Some estimation methods have a computational effort that rises exponentially with n if done naively. An example of this is a method of data cleaning that depends on finding the most compact half of the data and then evaluating each point against this half. Specifically, the MCD method finds that half of the data for which the determinant of the covariance matrix of the data is smallest. Data Mining Computer Science theorists usually strive to find methods that are deterministic, get the right answer every time, and run in worst-case polynomial time. The problems that we face cannot apparently be accomplished without giving up something from this list most likely, we will need to give up both determinism and sure correctness.
Many problems have both a discrete and a continuous formulation.
Discrete methods can yield search techniques with no obvious or easy continuous analog, thus improving the search for the local optimum. Often it is very effective to use a discrete heuristic search method to provide one or more starting points for locating optima of a continuous global optimization problem. Simulated annealing can perform well if tuned properly, but we have had more success with other methods. The Role of Algorithms in Statistical Science At one time, it would have been feasible to argue that algorithms were not central to statistical science because all a better algorithm did was somewhat speed up arriving at essentially the same estimate. Things have changed.