Comparing Structure Learning Methods for RKHS Embeddings of Protein Structures

Non-parametric graphical models, embedded in reproducing kernel Hilbert spaces, provide a framework to model multi-modal and arbitrary multi-variate distributions, which are essential when modeling complex protein structures. Non-parametric belief propagation requires the structure of the graphical model to be known a priori. Currently there are nonparametric structure learning algorithms available for tree structures, but a tree structure is not reasonable when modeling protein molecular networks. In this paper, we compare parametric neighborhood selection structure learning method, which is capable of recovering true general graph structures, to the non-parametric tree learning method, for the particular task of modeling protein structures represented as sequences of torsion angles. Our experiments, performed on molecular dynamics simulation data of Engrailed Homeodomain protein, show that neighborhood selection method outperforms nonparametric tree structure learning method. We also find that non-parametric models outperform the semi-parametric non-paranormal model as well as the parametric sparse Gaussian graphical model, when an appropriate kernel is used.