Why does Monte Carlo fail to work properly in high-dimensional optimization problems?
The paper proposes an answer to the question formulated in the title.
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arXiv subjects
Pavel Shcherbakov
Publications and source records attributed to Pavel Shcherbakov.
Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a nonlinear function.We introduce minimum-volume approximations which have the characteristic of guaranteeing a low probability of violation, i.e.,we admit for a probability that some points in the image set are not contained in the approximating set,but this probability is kept below a pre-specified threshold.In the second part of the paper, this idea is then exploited to develop a new family of randomized prediction-corrector filters.These filters represent a natural extension and rapprochement of Gaussian and set-valued filters,and bear similarities with modern tools such as particle filters.
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