving predictive accuracy and handling censoring, they inherit the significant challenge of black-box interpretability. The recent introduction of CoxKAN demonstrated the successful integration of Kolmogorov-Arnold Networks (KANs), a novel architecture that yields highly accurate and interpretable symbolic representations, within the CoxPH framework. Motivated by the interpretability gains of CoxKAN, we introduce KAN-AFT (Kolmogorov Arnold Network-based AFT), the first framework to apply KANs to the AFT model. Our primary contributions include: (i) a principled AFT-KAN formulation, (ii) robust optimization strategies for right-censored observations (e.g., Buckley-James and IPCW), and (iii) an interpretability pipeline that converts the learned spline functions into closed-form symbolic equations for survival time. Empirical results on multiple datasets confirm that KAN-AFT achieves performance comparable to or better than DeepAFT, while uniquely providing transparent, symbolic models of the survival process.

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, \textit{double-descent}, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define \textit{interpolation} and \textit{finite-norm interpolation}, two key characteristics of loss-based models to understand \textit{double-descent}. We then show the existence (or absence) of \textit{(finite-norm) interpolation} of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of \textit{interpolation} and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.

Abstract--Ride-hailing platforms are characterized by high-frequency, behavior-driven environments, such as shared mobility platforms. Although survival analysis has been widely applied to recurrent events in other domains, its use for modeling ride-hailing driver behavior remains largely unexplored. T o the best of our knowledge, this study is the first to formulate driver idle behavior as a recurrent survival process using large-scale platform data. This study proposes a survival analysis framework that uses a Transformer-based temporal encoder with causal masking to capture long-term temporal dependencies and embeds driver-specific embeddings to represent latent individual characteristics, significantly enhancing the personalized prediction of driver retention risk, modeling how historical idle sequences influence the current risk of leaving the platform via trip acceptance or log-off. The model is validated on datasets from the City of T oronto over the period January 2 to March 13, 2020. The results show that the proposed Frailty-A ware Cox Transformer (F ACT) delivers the highest time-dependent C-indices and the lowest Brier Scores across early, median, and late follow-up, demonstrating its robustness in capturing evolving risk over a driver's lifecycle. This study enables operators to optimize retention strategies and helps policy makers assess shared mobility's role in equitable and integrated transportation systems. The purpose of this study is to model the driver retention behavior through a transformer-based survival model. Shared mobility services, such as ride-hailing, car-sharing, and bike-sharing, are becoming an increasingly prominent component of contemporary transportation systems. These services are central to the broader concept of Mobility as a Service (MaaS) [1], which aims to integrate various forms of transport into a unified and user-centric platform.

Designing optimal treatment plans for patients with comorbidities requires accurate cause-specific mortality prognosis. Motivated by the recent availability of linked electronic health records, we develop a nonparametric Bayesian model for survival analysis with competing risks, which can be used for jointly assessing a patient's risk of multiple (competing) adverse outcomes. The model views a patient's survival times with respect to the competing risks as the outputs of a deep multi-task Gaussian process (DMGP), the inputs to which are the patients' covari-ates. Unlike parametric survival analysis methods based on Cox and Weibull models, our model uses DMGPs to capture complex non-linear interactions between the patients' covariates and cause-specific survival times, thereby learning flexible patient-specific and cause-specific survival curves, all in a data-driven fashion without explicit parametric assumptions on the hazard rates. We propose a varia-tional inference algorithm that is capable of learning the model parameters from time-to-event data while handling right censoring. Experiments on synthetic and real data show that our model outperforms the state-of-the-art survival models.