@article{KlebanovSchusterSullivan, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, series = {SIAM Journal on Mathematics of Data Science}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, language = {en} } @article{KlebanovSchuster, author = {Klebanov, Ilja and Schuster, Ingmar}, title = {Markov Chain Importance Sampling - a highly efficient estimator for MCMC}, series = {Journal of Computational and Graphical Statistics}, journal = {Journal of Computational and Graphical Statistics}, doi = {10.1080/10618600.2020.1826953}, abstract = {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.}, language = {en} }