The Wiener Theory of Causal Linear Prediction Is Not Effective

Holger Boche; Volker Pohl; H. Vincent Poor

doi:10.1109/CDC49753.2023.10383355

The Wiener Theory of Causal Linear Prediction Is Not Effective

Holger Boche, Volker Pohl, H. Vincent Poor

Chair of Theoretical Information Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a stationary stochas-tic time series from its past observations is not generally Turing computable, even if the spectral density of the stochastic process is differentiable with a computable first derivative. This implies that for any approximation sequence that converges to the MMSE there does not exist an algorithmic stopping criterion that guarantees that the computed approximation is sufficiently close to the true value of the MMSE. Furthermore, it will be shown that under the same conditions on the spectral density, it is also the case that coefficients of the optimal prediction filter are not generally Turing computable.

Original language	English
Title of host publication	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	8229-8234
Number of pages	6
ISBN (Electronic)	9798350301243
DOIs	https://doi.org/10.1109/CDC49753.2023.10383355
State	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

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10.1109/CDC49753.2023.10383355

Cite this

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title = "The Wiener Theory of Causal Linear Prediction Is Not Effective",

abstract = "In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a stationary stochas-tic time series from its past observations is not generally Turing computable, even if the spectral density of the stochastic process is differentiable with a computable first derivative. This implies that for any approximation sequence that converges to the MMSE there does not exist an algorithmic stopping criterion that guarantees that the computed approximation is sufficiently close to the true value of the MMSE. Furthermore, it will be shown that under the same conditions on the spectral density, it is also the case that coefficients of the optimal prediction filter are not generally Turing computable.",

author = "Holger Boche and Volker Pohl and Poor, \{H. Vincent\}",

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year = "2023",

doi = "10.1109/CDC49753.2023.10383355",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Boche, H, Pohl, V & Poor, HV 2023, The Wiener Theory of Causal Linear Prediction Is Not Effective. in 2023 62nd IEEE Conference on Decision and Control, CDC 2023. Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 8229-8234, 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, 13/12/23. https://doi.org/10.1109/CDC49753.2023.10383355

The Wiener Theory of Causal Linear Prediction Is Not Effective. / Boche, Holger; Pohl, Volker; Poor, H. Vincent.
2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 8229-8234 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a stationary stochas-tic time series from its past observations is not generally Turing computable, even if the spectral density of the stochastic process is differentiable with a computable first derivative. This implies that for any approximation sequence that converges to the MMSE there does not exist an algorithmic stopping criterion that guarantees that the computed approximation is sufficiently close to the true value of the MMSE. Furthermore, it will be shown that under the same conditions on the spectral density, it is also the case that coefficients of the optimal prediction filter are not generally Turing computable.

AB - In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a stationary stochas-tic time series from its past observations is not generally Turing computable, even if the spectral density of the stochastic process is differentiable with a computable first derivative. This implies that for any approximation sequence that converges to the MMSE there does not exist an algorithmic stopping criterion that guarantees that the computed approximation is sufficiently close to the true value of the MMSE. Furthermore, it will be shown that under the same conditions on the spectral density, it is also the case that coefficients of the optimal prediction filter are not generally Turing computable.

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ER -

The Wiener Theory of Causal Linear Prediction Is Not Effective

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