10 citations · 12 across the 8 of their papers we have counts for
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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…
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…