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N. Cvetkovic and H. C. Lie, "Upper and lower bounds for local Lipschitz stability of Bayesian posteriors" (2025) [arxiv]
G. Carere and H. C. Lie, "Optimal low-rank posterior mean and distribution approximation in linear Gaussian inverse problems on Hilbert spaces" (2025) [arxiv]
G. Carere and H. C. Lie, "Optimal low-rank posterior covariance approximation in linear Gaussian inverse problems on Hilbert spaces" (2025) [arxiv]
G. Carere and H. C. Lie, "Generalised rank-constrained approximations of Hilbert-Schmidt operators on separable Hilbert spaces and applications" (2024) [arxiv]
H. C. Lie, "Bayesian inference of covariate-parameter relationships for population modelling" (2024) [arxiv]
H. C. Lie, "Frechet derivatives of expected functionals of solutions to stochastic differential equations" (2021) [arxiv]
N. Cvetkovic, H. C. Lie, "On a degeneracy ratio for bounded convex polytopes" (2019) [arxiv]
2024
A. Munteanu, H. C. Lie, "Data subsampling for Poisson regression with pth-root link" [arxiv][OpenReview][NeurIPS proceedings]
N. Cvetkovic, H. C. Lie*, H. Bansal, K. Veroy-Grepl, "Choosing observation operators to mitigate model error in Bayesian inverse problems" [arxiv][journal]
2023
H. C. Lie*, D. Rudolf, B. Sprungk, T. J. Sullivan, "Dimension-independent Markov chain Monte Carlo on the sphere" [arxiv][journal]
2022
H. C. Lie*, M. Stahn, T. J. Sullivan, "Randomised one-step time integration methods for deterministic operator differential equations" [arxiv][journal]
2021
B. Ayanbayev, I. Klebanov, H. C. Lie, T.J. Sullivan, "Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems" (2021) [arxiv][journal]
B. Ayanbayev, I. Klebanov, H. C. Lie, T.J. Sullivan, "Gamma-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces" (2021) [arxiv][journal]
N. Cvetkovic, T. Conrad, H. C. Lie, "Convergent discretisation schemes for transition path theory for diffusion processes", accepted for publication in SIAM Multiscale Modelling and Simulation [arxiv][journal]
H. C. Lie*, T. J. Sullivan and Aretha Teckentrup, "Error bounds for some approximate posterior measures in Bayesian inference", accepted in proceedings of EnuMATH 2019 [arxiv][journal]
2019
P. Koltai, H. C. Lie, and M. Plonka, "Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic systems", Nonlinearity [arxiv][journal]
H. C. Lie*, A. M. Stuart and T. J. Sullivan, "Strong convergence rates of probabilistic integrators for ordinary differential equations", Stat. Comput. [arxiv][journal]
2018
H. C. Lie, T. J. Sullivan, and A. L. Teckentrup, "Random forward models and log-likelihoods in Bayesian inverse problems", ASA/SIAM J. Uncertain. Quantif. [arxiv][journal]
O. Teymur, H. C. Lie, T. J. Sullivan, and B. Calderhead, "Implicit probabilistic integrators for ODEs", Neural Information Processing Systems (NeurIPS) [arxiv][proceedings]
H. C. Lie* and T. J. Sullivan, "Equivalence of weak and strong modes of measures on topological vector spaces" [arxiv][journal]
H. C. Lie* and T. J. Sullivan, "Quasi-invariance of countable products of Cauchy measures under non-unitary dilations", Electron. Commun. Probab. [arxiv] [journal]
2017
H. C. Lie* and J. Quer, "Some connections between importance sampling and enhanced sampling methods in molecular dynamics", J. Chem. Phys. [journal]
2014
H. C. Lie, "Towards breaking the curse of dimensionality in computational methods for the conformational analysis of molecules", BMC Bioinformatics [journal]
2013
H. C. Lie*, K. Fackeldey and M. Weber, "A square root approximation of transition rates for a Markov state model", SIAM J. Matrix Analysis and Applications [journal]
Thesis: "On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions" [Link to FU Berlin dissertation repository]