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Arxiv
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Graphical Transformation Models
- Graphical Transformation Models (GTMs) are a novel approach for modeling intricate multivariate data with complex dependency structures non-parametrically.
- GTMs maintain interpretability by identifying varying conditional independencies and extend multivariate transformation models.
- GTMs replace the Gaussian copula with a custom-designed multivariate transformation, allowing for capturing more complex interdependencies using penalized splines.
- Penalized splines in GTMs also offer an efficient regularization scheme.
- Approximate regularization of GTMs is achieved using a lasso penalty towards pairwise conditional independencies, similar to Gaussian graphical models.
- The robustness and effectiveness of GTMs are validated through simulations, showcasing accurate learning of parametric vine copulas and identification of conditional independencies.
- In a benchmark astrophysics dataset application, GTMs outperform non-parametric vine copulas in learning complex multivariate distributions.
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