# Probabilistic Imputation for Time-series Classification with Missing Data

arXiv: https://arxiv.org/abs/2308.06738 · HTML: https://mlsanity.com/paper/2308.06738/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 13 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [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)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [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)
- [Set Functions for Time Series](https://mlsanity.com/paper/1909.12064/) (2019)
- [Phased LSTM: Accelerating Recurrent Network Training for Long or Event-based Sequences](https://mlsanity.com/paper/1610.09513/) (2016)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)

## Built on by (most cited first, 22 of 22)

- [UniTS: A Unified Multi-Task Time Series Model](https://mlsanity.com/paper/2403.00131/) (2024)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [TSI-Bench: Benchmarking Time Series Imputation](https://mlsanity.com/paper/2406.12747/) (2024)
- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [SciTS: Scientific Time Series Understanding and Generation with LLMs](https://mlsanity.com/paper/2510.03255/) (2025)
- [Glocal Information Bottleneck for Time Series Imputation](https://mlsanity.com/paper/2510.04910/) (2025)
- [SMART: Towards Pre-trained Missing-Aware Model for Patient Health Status Prediction](https://mlsanity.com/paper/2405.09039/) (2024)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Cross-Domain Conditional Diffusion Models for Time Series Imputation](https://mlsanity.com/paper/2506.12412/) (2025)
- [Diffusion model for relational inference](https://mlsanity.com/paper/2401.16755/) (2024)
- [Risk-based Calibration for Generative Classifiers](https://mlsanity.com/paper/2409.03542/) (2024)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism](https://mlsanity.com/paper/2505.07180/) (2025)
- [Modular Deep Learning for Multivariate Time-Series: Decoupling Imputation and Downstream Tasks](https://mlsanity.com/paper/2411.03941/) (2024)
- [Decentralized Federated Learning of Probabilistic Generative Classifiers](https://mlsanity.com/paper/2507.17285/) (2025)
- [Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification](https://mlsanity.com/paper/2510.02216/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [CINDI: Conditional Imputation and Noisy Data Integrity with Flows in Power Grid Data](https://mlsanity.com/paper/2603.11745/) (2026)
- [MBDiff: Multi-view Behavior-aware Diffusion Model for Probabilistic Utility Data Imputation](https://mlsanity.com/paper/2607.29177/) (2026)
- [Discretizing Continuous Time Series for Imputation with Masked Diffusion Training](https://mlsanity.com/paper/2608.19119/) (2026)
- [Domain Generalization under Sampling Pattern Shifts in Irregular Time Series](https://mlsanity.com/paper/2609.33279/) (2026)
- [The Effect of Missingness-Pattern Mismatch on Method Selection for Time-Series Classification: A Controlled Empirical Study](https://mlsanity.com/paper/2610.05368/) (2026)

## Abstract (arXiv)

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values (zero, mean, values of adjacent time-steps) or learnable parameters. However, these simple strategies do not take the data generative process into account, and more importantly, do not effectively capture the uncertainty in prediction due to the multiple possibilities for the missing values. In this paper, we propose a novel probabilistic framework for classification with multivariate time series data with missing values. Our model consists of two parts; a deep generative model for missing value imputation and a classifier. Extending the existing deep generative models to better capture structures of time-series data, our deep generative model part is trained to impute the missing values in multiple plausible ways, effectively modeling the uncertainty of the imputation. The classifier part takes the time series data along with the imputed missing values and classifies signals, and is trained to capture the predictive uncertainty due to the multiple possibilities of imputations. Importantly, we show that na"ively combining the generative model and the classifier could result in trivial solutions where the generative model does not produce meaningful imputations. To resolve this, we present a novel regularization technique that can promote the model to produce useful imputation values that help classification. Through extensive experiments on real-world time series data with missing values, we demonstrate the effectiveness of our method.