A1279
Title: Mixing conditions for functional autoregressive models and their application to generalization error analysis
Authors: Yoshikazu Terada - Osaka University; RIKEN (Japan)
Shuntaro Suzuki - Osaka University (Japan) [presenting]
Abstract: The focus is on nonlinear functional autoregressive models (N-FAR), which are useful for modeling large-scale time series data such as meteorological and temperature fields. First, sufficient conditions are derived under which N-FAR satisfies exponential mixing as its statistical dependence structure, thereby providing a foundation for analyzing the asymptotic behavior of estimators. Next, under these sufficient conditions, we establish variance evaluation when the nonlinear operator is learned by a broad range of estimation methods, including deep learning. Furthermore, as an application, the focus is on the case where the nonlinear operator belongs to the class of integral-type Urysohn operators, and the generalization error is theoretically derived when the integral kernel is estimated using deep learning. The present results provide an integrated guarantee of mixing properties for N-FAR together with variance and generalization error analysis of learners, thereby offering theoretical guidance for practical learning design of functional time series.
