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 - Nava-Yazdani, Esfandiar A1 - Hege, Hans-Christian A1 - Sullivan, T. J. A1 - von Tycowicz, Christoph T1 - Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications JF - Journal of Mathematical Imaging and Vision N2 - We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone. Y1 - 2020 U6 - https://doi.org/10.1007/s10851-020-00945-w VL - 62 IS - 4 SP - 549 EP - 559 ER - TY - JOUR A1 - Bonnet, Luc A1 - Akian, Jean-Luc A1 - Savin, Éric A1 - Sullivan, T. J. T1 - Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification JF - Algorithms N2 - Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design. Y1 - 2020 U6 - https://doi.org/10.3390/a13080196 VL - 13 IS - 8 SP - 196 ER - TY - GEN A1 - Oates, Chris A1 - Cockayne, Jon A1 - Prangle, Dennis A1 - Sullivan, T. J. A1 - Girolami, Mark ED - Hickernell, F. J. ED - Kritzer, P. T1 - Optimality criteria for probabilistic numerical methods T2 - Multivariate Algorithms and Information-Based Complexity N2 - It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed. Y1 - 2020 U6 - https://doi.org/10.1515/9783110635461-005 VL - 27 SP - 65 EP - 88 PB - De Gruyter ER - TY - JOUR A1 - Kersting, Hans A1 - Sullivan, T. J. A1 - Hennig, Philipp T1 - Convergence rates of Gaussian ODE filters JF - Statistics and Computing Y1 - 2020 U6 - https://doi.org/10.1007/s11222-020-09972-4 VL - 30 SP - 1791 EP - 1816 PB - Springer CY - Statistics and Computing ER -