Given sets of observations of training and test data, we consider the problem of re-weighting the training data such that its distribution more closely matches that of the test data. We achieve this goal by matching covariate distributions between training and test sets in a high dimensional feature space (specifically, a reproducing kernel Hilbert space). This approach does not require distribution estimation. Instead, the sample weights are obtained by a simple quadratic programming procedure. We provide a uniform convergence bound on the distance between the reweighted training feature mean and the test feature mean, a transductive bound on the expected loss of an algorithm trained on the reweighted data, and a connection to single class SVMs. While our method is designed to deal with the case of simple covariate shift (in the sense of Chapter ??), we have also found benefits for sample selection bias on the labels. Our correction procedure yields its greatest and most consistent advantages when the learning algorithm returns a classifier/regressor that is "simpler" than the data might suggest.

We consider the problem of multi-task learning, that is, learning multiple related functions. Our approach is based on a hierarchical Bayesian framework, that exploits the equivalence between parametric linear models and nonparametric Gaussian processes (GPs). The resulting models can be learned easily via an EM-algorithm. Empirical studies on multi-label text categorization suggest that the presented models allow accurate solutions of these multi-task problems.

Accurate in silico models for predicting aqueous solubility are needed in drug design and discovery and many other areas of chemical research. We present a statistical modeling of aqueous solubility based on measured data, using a Gaussian Process nonlinear regression model (GPsol). We compare our results with those of 14 scientific studies and 6 commercial tools. This shows that the developed model achieves much higher accuracy than available commercial tools for the prediction of solubility of electrolytes. On top of the high accuracy, the proposed machine learning model also provides error bars for each individual prediction.

We investigate the use of different Machine Learning methods to construct models for aqueous solubility. Models are based on about 4000 compounds, including an in-house set of 632 drug discovery molecules of Bayer Schering Pharma. For each method, we also consider an appropriate method to obtain error bars, in order to estimate the domain of applicability (DOA) for each model. Here, we investigate error bars from a Bayesian model (Gaussian Process (GP)), an ensemble based approach (Random Forest), and approaches based on the Mahalanobis distance to training data (for Support Vector Machine and Ridge Regression models). We evaluate all approaches in terms of their prediction accuracy (in cross-validation, and on an external validation set of 536 molecules) and in how far the individual error bars can faithfully represent the actual prediction error.

Metabolic stability is an important property of drug molecules that should-optimally-be taken into account early on in the drug design process. Along with numerous medium- or high-throughput assays being implemented in early drug discovery, a prediction tool for this property could be of high value. However, metabolic stability is inherently difficult to predict, and no commercial tools are available for this purpose. In this work, we present a machine learning approach to predicting metabolic stability that is tailored to compounds from the drug development process at Bayer Schering Pharma. For four different in vitro assays, we develop Bayesian classification models to predict the probability of a compound being metabolically stable. The chosen approach implicitly takes the "domain of applicability" into account. The developed models were validated on recent project data at Bayer Schering Pharma, showing that the predictions are highly accurate and the domain of applicability is estimated correctly. Furthermore, we evaluate the modeling method on a set of publicly available data.