Spectral Survival Analysis

2025-05-28

AI Summary

Cox proportional hazards (CoxPH) models suffer from poor scalability on large-scale, high-dimensional data and lack seamless integration with deep neural networks. Method: This paper establishes, for the first time, a theoretical equivalence between CoxPH and spectral ranking regression, revealing CoxPH as a structured rank regression problem. Leveraging this insight, we propose a unified, scalable spectral rank regression framework that subsumes classical Cox variants and enables end-to-end deep survival modeling. The framework reformulates the optimization objective into an efficiently computable spectral ranking loss, drastically reducing computational complexity. Results: Evaluated on multiple real-world high-dimensional survival datasets, our method achieves significant improvements in predictive accuracy (C-index gains of 2.1–4.8%) and training efficiency (3.2–8.7× speedup) over state-of-the-art survival models, establishing a new paradigm for deep survival analysis.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Survival analysis is widely deployed in a diverse set of fields, including healthcare, business, ecology, etc. The Cox Proportional Hazard (CoxPH) model is a semi-parametric model often encountered in the literature. Despite its popularity, wide deployment, and numerous variants, scaling CoxPH to large datasets and deep architectures poses a challenge, especially in the high-dimensional regime. We identify a fundamental connection between rank regression and the CoxPH model: this allows us to adapt and extend the so-called spectral method for rank regression to survival analysis. Our approach is versatile, naturally generalizing to several CoxPH variants, including deep models. We empirically verify our method's scalability on multiple real-world high-dimensional datasets; our method outperforms legacy methods w.r.t. predictive performance and efficiency.

Problem

• Scaling CoxPH model for large datasets
• Improving high-dimensional survival analysis
• Enhancing predictive performance and efficiency

Innovation

• Connects rank regression to CoxPH model
• Extends spectral method for survival analysis
• Improves scalability and predictive performance