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About this paper
Hiroshi Morioka, Hermanni Hälvä, Aapo Hyvärinen
The authors introduce IIA, a framework for recovering innovations in nonlinear vector autoregressive processes. It infers inputs from successive observations using changes in innovation distributions linked to an auxiliary variable. In a synthetic two-dimensional example, IIA-TCL reaches 0.99 mean absolute correlation, versus 0.72 for AD-NVAR and 0.29 for NICA-TCL; recovery is conditional and up to permutation and component-wise invertible transformations.
Key insights
- Innovations in general nonlinear Vector Autoregressive (NVAR) processes can be uniquely identified (up to permutation and component-wise invertible nonlinearities) by leveraging temporal structure and auxiliary variables.
- Allowing arbitrary nonlinear interactions between observations and innovations, beyond the restrictive additive assumption, enables a more realistic and flexible modeling of complex dynamical systems.
- Deep learning architectures and self-supervised learning paradigms, specifically contrastive learning or Expectation-Maximization, can effectively implement and optimize the demixing functions required for innovation extraction.
Summary by alphaXiv.
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