Before revision: The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a real d \times n matrix A, a vector yin^d, a point y\in } R^d, and an integer 2 \leq k \leq d, find an affine combination of at most k columns of A that is closest to y.
After revision: The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set S of n points in \mathbb{R^d, a point y\in } R^d, and an integer 2 \leq k \leq d, find an affine combination of at most k columns of A that is closest to y.