The Library
Higher order kernel mean embeddings to capture filtrations of stochastic processes
Tools
Salvi, Cristopher, Lemercier, Maud, Liu, Chong, Horvath, Blanka, Damoulas, Theodoros and Lyons, Terry (2021) Higher order kernel mean embeddings to capture filtrations of stochastic processes. In: Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2021), Virtual, 6-14 Dec 2021. Published in: Advances in Neural Information Processing Systems 34 (NeurIPS 2021), 34 pp. 16635-16647.
|
PDF
WRAP-higher-order-kernel-mean-embeddings-capture-filtrations-stochastic-processes-Damoulas-2021-.pdf - Accepted Version - Requires a PDF viewer. Download (952Kb) | Preview |
Official URL: https://papers.nips.cc/paper/2021/hash/8b2dfbe0c1d...
Abstract
Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME to capture additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to capture information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories.
Item Type: | Conference Item (Paper) | ||||||
---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
Library of Congress Subject Headings (LCSH): | Kernel functions, Hilbert space, Stochastic analysis | ||||||
Journal or Publication Title: | Advances in Neural Information Processing Systems 34 (NeurIPS 2021) | ||||||
Publisher: | Curran Associates, Inc | ||||||
Official Date: | 2021 | ||||||
Dates: |
|
||||||
Volume: | 34 | ||||||
Page Range: | pp. 16635-16647 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Description: | Proceedings edited by M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan |
||||||
Date of first compliant deposit: | 20 October 2021 | ||||||
Date of first compliant Open Access: | 20 October 2021 | ||||||
Conference Paper Type: | Paper | ||||||
Title of Event: | Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2021) | ||||||
Type of Event: | Conference | ||||||
Location of Event: | Virtual | ||||||
Date(s) of Event: | 6-14 Dec 2021 | ||||||
Related URLs: | |||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year