Absolute Fused Lasso and Its Application to Genome-Wide Association Studies
Tao Yang*, Arizona State University; Jun Liu, SAS Institute Inc.; Pinghua Gong, University of Michigan; Ruiwen Zhang, SAS Institute Inc.; Xiaotong Shen, University of Minnesota; Jieping Ye, University of Michigan at Ann Arbor
In many real-world applications, the samples/features acquired are in spatial or temporal order. In such cases, the magnitudes of adjacent samples/features are typically close to each other. Meanwhile, in the high-dimensional scenario, identifying the most relevant samples/features is also desired. In this paper, we consider a regularized model which can simultaneously identify important features and group similar features together. The model is based on a penalty called Absolute Fused Lasso (AFL). The AFL penalty encourages sparsity in the coeﬃcients as well as their successive diﬀerences of absolute values—i.e., local constancy of the coeﬃcient components in absolute values. Due to the non-convexity of AFL, it is challenging to develop eﬃcient algorithms to solve the optimization problem. To this end, we employ the Diﬀerence of Convex functions (DC) programming to optimize the proposed non-convex problem. At each DC iteration, we adopt the proximal algorithm to solve a convex regularized sub-problem. One of the major contributions of this paper is to develop a highly eﬃcient algorithm to compute the proximal operator. Empirical studies on both synthetic and real-world data sets from Genome-Wide Association Studies demonstrate the eﬃciency and eﬀectiveness of the proposed approach in simultaneous identifying important features and grouping similar features.
Filed under: Mining Rich Data Types