Independent Innovation Analysis for Nonlinear Vector Autoregressive Process

Hiroshi Morioka, Hermanni Hälvä, Aapo Hyvarinen
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1549-1557, 2021.

Abstract

The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the dynamics, is almost always assumed to be additive. Additivity greatly limits the generality of the model, hindering analysis of general NVAR processes which have nonlinear interactions between the innovations. Here, we propose a new general framework called independent innovation analysis (IIA), which estimates the innovations from completely general NVAR. We assume mutual independence of the innovations as well as their modulation by an auxiliary variable (which is often taken as the time index and simply interpreted as nonstationarity). We show that IIA guarantees the identifiability of the innovations with arbitrary nonlinearities, up to a permutation and component-wise invertible nonlinearities. We also propose three estimation frameworks depending on the type of the auxiliary variable. We thus provide the first rigorous identifiability result for general NVAR, as well as very general tools for learning such models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-morioka21a, title = { Independent Innovation Analysis for Nonlinear Vector Autoregressive Process }, author = {Morioka, Hiroshi and H{\"a}lv{\"a}, Hermanni and Hyvarinen, Aapo}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1549--1557}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/morioka21a/morioka21a.pdf}, url = {https://proceedings.mlr.press/v130/morioka21a.html}, abstract = { The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the dynamics, is almost always assumed to be additive. Additivity greatly limits the generality of the model, hindering analysis of general NVAR processes which have nonlinear interactions between the innovations. Here, we propose a new general framework called independent innovation analysis (IIA), which estimates the innovations from completely general NVAR. We assume mutual independence of the innovations as well as their modulation by an auxiliary variable (which is often taken as the time index and simply interpreted as nonstationarity). We show that IIA guarantees the identifiability of the innovations with arbitrary nonlinearities, up to a permutation and component-wise invertible nonlinearities. We also propose three estimation frameworks depending on the type of the auxiliary variable. We thus provide the first rigorous identifiability result for general NVAR, as well as very general tools for learning such models. } }
Endnote
%0 Conference Paper %T Independent Innovation Analysis for Nonlinear Vector Autoregressive Process %A Hiroshi Morioka %A Hermanni Hälvä %A Aapo Hyvarinen %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-morioka21a %I PMLR %P 1549--1557 %U https://proceedings.mlr.press/v130/morioka21a.html %V 130 %X The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the dynamics, is almost always assumed to be additive. Additivity greatly limits the generality of the model, hindering analysis of general NVAR processes which have nonlinear interactions between the innovations. Here, we propose a new general framework called independent innovation analysis (IIA), which estimates the innovations from completely general NVAR. We assume mutual independence of the innovations as well as their modulation by an auxiliary variable (which is often taken as the time index and simply interpreted as nonstationarity). We show that IIA guarantees the identifiability of the innovations with arbitrary nonlinearities, up to a permutation and component-wise invertible nonlinearities. We also propose three estimation frameworks depending on the type of the auxiliary variable. We thus provide the first rigorous identifiability result for general NVAR, as well as very general tools for learning such models.
APA
Morioka, H., Hälvä, H. & Hyvarinen, A.. (2021). Independent Innovation Analysis for Nonlinear Vector Autoregressive Process . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1549-1557 Available from https://proceedings.mlr.press/v130/morioka21a.html.

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