8 papers
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Maximiliano Hertel, Ilja Klebanov, Manuel Schaller +1
Conditional expectation operators (CEOs) and their associated conditional mean embeddings (CMEs) play a central role across applied mathematics and machine learning, appearing in n…
Lattice Rules Meet Kernel Cubature
Vesa Kaarnioja, Ilja Klebanov, Claudia Schillings +1
Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space…
Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport
Ilja Klebanov, Claudia Schillings, Dana Wrischnig
The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suf…
Error Bounds for Importance Sampling with Estimated Proposal Distributions
Cathrine Aeckerle-Willems, Ilja Klebanov, Simon Weissmann
Importance sampling with data-driven proposal distributions is widely used in practice. A common workflow first generates an auxiliary sample of size from an approximation of t…
Classification of small-ball modes and maximum a posteriori estimators in metric spaces
Ilja Klebanov, Hefin Lambley, T. J. Sullivan
A mode, or `most likely point', for a probability measure can be defined in various ways via the asymptotic behaviour of the -mass of balls as their radius tends to zero.…
Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo
Ilja Klebanov
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting…