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- W4297848771 abstract "In this article we consider the smoothing problem for hidden Markov models (HMM). Given a hidden Markov chain ${X_n}_{ngeq 0}$ and observations ${Y_n}_{ngeq 0}$, our objective is to compute $mathbb{E}[varphi(X_0,dots,X_k)|y_{0},dots,y_n]$ for some real-valued, integrable functional $varphi$ and $k$ fixed, $k ll n$ and for some realisation $(y_0,dots,y_n)$ of $(Y_0,dots,Y_n)$. We introduce a novel application of the multilevel Monte Carlo (MLMC) method with a coupling based on the Knothe-Rosenblatt rearrangement. We prove that this method can approximate the afore-mentioned quantity with a mean square error (MSE) of $mathcal{O}(epsilon^2)$, for arbitrary $epsilon>0$ with a cost of $mathcal{O}(epsilon^{-2})$. This is in contrast to the same direct Monte Carlo method, which requires a cost of $mathcal{O}(nepsilon^{-2})$ for the same MSE. The approach we suggest is, in general, not possible to implement, so the optimal transport methodology of cite{span} is used, which directly approximates our strategy. We show that our theoretical improvements are achieved, even under approximation, in several numerical examples." @default.
- W4297848771 created "2022-10-01" @default.
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- W4297848771 date "2018-04-19" @default.
- W4297848771 modified "2023-09-27" @default.
- W4297848771 title "On Large Lag Smoothing for Hidden Markov Models" @default.
- W4297848771 doi "https://doi.org/10.48550/arxiv.1804.07117" @default.
- W4297848771 hasPublicationYear "2018" @default.
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