# Continuous-time Autoencoders for Regular and Irregular Time Series Imputation

arXiv: https://arxiv.org/abs/2312.16581 · HTML: https://mlsanity.com/paper/2312.16581/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 59 references that are in the map.
- First posted on arXiv 27 Dec 2023.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Learning Stochastic Recurrent Networks](https://mlsanity.com/paper/1411.7610/) (2014)
- [Applications of deep learning in stock market prediction: recent progress](https://mlsanity.com/paper/2003.01859/) (2020)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)
- [CDSA: Cross-Dimensional Self-Attention for Multivariate, Geo-tagged Time Series Imputation](https://mlsanity.com/paper/1905.09904/) (2019)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [Accurate Stock Price Forecasting Using Robust and Optimized Deep Learning Models](https://mlsanity.com/paper/2103.15096/) (2021)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)

## Built on by (most cited first, 6 of 6)

- [Glocal Information Bottleneck for Time Series Imputation](https://mlsanity.com/paper/2510.04910/) (2025)
- [Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations](https://mlsanity.com/paper/2410.10174/) (2024)
- [Sampling-guided Heterogeneous Graph Neural Network with Temporal Smoothing for Scalable Longitudinal Data Imputation](https://mlsanity.com/paper/2411.04899/) (2024)
- [Boundary-enhanced time series data imputation with long-term dependency diffusion models](https://mlsanity.com/paper/2501.06585/) (2025)
- [InstructTime++: Time Series Classification with Multimodal Language Modeling via Implicit Feature Enhancement](https://mlsanity.com/paper/2601.14968/) (2026)
- [Bridging Dynamic Factor Models and Neural Controlled Differential Equations for Nowcasting GDP](https://mlsanity.com/paper/2409.08732/) (2024)

## Abstract (arXiv)

Time series imputation is one of the most fundamental tasks for time series. Real-world time series datasets are frequently incomplete (or irregular with missing observations), in which case imputation is strongly required. Many different time series imputation methods have been proposed. Recent self-attention-based methods show the state-of-the-art imputation performance. However, it has been overlooked for a long time to design an imputation method based on continuous-time recurrent neural networks (RNNs), i.e., neural controlled differential equations (NCDEs). To this end, we redesign time series (variational) autoencoders based on NCDEs. Our method, called continuous-time autoencoder (CTA), encodes an input time series sample into a continuous hidden path (rather than a hidden vector) and decodes it to reconstruct and impute the input. In our experiments with 4 datasets and 19 baselines, our method shows the best imputation performance in almost all cases.