Speedy Model Selection (SMS) for Copula Models
This work improves model selection efficiency for copula-based multivariate density estimation, which is useful for statistical modeling in fields like finance or biology, though it appears incremental as it builds on existing copula theory.
The paper addresses efficient structure learning for copula graphical models by theoretically proving Spearman's rank correlation's monotonic relationship with edge importance and proposing a novel Bayesian method using Spearman's rho priors for mixed copula families, demonstrating effectiveness on large real-world datasets.
We tackle the challenge of efficiently learning the structure of expressive multivariate real-valued densities of copula graphical models. We start by theoretically substantiating the conjecture that for many copula families the magnitude of Spearman's rank correlation coefficient is monotone in the expected contribution of an edge in network, namely the negative copula entropy. We then build on this theory and suggest a novel Bayesian approach that makes use of a prior over values of Spearman's rho for learning copula-based models that involve a mix of copula families. We demonstrate the generalization effectiveness of our highly efficient approach on sizable and varied real-life datasets.