Transparent Data Mining for Big and Small Data by Tania Cerquitelli Daniele Quercia & Frank Pasquale

Author:Tania Cerquitelli, Daniele Quercia & Frank Pasquale
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

This pair , is feasible for the large LP and the scaled objective value provides an upper bound on . In a similar manner, the solution to the small IP can be extended to a feasible solution of the large IP, thereby giving an upper bound to the optimal IP solution; note that gives a lower bound.

To find a lower bound on we extend the dual solution of the small LP to give a feasible (but generally sub-optimal) dual solution of the large LP. We describe the details in Appendix 3.

The discussion so far has been in the batch setting where all training samples are available at the outset; the only goal is to reduce the computations in solving the linear program. We may also be in an online setting where we can request additional i.i.d. samples and would like to declare that we are close to a solution that will not change much with additional samples. This may be accomplished by computing expected upper and lower bounds on the objective value of the large LP as described in [13].

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