# Causal Hidden Markov Model for Time Series Disease Forecasting

arXiv: https://arxiv.org/abs/2103.16391 · HTML: https://mlsanity.com/paper/2103.16391/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Diverse Image Captioning with Context-Object Split Latent Spaces](https://mlsanity.com/paper/2011.00966/) (2020)
- [Latent Causal Invariant Model](https://mlsanity.com/paper/2011.02203/) (2020)
- [GSplit LBI: Taming the Procedural Bias in Neuroimaging for Disease Prediction](https://mlsanity.com/paper/1705.09249/) (2017)

## Built on by (most cited first, 19 of 19)

- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Causal conditional hidden Markov model for multimodal traffic prediction](https://mlsanity.com/paper/2301.08249/) (2023)
- [Probabilistic Decomposition Transformer for Time Series Forecasting](https://mlsanity.com/paper/2210.17393/) (2022)
- [Structure Causal Models and LLMs Integration in Medical Visual Question Answering](https://mlsanity.com/paper/2505.02703/) (2025)
- [Learning Time-Aware Causal Representation for Model Generalization in Evolving Domains](https://mlsanity.com/paper/2506.17718/) (2025)
- [Instrumental Variable Learning for Chest X-ray Classification](https://mlsanity.com/paper/2305.12070/) (2023)
- [Artificial Intelligence for Biomedical Video Generation](https://mlsanity.com/paper/2411.07619/) (2024)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [Evidence-aware multi-modal data fusion and its application to total knee replacement prediction](https://mlsanity.com/paper/2303.13810/) (2023)
- [Dynamic Causal Disentanglement Model for Dialogue Emotion Detection](https://mlsanity.com/paper/2309.06928/) (2023)
- [Beyond All-to-All: Causal-Aligned Transformer with Dynamic Structure Learning for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.16308/) (2025)
- [Context-LGM: Leveraging Object-Context Relation for Context-Aware Object Recognition](https://mlsanity.com/paper/2110.04042/) (2021)
- [Causal Disentanglement Hidden Markov Model for Fault Diagnosis](https://mlsanity.com/paper/2308.03027/) (2023)
- [MCNS: Mining Causal Natural Structures Inside Time Series via A Novel Internal Causality Scheme](https://mlsanity.com/paper/2309.06739/) (2023)
- [Pyramidal Hidden Markov Model For Multivariate Time Series Forecasting](https://mlsanity.com/paper/2310.14341/) (2023)
- [Towards Causal Relationship in Indefinite Data: Baseline Model and New Datasets](https://mlsanity.com/paper/2401.08221/) (2024)
- [When are radiology reports useful for training medical image classifiers?](https://mlsanity.com/paper/2510.24385/) (2025)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## Abstract (arXiv)

We propose a causal hidden Markov model to achieve robust prediction of irreversible disease at an early stage, which is safety-critical and vital for medical treatment in early stages. Specifically, we introduce the hidden variables which propagate to generate medical data at each time step. To avoid learning spurious correlation (e.g., confounding bias), we explicitly separate these hidden variables into three parts: a) the disease (clinical)-related part; b) the disease (non-clinical)-related part; c) others, with only a),b) causally related to the disease however c) may contain spurious correlations (with the disease) inherited from the data provided. With personal attributes and the disease label respectively provided as side information and supervision, we prove that these disease-related hidden variables can be disentangled from others, implying the avoidance of spurious correlation for generalization to medical data from other (out-of-) distributions. Guaranteed by this result, we propose a sequential variational auto-encoder with a reformulated objective function. We apply our model to the early prediction of peripapillary atrophy and achieve promising results on out-of-distribution test data. Further, the ablation study empirically shows the effectiveness of each component in our method. And the visualization shows the accurate identification of lesion regions from others.