Finite-dimensional approximations of push-forwards on locally analytic functionals
NeutralArtificial Intelligence
- A new paper presents a functional-analytic framework for approximating the push-forward induced by analytic maps using finitely many samples. The study focuses on the push-forward in the space of locally analytic functionals, employing the Fourier-Borel transform to connect it with operators on entire functions of exponential type, leading to finite-dimensional approximations and error bounds based on Hankel moment matrices.
- This development is significant as it provides explicit sample complexity bounds for approximations from i.i.d. sampled data, enabling the reconstruction of analytic vector fields from discrete trajectory data. The convergence of a data-driven method for recovering vector fields from ordinary differential equations is also established, enhancing the understanding of dynamic systems.
- The research aligns with ongoing advancements in the field of artificial intelligence, particularly in the context of improving computational efficiency in various models. The introduction of frameworks that enhance the performance of analytic methods reflects a broader trend of integrating mathematical rigor with practical applications in AI, potentially influencing future developments in machine learning and data analysis.
— via World Pulse Now AI Editorial System
