A Parameterized Theory of PAC Learning

Statistical Learning Theory: A PAC-Bayesian Approach

Computational Learning Theory: PAC Model

Data-driven learning has shown great promise in a number of practical applications, ranging from financial forecasting to medical diagnosis, computer vision, search engines, recommendation systems etc. They are particularly effective where concepts are somewhat fuzzy and difficult to model precisely and rigorously. For instance, how does Netflix recommend movies for you to watch? Prescribing ou...

une approche PAC-Bayésienne PAC-Bayesian Statistical Learning Theory

This PhD thesis is a mathematical study of the learning task – specifically classification and least square regression – in order to better understand why an algorithm works and to propose more efficient procedures. The thesis consists in four papers. The first one provides a PAC bound for the L generalization error of methods based on combining regression procedures. This bound is tight to the...

PAC-Bayesian Theory for Transductive Learning

We propose a PAC-Bayesian analysis of the transductive learning setting by proposing a family of new bounds on the generalization error. Inductive Learning Training set We draw m examples i.i.d. from a distribution D on X×{−1,+1}: S = {(x1, y1), (x2, y2), . . . , (xm, ym)} ∼ D . Task of an inductive learner Using S, learn a classifier h : X 7→ {−1,+1} that has a low generalization risk on new e...

A. Pac Learning

• Let X=R with orthonormal basis (e1, e2) and consider the set of concepts defined by the area inside a right triangle ABC with two sides parallel to the axes, with −−→ AB/AB = e1 and −→ AC/AC = e2, and AB/AC = α for some positive real α ∈ R+. Show, using similar methods to those used in the lecture slides for the axis-aligned rectangles, that this class can be (ǫ, δ)PAC-learned from training d...