We study regression problems in which an adversary can exercise some control over the data generation process. Learner and adversary have conflicting but not necessarily perfectly antagonistic objectives. We study the case in which the learner is not fully informed about the adversary’s objective; instead, any knowledge of the learner about parameters of the adversary’s goal may be reflected in a Bayesian prior. We model this problem as a Bayesian game, and characterize conditions under which a unique Bayesian equilibrium point exists. We experimentally compare the Bayesian equilibrium strategy to the Nash equilibrium strategy, the minimax strategy, and regular linear regression.

We address the problem of comparing the risks of two given predictive models - for instance, a baseline model and a challenger - as confidently as possible on a fixed labeling budget. This problem occurs whenever models cannot be compared on held-out training data, possibly because the training data are unavailable or do not reflect the desired test distribution. In this case, new test instances have to be drawn and labeled at a cost. We devise an active comparison method that selects instances according to an instrumental sampling distribution. We derive the sampling distribution that maximizes the power of a statistical test applied to the observed empirical risks, and thereby minimizes the likelihood of choosing the inferior model. Empirically, we investigate model selection problems on several classification and regression tasks and study the accuracy of the resulting p-values.

We address the problem of estimating the F-measure of a given model as accurately as possible on a fixed labeling budget. This problem occurs whenever an estimate cannot be obtained from held-out training data; for instance, when data that have been used to train the model are held back for reasons of privacy or do not reflect the test distribution. In this case, new test instances have to be drawn and labeled at a cost. An active estimation procedure selects instances according to an instrumental sampling distribution. An analysis of the sources of estimation error leads to an optimal sampling distribution that minimizes estimator variance. We explore conditions under which active estimates of F-measures are more accurate than estimates based on instances sampled from the test distribution.

We address the problem of learning classifiers for several related tasks that may differ in their joint distribution of input and output variables. For each task, small - possibly even empty - labeled samples and large unlabeled samples are available. While the unlabeled samples reflect the target distribution, the labeled samples may be biased. We derive a solution that produces resampling weights which match the pool of all examples to the target distribution of any given task. Our work is motivated by the problem of predicting sociodemographic features for users of web portals, based on the content which they have accessed. Here, questionnaires offered to a small portion of each portal's users produce biased samples. Transfer learning enables us to make predictions even for new portals with few or no training data and improves the overall prediction accuracy.