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In medical diagnosis, information about the health state of a patient can often be obtained through different tests, which may perhaps be combined into an overall decision rule. Practically, this leads to several important questions. For example, which test or which subset of tests should be selected, taking into account the effectiveness of individual tests, synergies and redundancies between them, as well as their cost. How to produce an optimal decision rule on the basis of the data given, which typically consists of test results for patients with or without confirmed health condition. To address questions of this kind, we develop an approach that combines (semi-supervised) machine learning methodology with concepts from (cooperative) game theory. Roughly speaking, while the former is responsible for optimally combining single tests into decision rules, the latter is used to judge the influence and importance of individual tests as well as the interaction between them. Our approach is motivated and illustrated by a concrete case study in veterinary medicine, namely the diagnosis of a disease in cats called feline infectious peritonitis.

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Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. Current approaches commonly focus on ranking by scoring, i.e., on learning an underlying latent utility function that seeks to capture the inherent utility of each object. These approaches, however, are not able to take possible effects of context-dependence into account, where contextdependence means that the utility or usefulness of an object may also depend on what other objects are available as alternatives. In this paper, we formalize the problem of context-dependent ranking and present two general approaches based on two natural representations of context-dependent ranking functions. Both approaches are instantiated by means of appropriate neural network architectures, which are evaluated on suitable benchmark task.