Alternatives to EM-based algorithm

The Expectation-Maximization (EM) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, particularly when the model depends on unobserved latent variables. It alternates between an expectation (E) step, which computes the expected value of the log-likelihood function with respect to the current estimate of the latent variables, and a maximization (M) step, which computes the parameters that maximize this expected log-likelihood.

At a glance

Executive summary

The EM-based algorithm is an iterative approach used for parameter estimation in models with latent variables, particularly in mixture models. It is a general framework that can be applied to various probabilistic models, often serving as a foundational method for learning complex data distributions.

TL;DR

If you need a flexible, iterative approach for latent variable models, use EM-based algorithms; if you have a linear causal structure with Gaussian noise and need direct causal inference, consider Gaussian Linear SCM.

Key points

Choose EM-based algorithms when dealing with latent variables or missing data that require iterative refinement of parameters.
Consider Gaussian Linear SCM when your data is known to follow a linear causal structure with Gaussian noise and you require direct causal discovery.
EM-based algorithms are more general and can handle non-linearities and non-Gaussian distributions, whereas Gaussian Linear SCM is specialized for linear Gaussian systems.
If interpretability of direct causal relationships is paramount and the model assumptions hold, Gaussian Linear SCM offers a more direct path.
EM-based algorithms are often used as a building block for more complex models, while Gaussian Linear SCM is a specific model class for causal inference.

Our Take

## Our Take In the realm of statistical modeling, particularly in the context of latent variable analysis, the Expectation-Maximization (EM) algorithm and Gaussian Linear Structural Causal Models (SCM) have emerged as powerful tools, each with its unique strengths and weaknesses. The EM algorithm excels in handling incomplete data and maximizing likelihood estimates, as evidenced by Dempster et al. (1977), who introduced the method as a robust approach for parameter estimation in the presence of latent variables. Its iterative nature allows for flexibility in various applications, from clustering to missing data imputation. However, the EM algorithm can be sensitive to initial conditions and may converge to local optima, which raises concerns about its reliability in complex models (McLachlan & Krishnan, 2008). On the other hand, Gaussian Linear SCM provides a structured framework for understanding causal relationships among variables. As noted by Pearl (2000), SCMs facilitate the identification of causal effects and enable the incorporation of prior knowledge into the modeling process. This framework allows for a clearer interpretation of the relationships between variables, making it particularly advantageous in fields such as epidemiology and social sciences. However, the reliance on the assumption of linearity and normality can be limiting, especially in real-world scenarios where these assumptions may not hold. In conclusion, while the EM algorithm offers flexibility and robustness in data handling, Gaussian Linear SCM provides a more interpretable framework for causal inference. The choice between these methods should be guided by the specific context of the analysis, the nature of the data, and the underlying assumptions that can be reasonably made. Balancing these factors is crucial for achieving reliable and meaningful results in statistical modeling.

Alternative	Difference	Papers (with EM-based algorithm)	Avg viability
Gaussian Linear SCM	—	1	—