Jonas Mueller

Rasool Fakoor, Taesup Kim, Jonas Mueller et al.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Jonas Mueller, Alex Smola

A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be more robustly addressed by leveraging the data values themselves rather than just relying on their arbitrarily selected variable names. Here, we present a computationally efficient method to identify high-confidence variable matches between a given set of data values and a large repository of previously encountered datasets. Our approach enjoys numerous advantages over distributional similarity based techniques because we leverage learned vector embeddings of datasets which adaptively account for natural forms of data variation encountered in practice. Based on the neural architecture of deep sets, our embeddings can be computed for both numeric and string data. In dataset search and schema matching tasks, our methods outperform standard statistical techniques and we find that the learned embeddings generalize well to new data sources.