Abstract: Estimating the full (conditional) distribution is crucial to applications that require uncertainty quantification. However, existing methods such as quantile regression typically fall short for high-dimensional response variables, such as spatial fields of climate variables. To address this, distributional learning aims to estimate a generative model to describe the target distribution, which enables inference by sampling. In this talk, we introduce a distributional learning method called engression. We discuss the potential of distributional learning for problems that persist even with access to the population of the training data, including extrapolation, distribution shifts, and causal inference. Specifically, we demonstrate that the reliability of engression does not break down immediately at the boundary of the training support, in contrast to neural network regression or tree ensembles. In addition, we present variants of engression for multi-environment data or under an instrumental variable setting to achieve robust prediction against distribution shifts and causal effect estimation. Engression has also been shown to be effective in modeling distributions of high-dimensional climate data. Finally, we point out several outlooks of engression in smoothing, classification, and dimensionality reduction.


Bio: Xinwei Shen is a postdoctoral researcher at the Seminar for Statistics at ETH Zürich working with Peter Bühlmann and Nicolai Meinshausen. In 2022, she obtained her PhD at Hong Kong University of Science and Technology advised by Tong Zhang. Her research interests include distributional learning, causality, robustness, and applications in climate science.