# Individualized Dosing Dynamics via Neural Eigen Decomposition

arXiv: https://arxiv.org/abs/2306.14020 · HTML: https://mlsanity.com/paper/2306.14020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 24 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [A systematic literature review on state-of-the-art deep learning methods for process prediction](https://mlsanity.com/paper/2101.09320/) (2021)
- [Detecting Rewards Deterioration in Episodic Reinforcement Learning](https://mlsanity.com/paper/2010.11660/) (2020)
- [Intermittent Kalman Filtering: Eigenvalue Cycles and Nonuniform Sampling](https://mlsanity.com/paper/1308.6107/) (2013)

## Abstract (arXiv)

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this temporal flexibility often comes with a high sensitivity to noise, whereas medical problems often present high noise and limited data. Moreover, medical dosing models must generalize reliably over individual patients and changing treatment policies. To address these challenges, we introduce the Neural Eigen Stochastic Differential Equation algorithm (NESDE). NESDE provides individualized modeling (using a hypernetwork over patient-level parameters); generalization to new treatment policies (using decoupled control); tunable expressiveness according to the noise level (using piecewise linearity); and fast, continuous, closed-form prediction (using spectral representation). We demonstrate the robustness of NESDE in both synthetic and real medical problems, and use the learned dynamics to publish simulated medical gym environments.