# Missing Value Imputation on Multidimensional Time Series

arXiv: https://arxiv.org/abs/2103.01600 · HTML: https://mlsanity.com/paper/2103.01600/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Jasper: An End-to-End Convolutional Neural Acoustic Model](https://mlsanity.com/paper/1904.03288/) (2019)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [Streaming Adaptation of Deep Forecasting Models using Adaptive Recurrent Units](https://mlsanity.com/paper/1906.09926/) (2019)

## Built on by (most cited first, 30 of 33)

- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [A Multi-Scale Decomposition MLP-Mixer for Time Series Analysis](https://mlsanity.com/paper/2310.11959/) (2023)
- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [PulseImpute: A Novel Benchmark Task for Pulsative Physiological Signal Imputation](https://mlsanity.com/paper/2212.07514/) (2022)
- [Pedestrian Trajectory Prediction with Missing Data: Datasets, Imputation, and Benchmarking](https://mlsanity.com/paper/2411.00174/) (2024)
- [Improving Diffusion Models for ECG Imputation with an Augmented Template Prior](https://mlsanity.com/paper/2310.15742/) (2023)
- [Versatile Cardiovascular Signal Generation with a Unified Diffusion Transformer](https://mlsanity.com/paper/2505.22306/) (2025)
- [On the Relation between Prediction and Imputation Accuracy under Missing Covariates](https://mlsanity.com/paper/2112.05248/) (2021)
- [How Much Can Time-related Features Enhance Time Series Forecasting?](https://mlsanity.com/paper/2412.01557/) (2024)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (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)
- [In-Database Data Imputation](https://mlsanity.com/paper/2401.03359/) (2024)
- [MH-GIN: Multi-scale Heterogeneous Graph-based Imputation Network for AIS Data (Extended Version)](https://mlsanity.com/paper/2507.20362/) (2025)
- [Iterative missing value imputation based on feature importance](https://mlsanity.com/paper/2311.08005/) (2023)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [TRACE: A Temporal Conditional Estimation for Multimodal Time Series Foundation Models](https://mlsanity.com/paper/2606.06285/) (2026)
- [Imputation-free Learning of Tabular Data with Missing Values using Incremental Feature Partitions in Transformer](https://mlsanity.com/paper/2504.14610/) (2025)
- [Temporal Variational Implicit Neural Representations](https://mlsanity.com/paper/2506.01544/) (2025)
- [Coherent Probabilistic Aggregate Queries on Long-horizon Forecasts](https://mlsanity.com/paper/2111.03394/) (2021)
- [Monitoring Time Series With Missing Values: a Deep Probabilistic Approach](https://mlsanity.com/paper/2203.04916/) (2022)
- [Data-Driven Cellular Network Selector for Vehicle Teleoperations](https://mlsanity.com/paper/2410.19791/) (2024)
- [Towards Resource-Efficient Federated Learning in Industrial IoT for Multivariate Time Series Analysis](https://mlsanity.com/paper/2411.03996/) (2024)
- [PIAD-SRNN: Physics-Informed Adaptive Decomposition in State-Space RNN](https://mlsanity.com/paper/2412.00994/) (2024)
- [PyPulse: A Python Library for Biosignal Imputation](https://mlsanity.com/paper/2412.06382/) (2024)
- [DIM-SUM: Dynamic IMputation for Smart Utility Management](https://mlsanity.com/paper/2506.20023/) (2025)
- [Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification](https://mlsanity.com/paper/2510.02216/) (2025)
- [A Unified Variational Imputation Framework for Electric Vehicle Charging Data Using Retrieval-Augmented Language Model](https://mlsanity.com/paper/2601.13476/) (2026)

## Abstract (arXiv)

We present DeepMVI, a deep learning method for missing value imputation in multidimensional time-series datasets. Missing values are commonplace in decision support platforms that aggregate data over long time stretches from disparate sources, and reliable data analytics calls for careful handling of missing data. One strategy is imputing the missing values, and a wide variety of algorithms exist spanning simple interpolation, matrix factorization methods like SVD, statistical models like Kalman filters, and recent deep learning methods. We show that often these provide worse results on aggregate analytics compared to just excluding the missing data. DeepMVI uses a neural network to combine fine-grained and coarse-grained patterns along a time series, and trends from related series across categorical dimensions. After failing with off-the-shelf neural architectures, we design our own network that includes a temporal transformer with a novel convolutional window feature, and kernel regression with learned embeddings. The parameters and their training are designed carefully to generalize across different placements of missing blocks and data characteristics. Experiments across nine real datasets, four different missing scenarios, comparing seven existing methods show that DeepMVI is significantly more accurate, reducing error by more than 50% in more than half the cases, compared to the best existing method. Although slower than simpler matrix factorization methods, we justify the increased time overheads by showing that DeepMVI is the only option that provided overall more accurate analytics than dropping missing values.