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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.

We address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution-problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. The problem of learning under covariate shift can be written as an integrated optimization problem. Instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift. The optimization problem is convex under certain conditions; our findings also clarify the relationship to the known kernel mean matching procedure. We report on experiments on problems of spam filtering, text classification, and landmine detection.

Evaluating the quality of ranking functions is a core task in web search and other information retrieval domains. Because query distributions and item relevance change over time, ranking models often cannot be evaluated accurately on held-out training data. Instead, considerable effort is spent on manually labeling the relevance of query results for test queries in order to track ranking performance. We address the problem of estimating ranking performance as accurately as possible on a fixed labeling budget. Estimates are based on a set of most informative test queries selected by an active sampling distribution. Query labeling costs depend on the number of result items as well as item-specific attributes such as document length. We derive cost-optimal sampling distributions for the commonly used performance measures Discounted Cumulative Gain and Expected Reciprocal Rank. Experiments on web search engine data illustrate significant reductions in labeling costs.