# Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series

**Authors:** Abdul Fatir Ansari, Alvin Heng, Andre Lim, Harold Soh  
**arXiv:** [2301.11308](https://arxiv.org/abs/2301.11308)  
**Date:** 2023-01-26  
**Summary page:** https://www.summarizepaper.com/en/paper/2301.11308v1/

## Key points

- Learning accurate predictive models of real-world dynamic phenomena is challenging due to irregular sampling and missing observations in the data.
- The authors propose a Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations.
- The NCDSSM separates recognition from dynamics using auxiliary variables, allowing for amortized inference only for the auxiliary variables.
- Techniques from continuous-discrete filtering theory are leveraged to perform accurate Bayesian inference for the dynamic states.
- Three flexible parameterizations of the latent dynamics are proposed, along with an efficient training objective that marginalizes the dynamic states during inference.
- Empirical results on multiple benchmark datasets show that NCDSSM outperforms existing models in terms of imputation and forecasting performance.
- NCDSSM is effective in handling irregularly sampled time series with missing observations.
- This work contributes to improving predictive modeling of real-world dynamic phenomena by addressing challenges posed by irregularly sampled data.

## Summary

Learning accurate predictive models of real-world dynamic phenomena is a challenging task due to the irregular sampling and missing observations in the data. To address this issue, the authors propose a Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. The NCDSSM utilizes auxiliary variables to separate recognition from dynamics, allowing for amortized inference only for the auxiliary variables. By leveraging techniques from continuous-discrete filtering theory, the authors demonstrate how to perform accurate Bayesian inference for the dynamic states. They propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. The empirical results on multiple benchmark datasets across various domains show that NCDSSM outperforms existing models in terms of imputation and forecasting performance. This suggests that NCDSSM is effective in handling irregularly sampled time series with missing observations. Overall, this work contributes to improving predictive modeling of real-world dynamic phenomena by providing a novel approach that addresses the challenges posed by irregularly sampled data.