## Institut für Informatik und Computational Science

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The field of machine learning studies algorithms that infer predictive models from data. Predictive models are applicable for many practical tasks such as spam filtering, face and handwritten digit recognition, and personalized product recommendation. In general, they are used to predict a target label for a given data instance. In order to make an informed decision about the deployment of a predictive model, it is crucial to know the model’s approximate performance. To evaluate performance, a set of labeled test instances is required that is drawn from the distribution the model will be exposed to at application time. In many practical scenarios, unlabeled test instances are readily available, but the process of labeling them can be a time- and cost-intensive task and may involve a human expert. This thesis addresses the problem of evaluating a given predictive model accurately with minimal labeling effort. We study an active model evaluation process that selects certain instances of the data according to an instrumental sampling distribution and queries their labels. We derive sampling distributions that minimize estimation error with respect to different performance measures such as error rate, mean squared error, and F-measures. An analysis of the distribution that governs the estimator leads to confidence intervals, which indicate how precise the error estimation is. Labeling costs may vary across different instances depending on certain characteristics of the data. For instance, documents differ in their length, comprehensibility, and technical requirements; these attributes affect the time a human labeler needs to judge relevance or to assign topics. To address this, the sampling distribution is extended to incorporate instance-specific costs. We empirically study conditions under which the active evaluation processes are more accurate than a standard estimate that draws equally many instances from the test distribution. We also address the problem of comparing the risks of two predictive models. The standard approach would be to draw instances according to the test distribution, label the selected instances, and apply statistical tests to identify significant differences. Drawing instances according to an instrumental distribution affects the power of a statistical test. We derive a sampling procedure that maximizes test power when used to select instances, and thereby minimizes the likelihood of choosing the inferior model. Furthermore, we investigate the task of comparing several alternative models; the objective of an evaluation could be to rank the models according to the risk that they incur or to identify the model with lowest risk. An experimental study shows that the active procedure leads to higher test power than the standard test in many application domains. Finally, we study the problem of evaluating the performance of ranking functions, which are used for example for web search. In practice, ranking performance is estimated by applying a given ranking model to a representative set of test queries and manually assessing the relevance of all retrieved items for each query. We apply the concepts of active evaluation and active comparison to ranking functions and derive 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.

In many applications one is faced with the problem of inferring some functional relation between input and output variables from given data. Consider, for instance, the task of email spam filtering where one seeks to find a model which automatically assigns new, previously unseen emails to class spam or non-spam. Building such a predictive model based on observed training inputs (e.g., emails) with corresponding outputs (e.g., spam labels) is a major goal of machine learning. Many learning methods assume that these training data are governed by the same distribution as the test data which the predictive model will be exposed to at application time. That assumption is violated when the test data are generated in response to the presence of a predictive model. This becomes apparent, for instance, in the above example of email spam filtering. Here, email service providers employ spam filters and spam senders engineer campaign templates such as to achieve a high rate of successful deliveries despite any filters. Most of the existing work casts such situations as learning robust models which are unsusceptible against small changes of the data generation process. The models are constructed under the worst-case assumption that these changes are performed such to produce the highest possible adverse effect on the performance of the predictive model. However, this approach is not capable to realistically model the true dependency between the model-building process and the process of generating future data. We therefore establish the concept of prediction games: We model the interaction between a learner, who builds the predictive model, and a data generator, who controls the process of data generation, as an one-shot game. The game-theoretic framework enables us to explicitly model the players' interests, their possible actions, their level of knowledge about each other, and the order at which they decide for an action. We model the players' interests as minimizing their own cost function which both depend on both players' actions. The learner's action is to choose the model parameters and the data generator's action is to perturbate the training data which reflects the modification of the data generation process with respect to the past data. We extensively study three instances of prediction games which differ regarding the order in which the players decide for their action. We first assume that both player choose their actions simultaneously, that is, without the knowledge of their opponent's decision. We identify conditions under which this Nash prediction game has a meaningful solution, that is, a unique Nash equilibrium, and derive algorithms that find the equilibrial prediction model. As a second case, we consider a data generator who is potentially fully informed about the move of the learner. This setting establishes a Stackelberg competition. We derive a relaxed optimization criterion to determine the solution of this game and show that this Stackelberg prediction game generalizes existing prediction models. Finally, we study the setting where the learner observes the data generator's action, that is, the (unlabeled) test data, before building the predictive model. As the test data and the training data may be governed by differing probability distributions, this scenario reduces to learning under covariate shift. We derive a new integrated as well as a two-stage method to account for this data set shift. In case studies on email spam filtering we empirically explore properties of all derived models as well as several existing baseline methods. We show that spam filters resulting from the Nash prediction game as well as the Stackelberg prediction game in the majority of cases outperform other existing baseline methods.