Against the Flow of Time with Multi-Output Models
Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has bee...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-08-01
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| Series: | Measurement Science Review |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/msr-2023-0023 |
| _version_ | 1827769629238362112 |
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| author | Jakubík Jozef Phuong Mary Chvosteková Martina Krakovská Anna |
| author_facet | Jakubík Jozef Phuong Mary Chvosteková Martina Krakovská Anna |
| author_sort | Jakubík Jozef |
| collection | DOAJ |
| description | Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X ↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X ⫫ Y . The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal. |
| first_indexed | 2024-03-11T12:27:55Z |
| format | Article |
| id | doaj.art-e911b831667d44b3989bbdff644627e6 |
| institution | Directory Open Access Journal |
| issn | 1335-8871 |
| language | English |
| last_indexed | 2024-03-11T12:27:55Z |
| publishDate | 2023-08-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Measurement Science Review |
| spelling | doaj.art-e911b831667d44b3989bbdff644627e62023-11-06T07:14:42ZengSciendoMeasurement Science Review1335-88712023-08-0123417518310.2478/msr-2023-0023Against the Flow of Time with Multi-Output ModelsJakubík Jozef0Phuong Mary1Chvosteková Martina2Krakovská Anna31Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, Slovakia2IST Austria, Am Campus 1, Klosterneuburg, Austria1Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, Slovakia1Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, SlovakiaRecent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X ↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X ⫫ Y . The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal.https://doi.org/10.2478/msr-2023-0023causalitydeterministic dynamical systemsreversibilitymulti-output prediction |
| spellingShingle | Jakubík Jozef Phuong Mary Chvosteková Martina Krakovská Anna Against the Flow of Time with Multi-Output Models Measurement Science Review causality deterministic dynamical systems reversibility multi-output prediction |
| title | Against the Flow of Time with Multi-Output Models |
| title_full | Against the Flow of Time with Multi-Output Models |
| title_fullStr | Against the Flow of Time with Multi-Output Models |
| title_full_unstemmed | Against the Flow of Time with Multi-Output Models |
| title_short | Against the Flow of Time with Multi-Output Models |
| title_sort | against the flow of time with multi output models |
| topic | causality deterministic dynamical systems reversibility multi-output prediction |
| url | https://doi.org/10.2478/msr-2023-0023 |
| work_keys_str_mv | AT jakubikjozef againsttheflowoftimewithmultioutputmodels AT phuongmary againsttheflowoftimewithmultioutputmodels AT chvostekovamartina againsttheflowoftimewithmultioutputmodels AT krakovskaanna againsttheflowoftimewithmultioutputmodels |