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

The Symmetry of a Simple Optimization Problem in Lasso Screening