  Recently dictionary screening has been proposed as an effective way to
improve the computational efficiency of solving the lasso problem, which is one
of the most commonly used method for learning sparse representations. To
address today's ever increasing large dataset, effective screening relies on a
tight region bound on the solution to the dual lasso. Typical region bounds are
in the form of an intersection of a sphere and multiple half spaces. One way to
tighten the region bound is using more half spaces, which however, adds to the
overhead of solving the high dimensional optimization problem in lasso
screening. This paper reveals the interesting property that the optimization
problem only depends on the projection of features onto the subspace spanned by
the normals of the half spaces. This property converts an optimization problem
in high dimension to much lower dimension, and thus sheds light on reducing the
computation overhead of lasso screening based on tighter region bounds.
