@article{KlebanovSchusterSullivan2020, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, arxiv = {http://arxiv.org/abs/1912.00671}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, year = {2020}, language = {en} } @article{KlebanovSprungkSullivan2021, author = {Klebanov, Ilja and Sprungk, Bj{\"o}rn and Sullivan, T. J.}, title = {The linear conditional expectation in Hilbert space}, volume = {27}, journal = {Bernoulli}, number = {4}, arxiv = {http://arxiv.org/abs/2008.12070}, doi = {10.3150/20-BEJ1308}, pages = {2299 -- 2299}, year = {2021}, language = {en} } @article{KlebanovSchuster2020, author = {Klebanov, Ilja and Schuster, Ingmar}, title = {Markov Chain Importance Sampling - a highly efficient estimator for MCMC}, journal = {Journal of Computational and Graphical Statistics}, doi = {10.1080/10618600.2020.1826953}, year = {2020}, 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} } @article{TackAmbellanZachow2021, author = {Tack, Alexander and Ambellan, Felix and Zachow, Stefan}, title = {Towards novel osteoarthritis biomarkers: Multi-criteria evaluation of 46,996 segmented knee MRI data from the Osteoarthritis Initiative}, volume = {16}, journal = {PLOS One}, number = {10}, doi = {10.1371/journal.pone.0258855}, year = {2021}, abstract = {Convolutional neural networks (CNNs) are the state-of-the-art for automated assessment of knee osteoarthritis (KOA) from medical image data. However, these methods lack interpretability, mainly focus on image texture, and cannot completely grasp the analyzed anatomies' shapes. In this study we assess the informative value of quantitative features derived from segmentations in order to assess their potential as an alternative or extension to CNN-based approaches regarding multiple aspects of KOA. Six anatomical structures around the knee (femoral and tibial bones, femoral and tibial cartilages, and both menisci) are segmented in 46,996 MRI scans. Based on these segmentations, quantitative features are computed, i.e., measurements such as cartilage volume, meniscal extrusion and tibial coverage, as well as geometric features based on a statistical shape encoding of the anatomies. The feature quality is assessed by investigating their association to the Kellgren-Lawrence grade (KLG), joint space narrowing (JSN), incident KOA, and total knee replacement (TKR). Using gold standard labels from the Osteoarthritis Initiative database the balanced accuracy (BA), the area under the Receiver Operating Characteristic curve (AUC), and weighted kappa statistics are evaluated. Features based on shape encodings of femur, tibia, and menisci plus the performed measurements showed most potential as KOA biomarkers. Differentiation between non-arthritic and severely arthritic knees yielded BAs of up to 99\%, 84\% were achieved for diagnosis of early KOA. Weighted kappa values of 0.73, 0.72, and 0.78 were achieved for classification of the grade of medial JSN, lateral JSN, and KLG, respectively. The AUC was 0.61 and 0.76 for prediction of incident KOA and TKR within one year, respectively. Quantitative features from automated segmentations provide novel biomarkers for KLG and JSN classification and show potential for incident KOA and TKR prediction. The validity of these features should be further evaluated, especially as extensions of CNN- based approaches. To foster such developments we make all segmentations publicly available together with this publication.}, language = {en} }