In close collaboration with Seoul National University's Structural Complexity Laboratory

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 — about:variable [2010/10/29 01:42] (current)rim created 2010/10/29 01:42 rim created 2010/10/29 01:42 rim created Line 1: Line 1: + ====== Variable complexity problems ====== + + Variable complexity problems are problems in which the main problem is to find a suitable set of values for a set of parameters, but we don't know how many. However we already know the relationships between the parameters. Problems falling into this class include + + * A few optimisation problems, where the aim is to find real-number coefficients x1,...,xn where we don't know how large n needs to be beforehand - this includes cases such as power or fourier series approximations  ​ + * Some discrete optimisation problems, we may not know ahead of time how many parameters x1,..., are required ​ + * For example knapsack problems, stock cutting problems ​ + * Polynomial regression, where we don't know ahead of time how high degree polynomial is required to get an acceptable fit + * Most interesting attribute learning problems fall into this class - decision trees, decision rules etc + * While solutions aren't completely unstructured,​ there are many transformation symmetries (transitivity,​ commutativity,​...) so discovering the structure is generally not the hard part of the problem ​ + + Methods for solving such problems include + * Gradient descent and similar deterministic eager search methods ​ + * Stochastic search (simulated annealing, tabu search, genetic algorithms) ​ + + While this isn't the primary focus of research in the structural complexity lab, we do some research in these areas from time to time; we tend to be more interested in + + * Dynamic problems, where the optimal solution changes with time + * Problems belonging to a family of problems, so tough versions can be solved incrementally from first solving simpler ones 