# Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism

arXiv: https://arxiv.org/abs/2505.07180 · HTML: https://mlsanity.com/paper/2505.07180/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 84 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 30 of 50)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [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)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (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)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)

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

- [Temporal Smoothness Doubly Robust Learning for Debiased Knowledge Tracing](https://mlsanity.com/paper/2605.05958/) (2026)

## Abstract (arXiv)

Time series imputation is one of the most challenge problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the generation process from the observed time series data. In real-world scenarios, different types of missing mechanisms, like MAR (Missing At Random), and MNAR (Missing Not At Random) can occur in time series data. However, existing methods often overlook the difference among the aforementioned missing mechanisms and use a single model for time series imputation, which can easily lead to misleading results due to mechanism mismatching. In this paper, we propose a framework for time series imputation problem by exploring Different Missing Mechanisms (DMM in short) and tailoring solutions accordingly. Specifically, we first analyze the data generation processes with temporal latent states and missing cause variables for different mechanisms. Sequentially, we model these generation processes via variational inference and estimate prior distributions of latent variables via normalizing flow-based neural architecture. Furthermore, we establish identifiability results under the nonlinear independent component analysis framework to show that latent variables are identifiable. Experimental results show that our method surpasses existing time series imputation techniques across various datasets with different missing mechanisms, demonstrating its effectiveness in real-world applications.