32 citations · 91 across the 16 of their papers we have counts for
19 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…
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…
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…
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…
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…
Transporting Higher-Order Quadrature Rules: Quasi-Monte Carlo Points and Sparse Grids for Mixture Distributions
Ilja Klebanov, T. J. Sullivan
Integration against, and hence sampling from, high-dimensional probability distributions is of essential importance in many application areas and has been an active research area f…
Coherent set identification via direct low rank maximum likelihood estimation
Robert Polzin, Ilja Klebanov, Nikolas Nüsken +1
We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach),…
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. Su…
Graph Convex Hull Bounds as generalized Jensen Inequalities
Ilja Klebanov
Jensen's inequality is ubiquitous in measure and probability theory, statistics, machine learning, information theory and many other areas of mathematics and data science. It state…
Maximum a posteriori estimators in are well-defined for diagonal Gaussian priors
Ilja Klebanov, Philipp Wacker
We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors on under common assumptions on the potential . Further, we show connecti…
Γ-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
We derive Onsager-Machlup functionals for countable product measures on weighted subspaces of the sequence space . Each measure in the product is…
Γ-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 +1
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with…
The linear conditional expectation in Hilbert space
Ilja Klebanov, Björn Sprungk, T. J. Sullivan
The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important rôle in approximate Bayesia…
A Rigorous Theory of Conditional Mean Embeddings
Ilja Klebanov, Ingmar Schuster, T. J. Sullivan
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distribu…
Adaptive Convolutions
Ilja Klebanov
When smoothing a function via convolution with some kernel, it is often desirable to adapt the amount of smoothing locally to the variation of . For this purpose, the consta…
Axiomatic Approach to Variable Kernel Density Estimation
Ilja Klebanov
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n…
Markov Chain Importance Sampling -- a highly efficient estimator for MCMC
Ingmar Schuster, Ilja Klebanov
Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection met…
Empirical Bayes Methods for Prior Estimation in Systems Medicine
Ilja Klebanov, Alexander Sikorski, Christof Schütte +1
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinica…
Objective Priors in the Empirical Bayes Framework
Ilja Klebanov, Alexander Sikorski, Christof Schütte +1
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating…