Machine Learning for Survival Analysis: A Survey <s> OSCAR-Cox: <s> High-dimensional regression/classification continues to be an important and challenging problem, especially when features are highly correlated. Feature selection, combined with additional structure information on the features has been considered to be promising in promoting regression/classification performance. Graph-guided fused lasso (GFlasso) has recently been proposed to facilitate feature selection and graph structure exploitation, when features exhibit certain graph structures. However, the formulation in GFlasso relies on pairwise sample correlations to perform feature grouping, which could introduce additional estimation bias. In this paper, we propose three new feature grouping and selection methods to resolve this issue. The first method employs a convex function to penalize the pairwise l∞ norm of connected regression/classification coefficients, achieving simultaneous feature grouping and selection. The second method improves the first one by utilizing a non-convex function to reduce the estimation bias. The third one is the extension of the second method using a truncated l1 regularization to further reduce the estimation bias. The proposed methods combine feature grouping and feature selection to enhance estimation accuracy. We employ the alternating direction method of multipliers (ADMM) and difference of convex functions (DC) programming to solve the proposed formulations. Our experimental results on synthetic data and two real datasets demonstrate the effectiveness of the proposed methods. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> OSCAR-Cox: <s> Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certain disease such as leukemia, even though humans have tens of thousands of genes, only a few genes are relevant to the disease; a gene network is sparse since a regulatory pathway involves only a small number of genes; many biomedical signals are sparse or compressible in the sense that they have concise representations when expressed in a proper basis. Therefore, finding sparse representations is fundamentally important for scientific discovery. Sparse methods based on the '1 norm have attracted a great amount of research efforts in the past decade due to its sparsity-inducing property, convenient convexity, and strong theoretical guarantees. They have achieved great success in various applications such as biomarker selection, biological network construction, and magnetic resonance imaging. In this paper, we review state-of-the-art sparse methods and their applications to biomedical data. <s> BIB002
The modified graph Octagonal Shrinkage and Clustering Algorithm for Regression (OSCAR) BIB001 BIB002 regularizer is incorporated in the basic Cox model as the OSCAR-Cox algorithm (Vinzamuri and Reddy 2013), which can perform variable selection for highly correlated features in the regression problem. The main advantage of using an OSCAR regularizer is that it tends to have equal coefficients for the features that relate to the outcome in similar ways. At the same time, it gains the advantages of both individual sparsity because of the 1 norm and group sparsity due to the ∞ norm. The regularizer used in the formulation of OSCAR-Cox is given in Table 3 , where T is the sparse symmetric edge set matrix generated by building a graph structure that considers each feature as an individual node. In this way, a pairwise feature regularizer can be incorporated into the basic Cox regression framework. Among the regularizers shown in Table 3 , the parameters λ ≥ 0 can be tuned to adjust the influence introduced by the regularizer term. The performance of these penalized estimators depends significantly on λ, and the optimal λ opt can be chosen via cross-validation.