TY - JOUR A1 - Klebanov, Ilja A1 - Schuster, Ingmar A1 - Sullivan, T. J. T1 - A rigorous theory of conditional mean embeddings JF - SIAM Journal on Mathematics of Data Science Y1 - 2020 U6 - https://doi.org/10.1137/19M1305069 VL - 2 IS - 3 SP - 583 EP - 606 ER - TY - JOUR A1 - Klebanov, Ilja A1 - Schuster, Ingmar T1 - Markov Chain Importance Sampling - a highly efficient estimator for MCMC JF - Journal of Computational and Graphical Statistics N2 - Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling (MCIS), which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides a novel way of correcting the discretization error. Our estimator satisfies a central limit theorem and improves on error per CPU cycle, often to a large extent. As a by-product it enables estimating the normalizing constant, an important quantity in Bayesian machine learning and statistics. Y1 - 2020 U6 - https://doi.org/10.1080/10618600.2020.1826953 ER -