Decision-making in personalized medicine such as cancer therapy or critical care must often make choices for dosage combinations, i.e., multiple continuous treatments. Existing work for this task has modeled the effect of multiple treatments independently, while estimating the joint effect has received little attention but comes with non-trivial challenges. In this paper, we propose a novel method for reliable off-policy learning for dosage combinations. Our method proceeds along three steps: (1) We develop a tailored neural network that estimates the individualized dose-response function while accounting for the joint effect of multiple dependent dosages. (2) We estimate the generalized propensity score using conditional normalizing flows in order to detect regions with limited overlap in the shared covariate-treatment space. (3) We present a gradient-based learning algorithm to find the optimal, individualized dosage combinations. Here, we ensure reliable estimation of the policy value by avoiding regions with limited overlap. We finally perform an extensive evaluation of our method to show its effectiveness. To the best of our knowledge, ours is the first work to provide a method for reliable off-policy learning for optimal dosage combinations.
Learning from positive and unlabeled (PU) data is a setting where the learner only has access to positive and unlabeled samples while having no information on negative examples. Such PU setting is of great importance in various tasks such as medical diagnosis, social network analysis, financial markets analysis, and knowledge base completion, which also tend to be intrinsically imbalanced, i.e., where most examples are actually negatives. Most existing approaches for PU learning, however, only consider artificially balanced datasets and it is unclear how well they perform in the realistic scenario of imbalanced and long-tail data distribution. This paper proposes to tackle this challenge via robust and efficient self-supervised pretraining. However, training conventional self-supervised learning methods when applied with highly imbalanced PU distribution needs better reformulation. In this paper, we present \textit{ImPULSeS}, a unified representation learning framework for \underline{Im}balanced \underline{P}ositive \underline{U}nlabeled \underline{L}earning leveraging \underline{Se}lf-\underline{S}upervised debiase pre-training. ImPULSeS uses a generic combination of large-scale unsupervised learning with debiased contrastive loss and additional reweighted PU loss. We performed different experiments across multiple datasets to show that ImPULSeS is able to halve the error rate of the previous state-of-the-art, even compared with previous methods that are given the true prior. Moreover, our method showed increased robustness to prior misspecification and superior performance even when pretraining was performed on an unrelated dataset. We anticipate such robustness and efficiency will make it much easier for practitioners to obtain excellent results on other PU datasets of interest. The source code is available at \url{https://github.com/JSchweisthal/ImPULSeS}