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Birkbeck Knowledge Lab seminar: Identifying distinct solutions to continuous optimisation problems

Venue: Online

Estimating (fitting) a model on data always involves the optimisation of an objective function. Frequently, this function does not admit a closed form solution, and is non-convex. The latter property means that the function can have multiple global and local optima. There are numerous ways of estimating different optima of a non-convex function (the simplest being running the optimisation algorithm repeatedly from different random starting locations). A natural question that arises is the following: Given a set of candidate solutions, how many different optima are actually approximated (represented)? This problem is relevant because different optima can be associated with qualitatively different (machine learning/ statistical) models. To the best of our knowledge this problem is studied only from a very practical perspective where computational efficiency is the top priority. We provide a formulation to study this problem and an algorithm derived from this. We establish theoretical results that outline conditions under which our algorithm correctly allocates an arbitrary set of points to basins of attraction of the function. Unlike all existing algorithms, our approach makes no implicit assumptions about the distribution of points relative to the modes (or any other aspect of the morphology) of the objective function.

Contact name:

  • Dr Nicos Pavlidis -

    Nicos Pavlidis has studied Economics at Cambridge University and holds an M.Sc. and Ph.D. in Mathematics of Computers and Decision Making from the University of Patras, Greece. He is currently a senior lecturer at the Department of Management Science, Lancaster University. His research interests are in machine learning, data mining and statistics.