Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.
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August 2021
July 26 2021
Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks Unavailable
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Germán Abrevaya,
Germán Abrevaya
Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina [email protected]
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Guillaume Dumas,
Guillaume Dumas
Mila–Quebec Artificial Intelligence Institute, and CHU Sainte-Justine Research Center, Department of Psychiatry, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
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Aleksandr Y. Aravkin,
Aleksandr Y. Aravkin
University of Washington, Seattle, WA 98195, U.S.A. [email protected]
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Peng Zheng,
Peng Zheng
University of Washington, Seattle, WA 98195, U.S.A. [email protected]
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Jean-Christophe Gagnon-Audet,
Jean-Christophe Gagnon-Audet
Mila–Quebec Artificial Intelligence Institute, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
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James Kozloski,
James Kozloski
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
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Pablo Polosecki,
Pablo Polosecki
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
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Guillaume Lajoie,
Guillaume Lajoie
Mila–Quebec Artificial Intelligence Institute, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
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David Cox,
David Cox
MIT-IBM Watson AI Lab, Cambridge, MA 02139, U.S.A. [email protected]
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Silvina Ponce Dawson,
Silvina Ponce Dawson
Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina [email protected]
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Guillermo Cecchi,
Guillermo Cecchi
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
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Irina Rish
Irina Rish
Mila–Quebec Artificial Intelligence Institute, Université de Montréal, Montreal H3A OE8, Canada [email protected]
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Germán Abrevaya
Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina [email protected]
Guillaume Dumas
Mila–Quebec Artificial Intelligence Institute, and CHU Sainte-Justine Research Center, Department of Psychiatry, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
Aleksandr Y. Aravkin
University of Washington, Seattle, WA 98195, U.S.A. [email protected]
Peng Zheng
University of Washington, Seattle, WA 98195, U.S.A. [email protected]
Jean-Christophe Gagnon-Audet
Mila–Quebec Artificial Intelligence Institute, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
James Kozloski
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
Pablo Polosecki
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
Guillaume Lajoie
Mila–Quebec Artificial Intelligence Institute, Universitéde Montréal, Montreal H3A OE8, Canada [email protected]
David Cox
MIT-IBM Watson AI Lab, Cambridge, MA 02139, U.S.A. [email protected]
Silvina Ponce Dawson
Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina [email protected]
Guillermo Cecchi
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. [email protected]
Irina Rish
Mila–Quebec Artificial Intelligence Institute, Université de Montréal, Montreal H3A OE8, Canada [email protected]
Received:
June 03 2020
Accepted:
February 19 2021
Online ISSN: 1530-888X
Print ISSN: 0899-7667
© 2021 Massachusetts Institute of Technology
2021
Massachusetts Institute of Technology
Neural Computation (2021) 33 (8): 2087–2127.
Article history
Received:
June 03 2020
Accepted:
February 19 2021
Citation
Germán Abrevaya, Guillaume Dumas, Aleksandr Y. Aravkin, Peng Zheng, Jean-Christophe Gagnon-Audet, James Kozloski, Pablo Polosecki, Guillaume Lajoie, David Cox, Silvina Ponce Dawson, Guillermo Cecchi, Irina Rish; Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks. Neural Comput 2021; 33 (8): 2087–2127. doi: https://doi.org/10.1162/neco_a_01401
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