Differential Privacy and the Fat-Shattering Dimension of Linear Queries

In this paper, we consider the task of answering linear queries under the constraint of differential privacy. This is a general and well-studied class of queries that captures other commonly studied classes, including predicate queries and histogram queries. We show that the accuracy to which a set of linear queries can be answered is closely related to its fat-shattering dimension, a property that characterizes the learnability of real-valued functions in the agnostic-learning setting.Comment: Appears in APPROX 201

Complexity of pattern classes and Lipschitz property

Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this property is non-trivial (in contrast to the other properties) and it is believed that the proof in the Gaussian case is conceptually more difficult then the one for the Rademacher case. In this paper we give a detailed prove of the Lipschitz property for the Rademacher case and generalize the same idea to an arbitrary complexity (including the Gaussian). We also discuss a related topic about the Rademacher complexity of a class consisting of all the Lipschitz functions with a given Lipschitz constant. We show that the complexity is surprisingly low in the one-dimensional case. The question for higher dimensions remains open

Calculation of electron-impact total-ionization cross sections

A computationally efficient analytic form of the Born-approximation electron-impact ionization amplitude is derived for general neutral-atom targets. High-quality Hartree-Fock Slater orbitals are used to model the target wave function. Full orthogonalization of the continuum Coulomb wave to all occupied orbitals of the target atom is enforced. Results are presented for noble gases (Ne, Ar, Kr, and Xe), selected transition metals (Fe, Cu, and Ag), and elements from the fourth, fifth, and sixth columns of the periodic table (Si, Ge, Sn, P, As, Sb, S, Se, and Te), where theoretical comparisons are lacking. Full orthogonalization significantly improves agreement with experimental data for the noble-gas series compared to previous Born models. Overall agreement with all elements is uniformly good and variations within each series are systematic

A chain rule for the expected suprema of Gaussian processes

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or the analysis of learning algorithms whenever hypotheses are chosen from composite classes, as is the case for multi-layer models

A Unifying View of Multiple Kernel Learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments

Gendering the careers of young professionals: some early findings from a longitudinal study. in Organizing/theorizing: developments in organization theory and practice

Wonders whether companies actually have employees best interests at heart across physical, mental and spiritual spheres. Posits that most organizations ignore their workforce – not even, in many cases, describing workers as assets! Describes many studies to back up this claim in theis work based on the 2002 Employment Research Unit Annual Conference, in Cardiff, Wales