# FastSurvival: Hidden Computational Blessings in Training Cox Proportional Hazards Models

arXiv: https://arxiv.org/abs/2410.19081 · HTML: https://mlsanity.com/paper/2410.19081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 71 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Sequence-to-Sequence Learning as Beam-Search Optimization](https://mlsanity.com/paper/1606.02960/) (2016)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Restricted Strong Convexity Implies Weak Submodularity](https://mlsanity.com/paper/1612.00804/) (2016)
- [FasterRisk: Fast and Accurate Interpretable Risk Scores](https://mlsanity.com/paper/2210.05846/) (2022)
- [Fast Sparse Classification for Generalized Linear and Additive Models](https://mlsanity.com/paper/2202.11389/) (2022)
- [SurvSet: An open-source time-to-event dataset repository](https://mlsanity.com/paper/2203.03094/) (2022)
- [abess: A Fast Best Subset Selection Library in Python and R](https://mlsanity.com/paper/2110.09697/) (2021)
- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Optimal Survival Trees](https://mlsanity.com/paper/2012.04284/) (2020)
- [OKRidge: Scalable Optimal k-Sparse Ridge Regression](https://mlsanity.com/paper/2304.06686/) (2023)
- [Optimal Survival Trees: A Dynamic Programming Approach](https://mlsanity.com/paper/2401.04489/) (2024)
- [Optimal Sparse Survival Trees](https://mlsanity.com/paper/2401.15330/) (2024)
- [The Digital Twin Landscape at the Crossroads of Predictive Maintenance, Machine Learning and Physics Based Modeling](https://mlsanity.com/paper/2206.10462/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning Survival Models with Right-Censored Reporting Delays](https://mlsanity.com/paper/2510.04421/) (2025)

## Abstract (arXiv)

Survival analysis is an important research topic with applications in healthcare, business, and manufacturing. One essential tool in this area is the Cox proportional hazards (CPH) model, which is widely used for its interpretability, flexibility, and predictive performance. However, for modern data science challenges such as high dimensionality (both n and p) and high feature correlations, current algorithms to train the CPH model have drawbacks, preventing us from using the CPH model at its full potential. The root cause is that the current algorithms, based on the Newton method, have trouble converging due to vanishing second order derivatives when outside the local region of the minimizer. To circumvent this problem, we propose new optimization methods by constructing and minimizing surrogate functions that exploit hidden mathematical structures of the CPH model. Our new methods are easy to implement and ensure monotonic loss decrease and global convergence. Empirically, we verify the computational efficiency of our methods. As a direct application, we show how our optimization methods can be used to solve the cardinality-constrained CPH problem, producing very sparse high-quality models that were not previously practical to construct. We list several extensions that our breakthrough enables, including optimization opportunities, theoretical questions on CPH's mathematical structure, as well as other CPH-related applications.