Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Conditioning on Stochastic Processes via Signatures

by R. Alaifari and A. Schell

(Report number 2023-45)

Abstract
In this working paper, the conditional expectation of a random vector given a stochastic process is characterised as the solution of some convex (semi-)infinite linear least squares problem. This result is based on a functional monotone class argument involving the robust signature of the conditioning process, and it enables the nonparametric and practically feasible computation of conditional distributions for very general classes of jointly distributed stochastic processes.

Keywords: conditional expectation, conditional distribution, conditional probability, supervised learning, nonparametric regression, functional regression, function approximation

@Techreport{AS23_1082,
  author = {R. Alaifari and A. Schell},
  title = {Conditioning on Stochastic Processes via Signatures},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-45},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-45.pdf },
  year = {2023}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).