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math.ST2025
A unified theory of the high-dimensional Laplace approximation with application to Bayesian inverse problems
Anya Katsevich, Vladimir Spokoiny
The Laplace approximation (LA) to posteriors is a ubiquitous tool to simplify Bayesian computation, particularly in the high-dimensional settings arising in Bayesian inverse proble…
math.ST2025
Dimension-free bounds in high-dimensional linear regression via error-in-operator approach
Fedor Noskov, Nikita Puchkin, Vladimir Spokoiny
We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design cova…