Title: From intuition to innovation: accelerating scientific discovery through black-box probabilistic inference
Abstract: Modern scientific discovery is often constrained by scarce, noisy, or expensive data, as well as by the need to model complex latent processes. Probabilistic modeling provides a principled framework for uncertainty quantification in latent-variable models, enabling scientists to encode domain-based intuition. Yet computational challenges frequently stand between modeling and scientific innovation. Variational inference (VI) is a popular approach for posterior inference in latent-variable models, and recent advances in automatic differentiation have made VI algorithms broadly accessible in practice. However, standard “black-box” VI (BBVI), based on stochastic gradient descent, often converges slowly for expressive variational families due to noisy gradients and sensitivity to learning parameters.
To address this limitation, I introduce the Batch-and-Match (BaM) algorithm, which performs variational inference by matching the scores of the variational and target distributions over a batch of samples. BaM admits closed-form updates for full-covariance Gaussians and converges in significantly fewer gradient evaluations than standard BBVI. I then discuss extensions to high-dimensional settings and richer variational families. Using materials design as a motivating application, I show how variational inference, combined with physical domain knowledge, enables an uncertainty-aware pipeline that accelerates the prediction of stable materials. I conclude by outlining a broader vision for probabilistic machine learning methodologies needed to address the challenges of modern scientific discovery.
