  This paper is about searching the combinatorial space of contingency tables
during the inner loop of a nonlinear statistical optimization. Examples of this
operation in various data analytic communities include searching for nonlinear
combinations of attributes that contribute significantly to a regression
(Statistics), searching for items to include in a decision list (machine
learning) and association rule hunting (Data Mining).
  This paper investigates a new, efficient approach to this class of problems,
called RADSEARCH (Real-valued All-Dimensions-tree Search). RADSEARCH finds the
global optimum, and this gives us the opportunity to empirically evaluate the
question: apart from algorithmic elegance what does this attention to
optimality buy us?
  We compare RADSEARCH with other recent successful search algorithms such as
CN2, PRIM, APriori, OPUS and DenseMiner. Finally, we introduce RADREG, a new
regression algorithm for learning real-valued outputs based on RADSEARCHing for
high-order interactions.
