A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature

• URL: http://arxiv.org/abs/2605.16208v1
• Date: Fri, 15 May 2026 17:25:17 GMT
• Title: A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature
• Abstract summary: We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling.<n>We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy.<n>We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation.
• Score: 6.630048574051614
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Flexible continuous-time survival modeling is critical for capturing complex time-varying hazard dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary hazard dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.

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