Learning under differing training and test distributions

One of the main problems in machine learning is to train a predictive model from training data and to make predictions on test data. Most predictive models are constructed under the assumption that the training data is governed by the exact same distribution which the model will later be exposed to. In practice, control over the data collection process is often imperfect. A typical scenario is when labels are collected by questionnaires and one does not have access to the test population. For example, parts of the test population are underrepresented in the survey, out of reach, or do not return the questionnaire. In many applications training data from the test distribution are scarce because they are difficult to obtain or very expensive. Data from auxiliary sources drawn from similar distributions are often cheaply available. This thesis centers around learning under differing training and test distributions and covers several problem settings with different assumptions on the relationship between training and test distributions—including multi-task learning and learning under covariate shift and sample selection bias. Several new models are derived that directly characterize the divergence between training and test distributions, without the intermediate step of estimating training and test distributions separately. The integral part of these models are rescaling weights that match the rescaled or resampled training distribution to the test distribution. Integrated models are studied where only one optimization problem needs to be solved for learning under differing distributions. With a two-step approximation to the integrated models almost any supervised learning algorithm can be adopted to biased training data. In case studies on spam filtering, HIV therapy screening, targeted advertising, and other applications the performance of the new models is compared to state-of-the-art reference methods.