Intrinsic Geometries in Learning

11 years 3 months ago
Intrinsic Geometries in Learning
In a seminal paper, Amari (1998) proved that learning can be made more efficient when one uses the intrinsic Riemannian structure of the algorithms' spaces of parameters to point the gradient towards better solutions. In this paper, we show that many learning algorithms, including various boosting algorithms for linear separators, the most popular top-down decision-tree induction algorithms, and some on-line learning algorithms, are spawns of a generalization of Amari's natural gradient to some particular non-Riemannian spaces. These algorithms exploit an intrinsic dual geometric structure of the space of parameters in relationship with particular integral losses that are to be minimized. We unite some of them, such as AdaBoost, additive regression with the square loss, the logistic loss, the top-down induction performed in CART and C4.5, as a single algorithm on which we show general convergence to the optimum and explicit convergence rates under very weak assumptions. As a ...
Richard Nock, Frank Nielsen
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where ETVC
Authors Richard Nock, Frank Nielsen
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