Abstract Quantification, i.e., the task of predicting the class prevalence values in bags of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing algorithms for binary and multi-class problems in which the classes are not ordered. Here, we study the ordinal case, i.e., the case in which a total order is defined on the set of $$n>2$$ n > 2 classes. We give three main contributions to this field. First, we create and make available two datasets for ordinal quantification (OQ) research that overcome the inadequacies of the previously available ones. Second, we experimentally compare the most important OQ algorithms proposed in the literature so far. To this end, we bring together algorithms proposed by authors from very different research fields, such as data mining and astrophysics, who were unaware of each others’ developments. Third, we propose a novel class of regularized OQ algorithms, which outperforms existing algorithms in our experiments. The key to this gain in performance is that our regularization prevents ordinally implausible estimates, assuming that ordinal distributions tend to be smooth in practice. We informally verify this assumption for several real-world applications.

The goal of active class selection (ACS) is to optimize the class proportions in newly acquired data; a classifier trained from that data should exhibit maximum performance during its deployment. This paper provides an information-theoretic examination of the problem, resulting in an upper bound of the classifier's error. This upper bound shows that the more data is acquired, the better is the performance of the class proportions that occur during deployment; other class proportions can outperform these natural proportions in the beginning of data acquisition, but natural proportions certainly yield optimal probabilistic classifiers in the limit. Put differently-and perhaps surprisingly-the more data is acquired, the less beneficial are ACS strategies. Our bound further reveals that the degree to which non-natural class proportions are eligible depends on the correlation between the features and the class label. Experiments on standard ACS data sets quantify these effects and also show that the conclusions drawn from our analysis take over to non-probabilistic classifiers.

Obtaining the distribution of a physical quantity is a frequent objective in experimental physics. In cases where the distribution of the relevant quantity cannot be accessed experimentally, it has to be reconstructed from distributions of correlated quantities that are measured, instead. This reconstruction is called deconvolution. Cherenkov astronomy is a deconvolution use case which studies the energy distribution of cosmic gamma radiation to reason about the characteristics of celestial objects emitting such radiation. We present a novel unified view on deconvolution methods, rephrasing them in the language of data science. Based on our unified formulation, we propose a novel stopping condition that guarantees fast convergence. We compare existing and new methods on synthetic and real-world data, showing that our method converges faster and more accurately than the existing machine learning based approach.