PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Compatible worlds
Bruno Apolloni, Simone Bassis and Dario Malchiodi
Nonlinear Analysis: Theory, Methods & Applications Volume 71, Number 12, pp. 2883-2901, 2009.


We discuss a bridge way of inference between Agnostic Learning and Prior Knowledge based on an inference goal represented not by the attainment of truth but simply by a suitable organization of the knowledge we have accumulated on the observed data. In a framework where this knowledge is not definite, we smear it across a series of possible models that we characterize through a probability measure of effectively explaining the observed data which denotes their compatibility with them. We point out the main features and benefits of our approach w.r.t. the two direct competitors: namely, the frequentist and Bayesian approaches, representative respectively of agnostic and a priori knowledge paradigms. Then we explore in greater depth its implementation for learning Boolean functions, showing an unprecedented relation between complexity of the concept class to be learnt and some peculiarities of the features through which the inference problem is represented. Exploiting this relation allows us to compute concretely suitable upper bounds to the classification errors of these functions when they are learnt through a soft-margin kernel-based Support Vector Machine.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:6102
Deposited By:Dario Malchiodi
Deposited On:08 March 2010