A0948
Title: Kolmogorov-Arnold networks for high-dimensional estimation: A method of sieves approach
Authors: Sami Abdurahman - Toronto Metropolitan University (Canada) [presenting]
Abstract: The aim is to introduce a \textbf{novel sieve extremum estimator based on Kolmogorov-Arnold networks (KANs)}, designed for nonparametric estimation in high-dimensional settings with time-series data. By integrating KANs with a method of sieves estimation approach and leveraging sparsity, the method achieves asymptotic convergence rates in the $L_{2}(\mu)$ norm that are \textbf{independent of the covariate dimension}, thereby directly circumventing the curse of dimensionality. Specifically, the approach yields an explicit convergence rate of $o_{P}(n^{-1/4})$. This framework accommodates diverse applications such as high-dimensional conditional density estimation and nuisance function estimation within double/debiased machine learning, areas where traditional deep neural networks often struggle due to their "black box" nature, reliance on i.i.d. assumptions, and slower convergence rates. The proposed KAN sieve estimator overcomes these limitations by learning activation functions using B-splines, and its theoretical framework rigorously permits stationary mixing processes. The efficacy of this framework is demonstrated in an empirical application to high-dimensional financial time series, including predicting asset returns and volatility based on a large set of economic and market indicators.
