Vive la Différence? Structural Diversity as a Challenge for Metanormative Theories

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and multi-stage aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three

Using nondeterministic learners to alert on coffee rust disease

Motivated by an agriculture case study, we discuss how to learn functions able to predict whether the value of a continuous target variable will be greater than a given threshold. In the application studied, the aim was to alert on high incidences of coffee rust, the main coffee crop disease in the world. The objective is to use chemical prevention of the disease only when necessary in order to obtain healthier quality products and reductions in costs and environmental impact. In this context, the costs of misclassifications are not symmetrical: false negative predictions may lead to the loss of coffee crops. The baseline approach for this problem is to learn a regressor from the variables that records the factors affecting the appearance and growth of the disease. However, the number of errors is too high to obtain a reliable alarm system. The approaches explored here try to learn hypotheses whose predictions are allowed to return intervals rather than single points. Thus,in addition to alarms and non-alarms, these predictors identify situations with uncertain classification, which we call warnings. We present 3 different implementations: one based on regression, and 2 more based on classifiers. These methods are compared using a framework where the costs of false negatives are higher than that of false positives, and both are higher than the cost of warning prediction

Convex Calibration Dimension for Multiclass Loss Matrices

We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be calibrated with respect to a loss matrix in this setting. We then introduce the notion of convex calibration dimension of a multiclass loss matrix, which measures the smallest `size' of a prediction space in which it is possible to design a convex surrogate that is calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, we apply our framework to study various subset ranking losses, and use the convex calibration dimension as a tool to show both the existence and non-existence of various types of convex calibrated surrogates for these losses. Our results strengthen recent results of Duchi et al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types of convex calibrated surrogates in subset ranking. We anticipate the convex calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.Comment: Accepted to JMLR, pending editin

A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl