# Deep sub-ensembles meets quantile regression: uncertainty-aware imputation for time series

arXiv: https://arxiv.org/abs/2312.01294 · HTML: https://mlsanity.com/paper/2312.01294/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 66 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [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)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [Uncertainty-Aware Deep Ensembles for Reliable and Explainable Predictions of Clinical Time Series](https://mlsanity.com/paper/2010.11310/) (2020)
- [Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data](https://mlsanity.com/paper/1704.00794/) (2017)
- [Imputation of Clinical Covariates in Time Series](https://mlsanity.com/paper/1812.00418/) (2018)
- [RDIS: Random Drop Imputation with Self-Training for Incomplete Time Series Data](https://mlsanity.com/paper/2010.10075/) (2020)
- [StackVAE-G: An efficient and interpretable model for time series anomaly detection](https://mlsanity.com/paper/2105.08397/) (2021)

## Built on by (most cited first, 1 of 1)

- [Unveiling Uncertainty: A Deep Dive into Calibration and Performance of Multimodal Large Language Models](https://mlsanity.com/paper/2412.14660/) (2024)

## Abstract (arXiv)

Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values to fill in. While previous deep learning methods have proven effective for time series imputation, they often produce overconfident imputations, which poses a potentially overlooked risk to the reliability of the intelligent system. Diffusion methods are proficient in estimating probability distributions but face challenges under a high missing rate and are, moreover, computationally expensive due to the nature of the generative model framework. In this paper, we propose Quantile Sub-Ensembles, a novel method that estimates uncertainty with ensembles of quantile-regression-based task networks and incorporate Quantile Sub-Ensembles into a non-generative time series imputation method. Our method not only produces accurate and reliable imputations, but also remains computationally efficient due to its non-generative framework. We conduct extensive experiments on five real-world datasets, and the results demonstrates superior performance in both deterministic and probabilistic imputation compared to baselines across most experimental settings. The code is available at https://github.com/yingliu-coder/QSE.