To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, I'll describe how Stein's method -- a tool developed to prove central limit theorems -- can be adapted to assess and improve the quality of practical inference procedures. Along the way, I’ll highlight applications to Markov chain Monte Carlo sampler selection, goodness-of-fit testing, and black-box importance sampling.
Speaker Bio: Lester Mackey is a Principal Researcher at Microsoft Research, where he develops machine learning methods, models, and theory for large-scale learning tasks driven by applications from climate forecasting, healthcare, and the social good. Lester moved to Microsoft from Stanford University, where he was an assistant professor of Statistics and (by courtesy) of Computer Science. He earned his PhD in Computer Science and MA in Statistics from UC Berkeley and his BSE in Computer Science from Princeton University. He co-organized the second place team in the Netflix Prize competition for collaborative filtering, won the Prize4Life ALS disease progression prediction challenge, won prizes for temperature and precipitation forecasting in the yearlong real-time Subseasonal Climate Forecast Rodeo, and received best paper and best student paper awards from the ACM Conference on Programming Language Design and Implementation and the International Conference on Machine Learning.