# Dynamical Survival Analysis with Controlled Latent States

arXiv: https://arxiv.org/abs/2401.17077 · HTML: https://mlsanity.com/paper/2401.17077/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 30 of 33)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)
- [Machine Learning for Predicting Epileptic Seizures Using EEG Signals: A Review](https://mlsanity.com/paper/2002.01925/) (2020)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [Predicting the impact of treatments over time with uncertainty aware neural differential equations](https://mlsanity.com/paper/2202.11987/) (2022)
- [Scaling ResNets in the Large-depth Regime](https://mlsanity.com/paper/2206.06929/) (2022)
- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [SurvLatent ODE : A Neural ODE based time-to-event model with competing risks for longitudinal data improves cancer-associated Venous Thromboembolism (VTE) prediction](https://mlsanity.com/paper/2204.09633/) (2022)
- [The Brier Score under Administrative Censoring: Problems and Solutions](https://mlsanity.com/paper/1912.08581/) (2019)
- [Functional linear regression with truncated signatures](https://mlsanity.com/paper/2006.08442/) (2020)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Controlled Singular Volterra Integral Equations and Pontryagin Maximum Principle](https://mlsanity.com/paper/1712.05911/) (2017)

## Built on by (most cited first, 7 of 7)

- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [TrajSurv: Learning Continuous Latent Trajectories from Electronic Health Records for Trustworthy Survival Prediction](https://mlsanity.com/paper/2508.00657/) (2025)
- [SeqRisk: Transformer-augmented latent variable model for robust survival prediction with longitudinal data](https://mlsanity.com/paper/2409.12709/) (2024)
- [SigBERT: Combining Narrative Medical Reports and Rough Path Signature Theory for Survival Risk Estimation in Oncology](https://mlsanity.com/paper/2507.22941/) (2025)
- [KANFormer for Predicting Fill Probabilities via Survival Analysis in Limit Order Books](https://mlsanity.com/paper/2512.05734/) (2025)
- [Subgroup Discovery with the Cox Model](https://mlsanity.com/paper/2512.20762/) (2025)
- [MultiSigBERT: Beyond Survival Analysis through Multimodal and Sequential Modeling in Oncology](https://mlsanity.com/paper/2608.16972/) (2026)

## Abstract (arXiv)

We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.