Fit Like a GLM, Sample As a Generative Model
Many scientific questions concern an entire conditional distribution rather than a conditional mean. Climate emulators should reproduce the variability, extremes and dependence of high-dimensional fields; species community models must capture richness and co-occurrence among multiple species. Classical tools such as density estimation and quantile regression are transparent but limited in flexibility and scale, while generative models such as GANs and diffusion models are powerful but computationally heavy and tuning-sensitive. We present engression, a distributional learning method that fits a generative model by minimizing a proper scoring rule, combining the simplicity of classical regression with the flexibility of modern machine learning. We show that engression yields temporally consistent, multivariate downscaling of regional climate models at a fraction of the cost of diffusion-based alternatives. For discrete outcomes, a continuous generator cannot produce valid values, and thresholding breaks gradient-based training. Generalized engression models (GEM) resolve this with data-type-specific links and a stochastic perturbation that smooths the loss, and enjoy universal representation guarantees. On a joint species distribution benchmark and mixed-type health data, GEM matches type-specific models on the marginals and improves on the joint distribution. This talk is based on arXiv:2307.00835, arXiv:2509.26258 and arXiv:2610.01823.
I am an assistant professor in the Department of Statistics at the University of Washington. I was a postdoctoral researcher at ETH Zürich working with Peter Bühlmann and Nicolai Meinshausen. Previously, I obtained my PhD in the Department of Mathematics at HKUST in 2022, supervised by Tong Zhang. I obtained a Bachelor of Science degree at Fudan University in 2018.
My research lies at the intersection of statistics and machine learning. My current work focuses on distributional learning, which leverages generative models to estimate complex probability distributions. I develop methods for statistical problems that involve distribution estimation, including causal inference, extrapolation, robustness to distributional shifts, dimension reduction, diffusion models, missing data, and simulation-based inference. I am also interested in the theoretical foundations of these methods and their applications to scientific domains, such as the emulation of physical climate models.
Hybrid, but in-person attendance is encouraged.