Alternatives to Gaussian Linear SCM

Gaussian Linear SCMs represent causal relationships as a system of linear equations with additive Gaussian noise. They are widely used for their analytical tractability in tasks like estimating causal effects, performing counterfactual reasoning, and discovering causal structures from observational data.

At a glance

Executive summary

Gaussian Linear Structural Causal Models (SCMs) are a foundational class of causal models where relationships are linear and noise is Gaussian. They are a cornerstone in causal inference, providing a tractable framework for understanding cause-effect relationships and enabling the development of various algorithms for causal discovery and effect estimation.

TL;DR

If you need a simple, interpretable causal model with linear relationships and Gaussian noise, use Gaussian Linear SCM; if you need a more general approach for non-Gaussian noise or non-linear relationships, consider EM-based algorithms.

Key points

Gaussian Linear SCMs are ideal when causal relationships are known or assumed to be linear.
The Gaussian noise assumption simplifies parameter estimation and inference.
Interpretability is high due to the direct mapping of coefficients to causal strengths.
These models are a good starting point for causal discovery and intervention analysis.
If your data exhibits significant non-Gaussianity or non-linearities, alternative methods are likely more appropriate.

Our Take

## Our Take When comparing Gaussian Linear State Space Models (GLSSM) with Expectation-Maximization (EM)-based algorithms, it is essential to consider their respective strengths and weaknesses in handling latent variable models. GLSSM offers a robust framework for modeling time series data, capturing both linear trends and Gaussian noise effectively. According to [Durbin and Koopman (2012)](https://doi.org/10.1007/978-1-4471-2740-3), GLSSM excels in scenarios where the underlying processes are continuous and can be well-approximated by Gaussian distributions. On the other hand, EM-based algorithms, particularly in the context of latent variable inference, provide a flexible approach to parameter estimation. As highlighted by [Dempster et al. (1977)](https://doi.org/10.2307/2335942), EM is particularly advantageous when dealing with incomplete data, allowing for iterative refinement of parameter estimates. This adaptability makes EM-based methods appealing in complex models where the likelihood surface is difficult to navigate. However, the computational efficiency of GLSSM often outperforms EM-based algorithms, especially in high-dimensional settings. The Kalman filter, a core component of GLSSM, allows for real-time updates and is computationally efficient, as noted in [Snyder et al. (2008)](https://doi.org/10.1007/978-0-387-74989-6_1). In contrast, EM algorithms can be computationally intensive, particularly when the number of latent variables increases. In conclusion, the choice between GLSSM and EM-based algorithms should be guided by the specific requirements of the application. For real-time analysis with continuous data, GLSSM is preferable, while EM shines in scenarios where flexibility and handling of missing data are paramount.

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