Probabilistic Numerics — Uncertainty in Computation
May 10, 2018, 12:00PM
The computational complexity of inference from data is dominated by the solution of non-analytic numerical problems (large-scale linear algebra, optimization, integration, the solution of differential equations). But a converse of sorts is also true — numerical algorithms for these tasks are inference engines! They estimate intractable, latent quantities by collecting the observable result of tractable computations. Because they also decide adaptively which computations to perform, these methods can be interpreted as autonomous learning machines. This observation lies at the heart of the emerging topic of Probabilistic Numerical Computation, which applies the concepts of probabilistic (Bayesian) inference to the design of algorithms, assigning a notion of probabilistic uncertainty to the result even of deterministic computations. I will outline how this viewpoint is connected to that of classic numerical analysis, and show that thinking about computation as inference affords novel, practical answers to the challenges of large-scale, big data, inference.
Philipp Hennig
Chair for the Methods of Machine Learning
University of Tübingen, Germany
Speaker: Philipp Hennig