Supervised learning deals with the inference of a distribution over an output or label space Y conditioned on points in an observation space X , given a training dataset D of pairs in X × Y. However, in a lot of applications of interest, acquisition of large amounts of observations is easy, while the process of generating labels is time-consuming or costly. One way to deal with this problem is active learning, where points to be labelled are selected with the aim of creating a model with better performance than that of an model trained on an equal number of randomly sampled points. In this paper, we instead propose to deal with the labelling cost directly: The learning goal is defined as the minimisation of a cost which is a function of the expected model performance and the total cost of the labels used. This allows the development of general strategies and specific algorithms for (a) optimal stopping, where the expected cost dictates whether label acquisition should continue (b) empirical evaluation, where the cost is used as a performance metric for a given combination of inference, stopping and sampling methods. Though the main focus of the paper is optimal stopping, we also aim to provide the background for further developments and discussion in the related field of active learning.

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Abstract. We present a multiclass classification system for gray value images through boosting. The feature selection is done using the LPBoost algorithm which selects suitable features of adequate type. In our experiments we use up to nine different kinds of feature types simultaneously. Furthermore, a greedy search strategy within the weak learner is used to find simple geometric relations between selected features from previous boosting rounds. The final hypothesis can also consist of more than one geometric model for an object class. Finally, we provide a weight optimization method for combining the learned one-vs-one classifiers for the multiclass classification. We tested our approach on a publicly available data set and compared our results to other state-of-the-art approaches, such as the "bag of keypoints" method.

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