2026 | Posterior error bounds for prior-driven balancing in linear Gaussian inverse problems | Josie König, Han Cheng LieZeitschrift: arXivLink zum Preprint
Posterior error bounds for prior-driven balancing in linear Gaussian inverse problems
Autoren: Josie König, Han Cheng Lie
(2026)
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with linear forward models, Gaussian priors, and Gaussian noise, we use perturbation theory for inverses to bound the error in the approximate posterior mean and posterior covariance resulting from a linear approximate forward model. We then focus on the smoothing problem of inferring the initial condition of linear time-invariant dynamical systems, using finitely many partial state observations. For such problems, and for a specific model order reduction method based on balanced truncation, we show that the impulse response of a certain prior-driven system is closely related to the prior-preconditioned Hessian of the inverse problem. This reveals a novel connection between systems theory and inverse problems. We exploit this connection to prove the first a priori error bounds for system-theoretic model order reduction methods applied to smoothing problems. The bounds control the approximation error of the posterior mean and covariance in terms of the truncated Hankel singular values of the underlying system.
2025 | Upper and lower bounds for local Lipschitz stability of Bayesian posteriors | Nada Cvetkovic, Han Cheng LieLink zum Preprint
Upper and lower bounds for local Lipschitz stability of Bayesian posteriors
Autoren: Nada Cvetkovic, Han Cheng Lie
(2025)
2025 | Optimal low-rank approximations of posteriors for linear Gaussian inverse problems on Hilbert spaces, Part II: posterior mean approximation | Giuseppe Carere, Han Cheng LieLink zum Preprint
Optimal low-rank approximations of posteriors for linear Gaussian inverse problems on Hilbert spaces, Part II: posterior mean approximation
Autoren: Giuseppe Carere, Han Cheng Lie
(2025)
2025 | Optimal low-rank approximations of posteriors for linear Gaussian inverse problems on Hilbert spaces, Part I: posterior covariance approximation | Giuseppe Carere, Han Cheng LieLink zum Preprint
Optimal low-rank approximations of posteriors for linear Gaussian inverse problems on Hilbert spaces, Part I: posterior covariance approximation
Autoren: Giuseppe Carere, Han Cheng Lie
(2025)
2024 | Generalised rank-constrained approximations of Hilbert-Schmidt operators on separable Hilbert spaces and applications | Giuseppe Carere, Han Cheng LieLink zum Preprint
Generalised rank-constrained approximations of Hilbert-Schmidt operators on separable Hilbert spaces and applications
Autoren: Giuseppe Carere, Han Cheng Lie
(2024)
2024 | Bayesian inference of covariate-parameter relationships for population modelling | Han Cheng LieLink zum Preprint
Bayesian inference of covariate-parameter relationships for population modelling
Autoren: Han Cheng Lie
(2024)
2024 | Data subsampling for Poisson regression with pth-root link | Han Cheng Lie, Alexander MunteanuZeitschrift: Advances in Neural Information Processing Systems 37 (NeurIPS 2024)Link zur Publikation
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Link zum Preprint
Data subsampling for Poisson regression with pth-root link
Autoren: Han Cheng Lie, Alexander Munteanu
(2024)
Zeitschrift:
Advances in Neural Information Processing Systems 37 (NeurIPS 2024)
2024 | Choosing Observation Operators to Mitigate Model Error in Bayesian Inverse Problems | Nada Cvetkovic, Han Cheng Lie, Harshit Bansal, Karen Veroy-GreplZeitschrift: SIAM/ASA Journal of Uncertainty QuantificationReihe: 12Seiten: 723-758Band: 3Link zur Publikation
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Link zum Preprint
Choosing Observation Operators to Mitigate Model Error in Bayesian Inverse Problems
Autoren: Nada Cvetkovic, Han Cheng Lie, Harshit Bansal, Karen Veroy-Grepl
(2024)
Zeitschrift:
SIAM/ASA Journal of Uncertainty Quantification
2023 | Dimension-independent Markov chain Monte Carlo on the sphere | Han Cheng Lie, Daniel Rudolf, Bjorn Sprungk, T. J. SullivanZeitschrift: Scandinavian Journal of StatisticsReihe: 50Seiten: 1818-1858Link zur Publikation
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Link zum Preprint
Dimension-independent Markov chain Monte Carlo on the sphere
Autoren: Han Cheng Lie, Daniel Rudolf, Bjorn Sprungk, T. J. Sullivan
(2023)
Zeitschrift:
Scandinavian Journal of Statistics
2022 | Randomised one-step time integration methods for deterministic operator differential equations | Han Cheng Lie, Martin Stahn, T. J. SullivanZeitschrift: CalcoloReihe: 59Seiten: 1-33Band: 13Link zur Publikation
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Link zum Preprint
Randomised one-step time integration methods for deterministic operator differential equations
Autoren: Han Cheng Lie, Martin Stahn, T. J. Sullivan
(2022)
2021 | Fréchet derivatives of expected functionals of solutions to stochastic differential equations | Han Cheng LieLink zum Preprint
Fréchet derivatives of expected functionals of solutions to stochastic differential equations
Autoren: Han Cheng Lie
(2021)
2021 | Error bounds for some approximate posterior measures in Bayesian inference | Han Cheng Lie, T. J. Sullivan, Aretha TeckentrupZeitschrift: Lecture Notes in Computational Science and EngineeringVerlag: Springer, ChamBuchtitel: Numerical Mathematics and Advanced Applications ENUMATH 2019Seiten: 275-283Band: 139Link zur Publikation
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Link zum Preprint
Error bounds for some approximate posterior measures in Bayesian inference
Autoren: Han Cheng Lie, T. J. Sullivan, Aretha Teckentrup
(2021)
Zeitschrift:
Lecture Notes in Computational Science and Engineering
Buchtitel:
Numerical Mathematics and Advanced Applications ENUMATH 2019
2021 | Gamma-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces | Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. SullivanZeitschrift: Inverse ProblemsReihe: 38Seiten: 025006Band: 2Link zur Publikation
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Link zum Preprint
Gamma-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Autoren: Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
(2021)
Zeitschrift:
Inverse Problems
2021 | Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems | Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. SullivanZeitschrift: Inverse ProblemsReihe: 38Seiten: 025005Band: 2Link zur Publikation
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Link zum Preprint
Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
Autoren: Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
(2021)
Zeitschrift:
Inverse Problems
2021 | Convergent discretisation schemes for transition path theory for diffusion processes | Nada Cvetković, Tim Conrad, Han Cheng LieZeitschrift: SIAM J. Multiscale Modeling and SimulationVerlag: Society for Industrial and Applied MathematicsSeiten: 242–266Band: 19(1)Link zur Publikation
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Link zum Preprint
Convergent discretisation schemes for transition path theory for diffusion processes
Autoren: Nada Cvetković, Tim Conrad, Han Cheng Lie
(2021)
Zeitschrift:
SIAM J. Multiscale Modeling and Simulation
Verlag:
Society for Industrial and Applied Mathematics
2019 | Strong convergence rates of probabilistic integrators for ordinary differential equations | H. C. Lie, A. M. Stuart, T. J. SullivanZeitschrift: Stat ComputVerlag: SpringerSeiten: 1265-1283Band: 29Link zur Publikation
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Link zum Preprint
Strong convergence rates of probabilistic integrators for ordinary differential equations
Autoren: H. C. Lie, A. M. Stuart, T. J. Sullivan
(2019)
2019 | On a degeneracy ratio for bounded convex polytopes | Nada Cvetković, Han Cheng LieLink zum Preprint
On a degeneracy ratio for bounded convex polytopes
Autoren: Nada Cvetković, Han Cheng Lie
(2019)
2018 | Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics | Péter Koltai, Han Cheng Lie, Martin PlonkaZeitschrift: NonlinearityVerlag: IOP PublishingSeiten: 4232Band: 32Link zur Publikation
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Link zum Preprint
Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics
Autoren: Péter Koltai, Han Cheng Lie, Martin Plonka
(2018)
2018 | Quasi-invariance of countable products of Cauchy measures under non-unitary dilations | Han Cheng Lie, T. J. SullivanZeitschrift: Electron. Commun. Probab.Seiten: 6 pagesBand: 23, paper no. 8Link zur Publikation
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Link zum Preprint
Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Autoren: Han Cheng Lie, T. J. Sullivan
(2018)
Zeitschrift:
Electron. Commun. Probab.
2018 | Equivalence of weak and strong modes of measures on topological vector spaces | Han Cheng Lie, T. J. SullivanZeitschrift: Inverse ProblemsVerlag: IOP PublishingSeiten: 115013Band: 34Link zur Publikation
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Link zum Preprint
Equivalence of weak and strong modes of measures on topological vector spaces
Autoren: Han Cheng Lie, T. J. Sullivan
(2018)
Zeitschrift:
Inverse Problems
2018 | Implicit Probabilistic Integrators for ODEs | Onur Teymur, Han Cheng Lie, Tim Sullivan, Ben CalderheadBuchtitel: Advances in Neural Information Processing Systems 31 (NIPS 2018)Link zur Publikation
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Link zum Preprint
Implicit Probabilistic Integrators for ODEs
Autoren: Onur Teymur, Han Cheng Lie, Tim Sullivan, Ben Calderhead
(2018)
Buchtitel:
Advances in Neural Information Processing Systems 31 (NIPS 2018)
2018 | Random forward models and log-likelihoods in Bayesian inverse problems | H. C. Lie, T. J. Sullivan, A. L. TeckentrupZeitschrift: SIAM/ASA J. Uncertainty QuantificationVerlag: SIAMSeiten: 1600-1629Band: 6(4)Link zur Publikation
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Link zum Preprint
Random forward models and log-likelihoods in Bayesian inverse problems
Autoren: H. C. Lie, T. J. Sullivan, A. L. Teckentrup
(2018)
Zeitschrift:
SIAM/ASA J. Uncertainty Quantification
2017 | Some connections between importance sampling and enhanced sampling methods in molecular dynamics | H. C. Lie, J. QuerZeitschrift: J. Chem. Phys.Verlag: AIP PublishingSeiten: 194107Band: 147Link zur Publikation
Some connections between importance sampling and enhanced sampling methods in molecular dynamics
Autoren: H. C. Lie, J. Quer
(2017)
Zeitschrift:
J. Chem. Phys.
2016 | On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions | Han Cheng LieVerlag: Dissertation, Freie Universität BerlinLink zur Publikation
On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions
Autoren: Han Cheng Lie
(2016)
Verlag:
Dissertation, Freie Universität Berlin
2016 | Convexity of a stochastic control functional related to importance sampling of Itô diffusions | Han Cheng LieLink zum Preprint
Convexity of a stochastic control functional related to importance sampling of Itô diffusions
Autoren: Han Cheng Lie
(2016)
2014 | Towards breaking the curse of dimensionality in computational methods for the conformational analysis of molecules | Han Cheng LieZeitschrift: BMC BioinformaticsVerlag: BioMed CentralBand: 15, A2Link zur Publikation
Towards breaking the curse of dimensionality in computational methods for the conformational analysis of molecules
Autoren: Han Cheng Lie
(2014)
Zeitschrift:
BMC Bioinformatics
2013 | A Square Root Approximation of Transition Rates for a Markov State Model | Han Cheng Lie, Konstantin Fackeldey, Marcus WeberZeitschrift: SIAM J. Matrix Anal. Appl.Verlag: SIAMSeiten: 738-756Band: 34(2)Link zur Publikation
A Square Root Approximation of Transition Rates for a Markov State Model
Autoren: Han Cheng Lie, Konstantin Fackeldey, Marcus Weber
(2013)
Zeitschrift:
SIAM J. Matrix Anal. Appl.
