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.

On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Public sector strategy classification system for shared service identification

The purpose of this conceptual paper is to address the lack of consistent means through which strategies are identified and discussed across theoretical perspectives in the field of business strategy. A standardised referencing system is offered to codify the means by which strategies can be identified, from which new business services and information systems may be derived. This taxonomy was developed using qualitative content analysis study of government agencies’ strategic plans. This taxonomy is useful for identifying strategy formation and determining gaps and opportunities. Managers will benefit from a more transparent strategic design process that reduces ambiguity, aids in identifying and correcting gaps in strategy formulation, and fosters enhanced strategic analysis. Key benefits to academics are the improved dialogue in strategic management field and suggest that progress in the field requires that fundamentals of strategy formulation and classification be considered more carefully. Finally, the formalization of strategy can lead to the clear identification of new business services, which inform ICT investment decisions and shared service prioritisation.

Exponentiated gradient algorithms for large-margin structured classification

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient—even in cases where the number of labels y is exponential in size—provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.

Identification of area-level influences on regions of high cancer incidence in Queensland, Australia : a classification tree approach

Background: Strategies for cancer reduction and management are targeted at both individual and area levels. Area-level strategies require careful understanding of geographic differences in cancer incidence, in particular the association with factors such as socioeconomic status, ethnicity and accessibility. This study aimed to identify the complex interplay of area-level factors associated with high area-specific incidence of Australian priority cancers using a classification and regression tree (CART) approach. Methods: Area-specific smoothed standardised incidence ratios were estimated for priority-area cancers across 478 statistical local areas in Queensland, Australia (1998-2007, n=186,075). For those cancers with significant spatial variation, CART models were used to identify whether area-level accessibility, socioeconomic status and ethnicity were associated with high area-specific incidence. Results: The accessibility of a person’s residence had the most consistent association with the risk of cancer diagnosis across the specific cancers. Many cancers were likely to have high incidence in more urban areas, although male lung cancer and cervical cancer tended to have high incidence in more remote areas. The impact of socioeconomic status and ethnicity on these associations differed by type of cancer. Conclusions: These results highlight the complex interactions between accessibility, socioeconomic status and ethnicity in determining cancer incidence risk.

Molecular classification of cutaneous malignant melanoma by gene expression profiling

The most common human cancers are malignant neoplasms of the skin. Incidence of cutaneous melanoma is rising especially steeply, with minimal progress in non-surgical treatment of advanced disease. Despite significant effort to identify independent predictors of melanoma outcome, no accepted histopathological, molecular or immunohistochemical marker defines subsets of this neoplasm. Accordingly, though melanoma is thought to present with different 'taxonomic' forms, these are considered part of a continuous spectrum rather than discrete entities. Here we report the discovery of a subset of melanomas identified by mathematical analysis of gene expression in a series of samples. Remarkably, many genes underlying the classification of this subset are differentially regulated in invasive melanomas that form primitive tubular networks in vitro, a feature of some highly aggressive metastatic melanomas. Global transcript analysis can identify unrecognized subtypes of cutaneous melanoma and predict experimentally verifiable phenotypic characteristics that may be of importance to disease progression.

An exploration of shared services types in higher education

The emerging global Higher Education (HE) market challenges all universities to reconsider their mission, in order to function effectively and efficiently, and to be responsive to changing marketplace demands. Universities are considering cooperating or sharing in a wide range of areas, in order to achieve sought after cost savings and improvements in performance.Studies suggest that a wide range of services could potentially be shared across Higher Education Institutions (HEIs),offering several potential benefits. While there are many individual documented examples of how shared services have been applied in the Higher Education sector, there has been little synthesis, conceptualization or discussion (in general or in the HE sector) around the different types of possible shared services options and how they are structured. A deeper understanding of potential types of sharing arrangements will be of value to those universities considering shared services, implementing shared services, and managing shared services. Through analysis of 36 documented case studies of shared services in HE, this study sought to synthesize a typology of sharing arrangements. An inductive approach was used to identify the core differentiating dimensions. The findings present eight types of sharing arrangements that occur in the HE sector, with descriptions and examples from the case studies observed.

On a Syntactic Characterization of Classification with a Mind Change Bound

Most learning paradigms impose a particular syntax on the class of concepts to be learned; the chosen syntax can dramatically affect whether the class is learnable or not. For classification paradigms, where the task is to determine whether the underlying world does or does not have a particular property, how that property is represented has no implication on the power of a classifier that just outputs 1’s or 0’s. But is it possible to give a canonical syntactic representation of the class of concepts that are classifiable according to the particular criteria of a given paradigm? We provide a positive answer to this question for classification in the limit paradigms in a logical setting, with ordinal mind change bounds as a measure of complexity. The syntactic characterization that emerges enables to derive that if a possibly noncomputable classifier can perform the task assigned to it by the paradigm, then a computable classifier can also perform the same task. The syntactic characterization is strongly related to the difference hierarchy over the class of open sets of some topological space; this space is naturally defined from the class of possible worlds and possible data of the learning paradigm.

The emergent male shopper : an identification of male supermarket shopper types

Grocery shopping is a routine activity widely considered the responsibility of the female spouse, yet modern social and demographic shifts are causing men to engage in this task. This study develops a retail shopping typology of male grocery shoppers, employing a cluster analysis technique. Five distinct cohorts emerge from the data of eight constructs, measured by seventy one items. One new shopper type emerges from this research. This shopper presented as a younger man, at the commencement of their family lifecycle, attracted by a strong value offer, focusing on price and promotional discounts. Our research offers a contribution to the marketing, consumer behaviour and supermarket retailing disciplines in three ways. By examining and identifying male shopping behaviour in the context of grocery shopping, the development of a retail shopping typology of male grocery shoppers and the extension and employment of a cluster analysis in identifying distinct groups. This research has implications for gender, segmentation studies and consumer behaviour disciplines in regard to grocery shopping. The identification of specific groups of male grocery shoppers will enable grocery retailers to effectively implement important, targeted marketing strategies.