Measures for the evaluation and comparison of graphical model structures

Structure learning is the identification of the structure of graphical models based solely on observational data and is NP-hard. An important component of many structure learning algorithms are heuristics or bounds to reduce the size of the search space. We argue that variable relevance rankings that can be easily calculated for many standard regression models can be used to improve the efficiency of structure learning algorithms. In this contribution, we describe measures that can be used to evaluate the quality of variable relevance rankings, especially the well-known normalized discounted cumulative gain (NDCG). We evaluate and compare different regression methods using the proposed measures and a set of linear and non-linear benchmark problems.