# NRTSI: Non-Recurrent Time Series Imputation

arXiv: https://arxiv.org/abs/2102.03340 · HTML: https://mlsanity.com/paper/2102.03340/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 61 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Builds on (most cited first, 30 of 37)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Set Functions for Time Series](https://mlsanity.com/paper/1909.12064/) (2019)
- [Lipschitz Continuity in Model-based Reinforcement Learning](https://mlsanity.com/paper/1804.07193/) (2018)
- [MaskGAN: Better Text Generation via Filling in the______](https://mlsanity.com/paper/1801.07736/) (2018)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [Modeling Missing Data in Clinical Time Series with RNNs](https://mlsanity.com/paper/1606.04130/) (2016)
- [Diverse and Admissible Trajectory Forecasting through Multimodal Context Understanding](https://mlsanity.com/paper/2003.03212/) (2020)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)

## Built on by (most cited first, 25 of 25)

- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [GinAR: An End-To-End Multivariate Time Series Forecasting Model Suitable for Variable Missing](https://mlsanity.com/paper/2405.11333/) (2024)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Phoneme Hallucinator: One-shot Voice Conversion via Set Expansion](https://mlsanity.com/paper/2308.06382/) (2023)
- [Pedestrian Trajectory Prediction with Missing Data: Datasets, Imputation, and Benchmarking](https://mlsanity.com/paper/2411.00174/) (2024)
- [Correlated Attention in Transformers for Multivariate Time Series](https://mlsanity.com/paper/2311.11959/) (2023)
- [Continuous-time Autoencoders for Regular and Irregular Time Series Imputation](https://mlsanity.com/paper/2312.16581/) (2023)
- [Understand Legal Documents with Contextualized Large Language Models](https://mlsanity.com/paper/2303.12135/) (2023)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Learnable Prompt as Pseudo-Imputation: Rethinking the Necessity of Traditional EHR Data Imputation in Downstream Clinical Prediction](https://mlsanity.com/paper/2401.16796/) (2024)
- [Transparent Single-Cell Set Classification with Kernel Mean Embeddings](https://mlsanity.com/paper/2201.07322/) (2022)
- [Trajectory Imputation in Multi-Agent Sports with Derivative-Accumulating Self-Ensemble](https://mlsanity.com/paper/2408.10878/) (2024)
- [ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data](https://mlsanity.com/paper/2505.10856/) (2025)
- [An End-to-End Time Series Model for Simultaneous Imputation and Forecast](https://mlsanity.com/paper/2306.00778/) (2023)
- [Towards Cost Sensitive Decision Making](https://mlsanity.com/paper/2410.03892/) (2024)
- [MTM: A Multi-Scale Token Mixing Transformer for Irregular Multivariate Time Series Classification](https://mlsanity.com/paper/2509.17809/) (2025)
- [Multistage Large Segment Imputation Framework Based on Deep Learning and Statistic Metrics](https://mlsanity.com/paper/2209.11766/) (2022)
- [PIAD-SRNN: Physics-Informed Adaptive Decomposition in State-Space RNN](https://mlsanity.com/paper/2412.00994/) (2024)
- [STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems](https://mlsanity.com/paper/2508.19011/) (2025)
- [A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting](https://mlsanity.com/paper/2601.21812/) (2026)
- [RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation](https://mlsanity.com/paper/2609.11648/) (2026)

## Abstract (arXiv)

Time series imputation is a fundamental task for understanding time series with missing data. Existing methods either do not directly handle irregularly-sampled data or degrade severely with sparsely observed data. In this work, we reformulate time series as permutation-equivariant sets and propose a novel imputation model NRTSI that does not impose any recurrent structures. Taking advantage of the permutation equivariant formulation, we design a principled and efficient hierarchical imputation procedure. In addition, NRTSI can directly handle irregularly-sampled time series, perform multiple-mode stochastic imputation, and handle data with partially observed dimensions. Empirically, we show that NRTSI achieves state-of-the-art performance across a wide range of time series imputation benchmarks.