A1340
Title: Learning implicit multivariate interactions via Gibbs relaxation
Authors: Tongseok Lim - Purdue University (United States) [presenting]
Wooseok Ha - KAIST (Korea, South)
Kyeongsik Nam - KAIST (Korea, South)
Abstract: Estimating joint densities in high dimensions is challenging, especially when dependence lies on lower-dimensional structures that classical nonparametric methods miss and parametric models oversimplify. A structured nonparametric framework is proposed based on an exponential-family form in which the log-density decomposes into marginal potentials and an interaction term capturing dependence beyond marginals. Interpreting maximum likelihood estimation through a statistical-mechanics lens as learning an energy landscape unifies three perspectives. First, it connects to entropic optimal transport (EOT): unlike EOT, which fixes interactions via a cost and uses empirical marginals, the approach learns both components from data. Second, jointly learning marginals and interactions separates marginal effects from intrinsic dependence, making the interaction directly interpretable. Third, imposing a one-sided constraint on the log-density yields a contact set that acts as a latent monotone structure, providing a soft (positive-temperature) relaxation of hard monotonic constraints. Theoretically, convergence rates for the MLE are derived using a pseudo self-concordance bound on the third derivative of the free energy, leading to error bounds governed by the complexity of the log-density class. Empirical results demonstrate the effectiveness of the approach.
