Non-Euclidean Conditional Expectation and Filtering
Abstract
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. This gives computationally tractable filtering equations for the dynamics of the intrinsic conditional expectation of a manifold-valued signal and is used to obtain accurate numerical forecasts of efficient portfolios by incorporating their geometric structure into the estimates.
Cite
@article{arxiv.1710.05829,
title = {Non-Euclidean Conditional Expectation and Filtering},
author = {Anastasis Kratsios and Cody B. Hyndman},
journal= {arXiv preprint arXiv:1710.05829},
year = {2018}
}
Comments
This updated version focuses on non Euclidean filtering applications. The content on geometric learning from version one separated and expanded in our paper "The NEU Meta-Algorithm for Geometric Learning with Applications in Finance" [arXiv:1809.00082]