# Toward Temporal Causal Representation Learning with Tensor Decomposition

arXiv: https://arxiv.org/abs/2507.14126 · HTML: https://mlsanity.com/paper/2507.14126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 64 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 19 of 19)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [Causal Inference in Recommender Systems: A Survey and Future Directions](https://mlsanity.com/paper/2208.12397/) (2022)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [COPA: Constrained PARAFAC2 for Sparse & Large Datasets](https://mlsanity.com/paper/1803.04572/) (2018)
- [SPARTan: Scalable PARAFAC2 for Large & Sparse Data](https://mlsanity.com/paper/1703.04219/) (2017)
- [An AO-ADMM approach to constraining PARAFAC2 on all modes](https://mlsanity.com/paper/2110.01278/) (2021)
- [A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings](https://mlsanity.com/paper/2007.09605/) (2020)
- [Unsupervised EHR-based Phenotyping via Matrix and Tensor Decompositions](https://mlsanity.com/paper/2209.00322/) (2022)
- [DAG-WGAN: Causal Structure Learning With Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2204.00387/) (2022)
- [MULTIPAR: Supervised Irregular Tensor Factorization with Multi-task Learning](https://mlsanity.com/paper/2208.00993/) (2022)
- [Adapting Projection-Based Reduced-Order Models using Projected Gaussian Process](https://mlsanity.com/paper/2410.14090/) (2024)

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

- [EDGE: Error Dependency Graph-Guided Multi-Error Attribution in Multi-Agent LLM Systems](https://mlsanity.com/paper/2609.01360/) (2026)

## Abstract (arXiv)

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are high-dimensional with varying input lengths and naturally take the form of irregular tensors. To analyze such data, irregular tensor decomposition is critical for extracting meaningful clusters that capture essential information. In this paper, we focus on modeling causal representation learning based on the transformed information. First, we present a novel causal formulation for a set of latent clusters. We then propose CaRTeD, a joint learning framework that integrates temporal causal representation learning with irregular tensor decomposition. Notably, our framework provides a blueprint for downstream tasks using the learned tensor factors, such as modeling latent structures and extracting causal information, and offers a more flexible regularization design to enhance tensor decomposition. Theoretically, we show that our algorithm converges to a stationary point. More importantly, our results fill the gap in theoretical guarantees for the convergence of state-of-the-art irregular tensor decomposition. Experimental results on synthetic and real-world electronic health record (EHR) datasets (MIMIC-III), with extensive benchmarks from both phenotyping and network recovery perspectives, demonstrate that our proposed method outperforms state-of-the-art techniques and enhances the explainability of causal representations.