Phase transitions in optimal unsupervised learning

Details Phase transitions in optimal unsupervised learning Phase transitions in optimal unsupervised learning

1997-09-25

arxiv.org/abs/cond-mat/9709274v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solution

Scientific paper

10.1103/PhysRevE.57.3326

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.

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