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This paper describes how to incorporate sampled curvature information in a Newton-CG method and in a limited memory quasi-Newton method for statistical learning. The motivation for this work stems from supervised machine learning applications involving a very large number of training points. We follow a batch approach, also known in the stochastic(More)
This paper presents a methodology for using varying sample sizes in batch-type optimization methods for large-scale machine learning problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the function and gradient. We propose a criterion for increasing the sample size based on variance estimates(More)
This paper is concerned with the minimization of an objective that is the sum of a convex function f and an 1 regularization term. Our interest is in methods that incorporate second-order information about the function f to accelerate convergence. We describe a semi-smooth Newton framework that can be used to generate a variety of second-order methods,(More)
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