Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Rademacher and Gaussian complexities: Risk bounds and structural results

We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

Sparseness vs estimating conditional probabilities : some asymptotic results

One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.

Die Geographie der Kreativen Klasse in Deutschland [The geography of the Creative Class in Germany]

We analyze the regional distribution of different categories of creative individuals in Germany. Generally, the share of creative people is higher in cities as compared to the rural area The freelancing artists are a kind of exception in this respect; they constitute a relatively high share of the population in some rural area A high share of creative people in a region can be explained by a high level of public provisions and a high share of foreign born population, which can be regarded as an indicator of the “openness” in the local milieu. Good employment opportunities have only a relatively weak impact. Regions with a high share of creatives tend to have an above average level of new business formation, a high level of innovation and a relatively high share of employees in high-tech industries.

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Watching football in marvellous Melbourne : spectators, barrackers and working class rituals

A study of crowds drawn to Australian football matches in colonial Victoria illuminates key aspects of the code's genesis, development and popularity. Australian football was codified by a middle-class elite that, as in Britain, created forms of mass entertainment that were consistent with the kind of industrial capitalist society they were attempting to organise. But the 'lower orders' were inculcated with traditional British folkways in matters of popular amusement, and introduced a style of 'barracking' for this new code that resisted the hegemony of the elite football administrators. By the end of the colonial period Australian football was firmly entrenched as a site of contestation between plebeian and bourgeois codes of spectating that reflected the social and ethnic diversity of the clubs making up the Victorian competition. Australian football thereby offers a classic vignette in the larger history of 'resistance through ritual'.

Multifractal analysis of geomagnetic storm and solar flare indices and their class dependence

The multifractal properties of two indices of geomagnetic activity, D st (representative of low latitudes) and a p (representative of the global geomagnetic activity), with the solar X-ray brightness, X l , during the period from 1 March 1995 to 17 June 2003 are examined using multifractal detrended fluctuation analysis (MF-DFA). The h(q) curves of D st and a p in the MF-DFA are similar to each other, but they are different from that of X l , indicating that the scaling properties of X l are different from those of D st and a p . Hence, one should not predict the magnitude of magnetic storms directly from solar X-ray observations. However, a strong relationship exists between the classes of the solar X-ray irradiance (the classes being chosen to separate solar flares of class X-M, class C, and class B or less, including no flares) in hourly measurements and the geomagnetic disturbances (large to moderate, small, or quiet) seen in D st and a p during the active period. Each time series was converted into a symbolic sequence using three classes. The frequency, yielding the measure representations, of the substrings in the symbolic sequences then characterizes the pattern of space weather events. Using the MF-DFA method and traditional multifractal analysis, we calculate the h(q), D(q), and τ (q) curves of the measure representations. The τ (q) curves indicate that the measure representations of these three indices are multifractal. On the basis of this three-class clustering, we find that the h(q), D(q), and τ (q) curves of the measure representations of these three indices are similar to each other for positive values of q. Hence, a positive flare storm class dependence is reflected in the scaling exponents h(q) in the MF-DFA and the multifractal exponents D(q) and τ (q). This finding indicates that the use of the solar flare classes could improve the prediction of the D st classes.

‘Please leave your mobile phone on’ : Social educational networking in a social society : Encouraging in-class engagement at QUT across physical and virtual learning environments

Though stadium style seating in large lecture theatres may suggest otherwise, effective teaching and learning is a not a spectator sport. A challenge in creating effective learning environments in both physical and virtual spaces is to provide optimal opportunity for student engagement in active learning. Queensland University of Technology (QUT) has developed the Open Web Lecture (OWL), a new web-based student response application, which seamlessly integrates a virtual learning environment within the physical learning space. The result is a blended learning experience; a fluid collaboration between academic and students connected to OWL via the University’s Wi-Fi using their own laptop or mobile web device. QUT is currently piloting the OWL application to encourage student engagement. OWL offers opportunities for participants to: • Post comments and questions • Reply to comments
 • "Like" comments
 • Poll students and review data • Review archived sessions. Many of these features instinctively appeal to student users of social networking media, yet avail the academic of control within the University network. Student privacy is respected through a system of preserving peer-peer anonymity, a functionality that seeks to address a traditional reluctance to speak up in large classes. The pilot is establishing OWL as an opportunity for engaging students in active learning opportunities by enabling • virtual learning in physical spaces for large group lectures, seminar groups, workshops and conferences • live collaborative technology connecting students and the academic via the wireless network using their own laptop or mobile device • an non- intimidating environment in which to ask questions • promotion of a sense of community • instant feedback • problem based learning. The student and academic response to OWL has been overwhelmingly positive, crediting OWL as an easy to use application, which creates effective learning opportunities though interactivity and immediate feedback. This poster and accompanying online presentation of the technology will demonstrate how OWL offers new possibilities for active learning in physical spaces by: • providing increased opportunity for student engagement • supporting a range of learners and learning activities • fostering blended learning experiences. The presentation will feature visual displays of the technology, its various interfaces and feedback including clips from interviews with students and academics participating in the early stages of the pilot.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.