In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna, 1996, Chem. Eng. Sci., 51, 1311-1332) for breakage problems. In particular, the convergence is investigated on four different types of uniform and non-uniform meshes. It is shown that the fixed pivot technique is second order convergent on a uniform and non-uniform smooth meshes. Furthermore, it gives fir...

Optimization has always played a central role in machine learning and advances in the field of optimization and mathematical programming have greatly influenced machine learning models. However the connection between optimization and learning is much deeper : one can phrase statistical and online learning problems directly as corresponding optimization problems. In this dissertation I take this...

The problem of characterizing learnability is the most basic question of learning theory. A fundamental and long-standing answer, formally proven for supervised classification and regression, is that learnability is equivalent to uniform convergence, and that if a problem is learnable, it is learnable via empirical risk minimization. Furthermore, for the problem of binary classification, unifor...