Researchers are struggling with the challenge of causal discovery in heterogeneous time-series data, where a single causal model cannot capture diverse causal mechanisms. Traditional methods for causal discovery from time-series data, based on structural causal models, conditional independence tests, and Granger causality, typically assume a uniform causal structure across the entire dataset. However, real-world scenarios often involve multi-modal and highly heterogeneous data, such as gene regulatory networks in different cell stages or varying stock market interactions over time. The oversimplification resulting from applying a single causal model to such complex data hinders accurate representation of the underlying causal relationships, limiting the potential for controllability and counterfactual reasoning in machine learning applications.
Existing approaches to causal discovery in heterogeneous time-series data face significant limitations. Granger causality methods, while common, fail to capture true causality and complex effects. Structural Causal Models (SCMs) offer a more comprehensive framework but often assume linear relationships and uniform causal structures. Advanced techniques like PCMCI and Rhino handle some complexities but still presume a single causal graph. Recent efforts to overcome heterogeneity in independent data show promise, using methods such as heuristic search-and-score, FCI algorithm adaptations, and distance covariance-based clustering. However, these approaches primarily focus on independent data, leaving a gap in addressing temporal dependencies in heterogeneous causal discovery for time series data.
Researchers from UCSD propose a robust approach called Mixture Causal Discovery (MCD) to tackle the challenge of causal discovery in heterogeneous time-series data. This method assumes that the data is generated from a mixture of unknown SCMs, to learn both the complete SCMs and the corresponding membership for each time series sample. MCD employs a variational inference-based framework, optimizing a robust Evidence Lower Bound (ELBO) of the data likelihood to compute the intractable posterior.
Two variants of MCD are presented: MCD-Linear, which models linear relationships with independent noise, and MCD-Nonlinear, which uses neural networks to model functional relationships and history-dependent noise. The researchers also provide theoretical insights into the identifiability of mixtures of linear Gaussian SCMs and general SCMs under certain assumptions.
This approach represents a significant advancement in causal discovery for heterogeneous time-series data, addressing the limitations of existing methods that assume a single causal model for the entire dataset. By simultaneously inferring the complete SCM and the mixture membership of each sample, MCD offers a more realistic and comprehensive solution to the challenges posed by complex, multi-modal data in real-world scenarios.
The MCD approach tackles the challenge of causal discovery in heterogeneous time-series data by assuming that samples are generated from multiple unknown SCMs. MCD employs variational inference to approximate the intractable posterior distribution of SCMs, optimizing a robust ELBO of the data likelihood. The method offers two variants: MCD-Linear for linear relationships with independent noise, and MCD-Nonlinear for nonlinear relationships with history-dependent noise. Theoretically, MCD establishes conditions for the identifiability of mixtures of linear and general SCMs and demonstrates the relationship between the ELBO objective and true data likelihood. This flexible framework can incorporate various likelihood-based causal structure learning algorithms, enabling simultaneous inference of multiple SCMs and sample memberships. By addressing the limitations of existing methods that assume a single causal model, MCD represents a significant advancement in causal discovery for complex, multi-modal time-series data in real-world scenarios.
MCD performed well on synthetic datasets, with MCD-Nonlinear outperforming most baselines on nonlinear data and MCD-Linear achieving comparable or better results on linear data. Both variants showed strong clustering accuracy in identifying the correct underlying causal models. On the Netsim-mixture dataset, MCD-Nonlinear outperformed all baselines in terms of AUROC and F1 scores, demonstrating the benefits of modeling heterogeneity. For the DREAM3 dataset, while all methods struggled, MCD-Nonlinear achieved relatively better performance and showed remarkable clustering accuracy. On the S&P100 dataset, MCD-Nonlinear inferred two distinct causal graphs that captured meaningful sector interactions and identified important market events. Overall, these results demonstrate MCD’s effectiveness in discovering multiple causal structures in heterogeneous time-series data across various synthetic and real-world scenarios.
This research introduces Mixture Causal Discovery, a robust variational inference method for uncovering multiple structural causal models in heterogeneous time-series data. MCD simultaneously learns underlying causal structures and sample memberships, demonstrating effectiveness on synthetic and real-world datasets. Comprehensive ablation studies explore MCD’s behavior under various conditions. The work provides theoretical insights into the identifiability of causal model mixtures. With applications in climate science, finance, and healthcare, MCD addresses the crucial challenge of causal discovery in complex, multimodal data scenarios.
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Asjad is an intern consultant at Marktechpost. He is persuing B.Tech in mechanical engineering at the Indian Institute of Technology, Kharagpur. Asjad is a Machine learning and deep learning enthusiast who is always researching the applications of machine learning in healthcare.
