Square root Cox's survival analysis by the fittest linear and neural networks model

2025-10-22

AI Summary

To address the low accuracy in feature selection and inefficiency in hyperparameter tuning within the Cox model, this paper proposes a direct optimization method for the regularization parameter based on the square-root Cox partial likelihood. We introduce the square-root partial likelihood into survival analysis for the first time, endowing the regularization parameter with asymptotic pivotality and revealing a phase-transition phenomenon—akin to compressed sensing—in correct variable recovery. The method integrates LASSO regularization, the linear Cox model, and neural network-based joint modeling, thereby circumventing high-variance tuning strategies such as cross-validation or information criteria. Empirical results demonstrate that our approach significantly outperforms CV-LASSO and BIC-based subset selection in both exact variable identification probability and model stability, while preserving statistical interpretability and delivering competitive predictive performance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We revisit Cox's proportional hazard models and LASSO in the aim of improving feature selection in survival analysis. Unlike traditional methods relying on cross-validation or BIC, the penalty parameter $λ$ is directly tuned for feature selection and is asymptotically pivotal thanks to taking the square root of Cox's partial likelihood. Substantially improving over both cross-validation LASSO and BIC subset selection, our approach has a phase transition on the probability of retrieving all and only the good features, like in compressed sensing. The method can be employed by linear models but also by artificial neural networks.

Problem

• Improving feature selection in survival analysis models
• Directly tuning penalty parameters for optimal feature selection
• Applying method to both linear models and neural networks

Innovation

• Square root transformation of Cox partial likelihood
• Direct penalty tuning for feature selection
• Applicable to both linear and neural network models