Abstract In transductive active learning, the goal is to determine the correct labels for an unlabeled, known dataset. Therefore, we can either ask an oracle to provide the right label at some cost or use the prediction of a classifier which we train on the labels acquired so far. In contrast, the commonly used (inductive) active learning aims to select instances for labeling out of the unlabeled set to create a generalized classifier, which will be deployed on unknown data. This article formally defines the transductive setting and shows that it requires new solutions. Additionally, we formalize the theoretically cost-optimal stopping point for the transductive scenario. Building upon the probabilistic active learning framework, we propose a new transductive selection strategy that includes a stopping criterion and show its superiority.

Density estimation is a versatile technique underlying many data mining tasks and techniques, ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming data. With the pervasiveness of embedded systems and digitisation, this latter type of streaming and evolving data becomes more important. Nevertheless, research in density estimation has so far focused on stationary data, leaving the task of of extrapolating and predicting density at time points outside a training window an open problem. For this task, temporal density extrapolation (TDX) is proposed. This novel method models and predicts gradual monotonous changes in a distribution. It is based on the expansion of basis functions, whose weights are modelled as functions of compositional data over time by using an isometric log-ratio transformation. Extrapolated density estimates are then obtained by extrapolating the weights to the requested time point, and querying the density from the basis functions with back-transformed weights. Our approach aims for broad applicability by neither being restricted to a specific parametric distribution, nor relying on cluster structure in the data. It requires only two additional extrapolation-specific parameters, for which reasonable defaults exist. Experimental evaluation on various data streams, synthetic as well as from the real-world domains of credit scoring and environmental health, shows that the model manages to capture monotonous drift patterns accurately and better than existing methods. Thereby, it requires not more than 1.5 times the run time of a corresponding static density estimation approach.