Keep it tighter -- A story on analytical mean embeddings

Chamakh, Linda and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2021) Keep it tighter -- A story on analytical mean embeddings. . arXiv. (Unpublished)

Text (2110.09516v3) - Submitted Version Available under License Creative Commons Attribution. Download (810kB)

• Author

Abstract

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a divergence measure referred to as maximum mean discrepancy (MMD) with existing quadratic-time estimators (w.r.t. the sample size) and known convergence properties for bounded kernels. In this paper we focus on the problem of MMD estimation when the mean embedding of one of the underlying distributions is available analytically. Particularly, we consider distributions on the real line (motivated by financial applications) and prove tighter concentration for the proposed estimator under this semi-explicit setting; we also extend the result to the case of unbounded (exponential) kernel with minimaxoptimal lower bounds. We demonstrate the efficiency of our approach beyond synthetic example in three real-world examples relying on one-dimensional random variables: index replication and calibration on loss-givendefault ratios and on S&P 500 data.

Item Type:	Monograph (Report)
Official URL:	https://arxiv.org/list/stat/recent
Additional Information:	© 2021 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	01 Aug 2022 09:27
Last Modified:	10 Jan 2025 10:42
URI:	http://eprints.lse.ac.uk/id/eprint/115723

Actions (login required)

View Item