2 research outputs found
Level Set Estimation from Compressive Measurements using Box Constrained Total Variation Regularization
Estimating the level set of a signal from measurements is a task that arises
in a variety of fields, including medical imaging, astronomy, and digital
elevation mapping. Motivated by scenarios where accurate and complete
measurements of the signal may not available, we examine here a simple
procedure for estimating the level set of a signal from highly incomplete
measurements, which may additionally be corrupted by additive noise. The
proposed procedure is based on box-constrained Total Variation (TV)
regularization. We demonstrate the performance of our approach, relative to
existing state-of-the-art techniques for level set estimation from compressive
measurements, via several simulation examples
Robust Super-Level Set Estimation using Gaussian Processes
This paper focuses on the problem of determining as large a region as
possible where a function exceeds a given threshold with high probability. We
assume that we only have access to a noise-corrupted version of the function
and that function evaluations are costly. To select the next query point, we
propose maximizing the expected volume of the domain identified as above the
threshold as predicted by a Gaussian process, robustified by a variance term.
We also give asymptotic guarantees on the exploration effect of the algorithm,
regardless of the prior misspecification. We show by various numerical examples
that our approach also outperforms existing techniques in the literature in
practice.Comment: Accepted to ECML 201