Efficient learning for models with DAG-structured parameter constraints

In high-dimensional models, hierarchical and structural relationships among features are often used to constrain the search for the more important interactions. These relationships may come from prior knowledge or traditional design principles, such as that low-order effects should have larger contributions than higher-order ones and should be included into the model earlier. However, these structural constraints also make the optimization problem more challenging. In this paper, we propose the use of the alternating direction method of multipliers (ADMM) and accelerated gradient methods. In particular, we show that ADMM can be used to either directly solve the problem or serve as a key building block. Experimental results on a number of synthetic and real-world data sets demonstrate that the proposed algorithm is efficient and flexible. Moreover, the use of the hierarchical relationships consistently improves generalization performance and parameter estimation.