Many modern biomedical applications study association between complex factors, which can be high-dimensional by nature, but the association itself can be captured via low-dimensional structures. Studies involving multiple biological factors such as genetic markers, gene expressions, and disease phenotypes is typical example. The traditional first step in these analyses is the assessment of linear association, formally known as the sparse canonical correlation analysis (SCCA). While SCCA succeeds at enforcing low dimensional structure (sparsity) through the likes of l1l1-penalty, it loses its amenability to classical inference such as testing and confidence intervals via traditional methods. However, proper inferential measures are essential for separating true signals from noise.