A1380
Title: Location-scale graphical model
Authors: Matthias Herp - Georg-August-Universitaet Goettingen (Germany) [presenting]
Abstract: The Location-Scale Graphical Model (LSGM) is a framework for learning multivariate dependencies that captures both location and scale interactions between variables with arbitrary continuous marginals. Built upon marginal transformation models, the approach maps each variable to a latent representation, enabling interpretable conditional dependencies in the spirit of GAMLSS. The joint density is specified as an unnormalized product of pairwise interaction terms, where spline-based effects modulate both the location and scale of each variable given its neighbors. Conditional independence is encoded through simultaneous zero constraints on both parameter types, yielding a sparse Graphical structure. Location effects are interpreted via monotone likelihood ratios implying first-order stochastic dominance, while scale effects are justified through the Brascamp-Lieb inequality, providing variance upper bounds. Estimation is performed via score matching, bypassing the intractable normalizing constant, resulting in a constrained quadratic program with ridge and group lasso penalties promoting sparsity. Simulation studies demonstrate accurate recovery of sparse graph structures and interpretable spline estimates. Compared to existing Graphical models, the LSGM offers a favorable trade-off between rich dependency modelling and interpretability of effects and conditional dependencies.
