Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.Complexity regularization, model selection, error estimation, concentration of measure

Connectivity of sparse Bluetooth networks

Consider a random geometric graph defined on n vertices uniformly distributed in the d-dimensional unit torus. Two vertices are connected if their distance is less than a “visibility radius ” rn. We consider Bluetooth networks that are locally sparsified random geometric graphs. Each vertex selects c of its neighbors in the random geometric graph at random and connects only to the selected points. We show that if the visibility radius is at least of the order of n−(1−δ)/d for some δ> 0, then a constant value of c is sufficient for the graph to be connected, with high probability. It suffices to take c ≥ √ (1 + ɛ)/δ + K for any positive ɛ where K is a constant depending on d only. On the other hand, with c ≤ √ (1 − ɛ)/δ, the graph is disconnected, with high probability. 1 Introduction an

The Production of Hospitable Space: Commercial Propositions and Consumer Co-Creation in a Bar Operation

This paper examines the processes through which a commercial bar is transformed into a hospitable space. Drawing on a study of a venue patronized by lesbian, gay, bisexual and transsexual/transgender consumers, it considers how social and commercial forms of hospitality are mobilized. The paper argues that hospitable space has an ideological, normative and situational dimension. More specifically, it suggests the bar’s operation is tied to a set of ideological conceptions, which become the potential basis of association and disassociation among consumers. It examines the forces and processes that shape who participates in the production and consumption of hospitality and how. Finally, it considers the situational, emergent nature of hospitality and the discontinuous production of hospitable space. Rather than focusing exclusively on host-guest or provider-customer relations, which dominates existing work on hospitality, the paper examines how consumers’ perceptions, actions and interactions shape the production of hospitality. By doing so the paper offers an alternative approach to understanding queer spaces, bar operation as well as hospitality

Calculation of the matrix elements of the Coulomb interaction involving relativistic hydrogenic wave functions

Abstract A program is presented for calculation of the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ψ † f (r)|R − r| −1 ψ i (r) dr. Bound-free transitions are considered. Relativistic hydrogenic wave functions are used for the numerical evaluation of the matrix elements. The applied algorithm is based on the multipole series expansion of the Coulomb potential. The radial part of the terms of this series expansion (known as G functions) can also be obtained. Nature of physical problem The theoretical description of the excitation and ionization of atoms by charged particle impact often requires the knowledge of the matrix elements of the Coulomb interaction. The program MTRD-COUL calculates the matrix elements between bound and free states represented by relativistic hydrogenic wave functions. Method of solution The multipole series expansion of the Coulomb potential is used to solve the problem. Restrictions on the complexity of the problem The matrix elements are calculated with the following restrictions. The initial bound states are limited to 1s 1/2 , 2s 1/2 , 2p 1/2 , 2p 3/2 , 3s 1/2 , 3p 1/2 , 3p 3/2 , 3d 3/2 , 3d 5/2 . The quantum number l in the final state has a maximum value of 10. Typical running time The test run requires about 170 s

Benign Overfitting in Linear Regression

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lies in an infinite dimensional space versus when the data lies in a finite dimensional space whose dimension grows faster than the sample size

The hospitality consumption experiences of parents and carers with children

Drawing on research conducted in Australia and the United Kingdom, this paper addresses two questions: first, how is parenting and childcare provision performed within restaurants, cafes and pubs; and second, how are different aspects of hospitality provision entangled with parent, carer and children’s experiences? The findings show how gestures of hospitality, particularly service interactions that are tailored to meet the specialist needs of these consumers, can create positive emotions and encourage customer loyalty. Furthermore, the data show the importance of recognising children as sovereign consumers. We conclude that responding directly to children’s needs can augment their experiences and hence, those of their carers and other patrons. The paper identifies a number of implications for management practice and several avenues for future research

Experiencing parenthood, care and spaces of hospitality

Drawing on research conducted in Australia and the United Kingdom, this paper explores how parenting and care provision is entangled with, and thus produced through, consumption in hospitality venues. We examine how the socio-material practices of hospitality provision shape the enactment of parenting, alongside the way child-parent/consumer-provider interactions impact upon experiences of hospitality spaces. We argue that venues provide contexts for care provision, acting as spaces of sociality, informing children’s socialization and offering temporary relief from the work of parenting. However, the data also highlight various practices of exclusion and multiple forms of emotional and physical labour required from careproviders. The data illustrate children’s ability to exercise power and the ways in which parents’/carers’ experiences of hospitality spaces are shaped by their enactment of discourses of ‘good parenting’. Finally, we consider parents’/carers’ coping behaviours as they manage social and psychological risks associated with consumption in such public spaces of leisure

Inhibition in multiclass classification

The role of inhibition is investigated in a multiclass support vector machine formalism inspired by the brain structure of insects. The so-called mushroom bodies have a set of output neurons, or classification functions, that compete with each other to encode a particular input. Strongly active output neurons depress or inhibit the remaining outputs without knowing which is correct or incorrect. Accordingly, we propose to use a classification function that embodies unselective inhibition and train it in the large margin classifier framework. Inhibition leads to more robust classifiers in the sense that they perform better on larger areas of appropriate hyperparameters when assessed with leave-one-out strategies. We also show that the classifier with inhibition is a tight bound to probabilistic exponential models and is Bayes consistent for 3-class problems. These properties make this approach useful for data sets with a limited number of labeled examples. For larger data sets, there is no significant comparative advantage to other multiclass SVM approaches