Projects per year
Abstract
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability distribution. This hypothesis is close, in certain respects, to the hypothesis of exchangeability, which postulates that the distribution of the observations is invariant with respect to their permutations. This paper reviews known methods of testing the two hypotheses concentrating on the online mode of testing, when the observations arrive sequentially. All known online methods for testing these hypotheses are based on conformal martingales, which are defined and studied in detail. An important variety of online testing is change detection, where the use of conformal martingales leads to conformal versions of the CUSUM and ShiryaevRoberts procedures; these versions work in the nonparametric setting where the data is assumed IID according to a completely unknown distribution before the change. The paper emphasizes conceptual and practical aspects and states two kinds of results. Validity results limit the probability of a false alarm or, in the case of change detection, the frequency of false alarms for various procedures based on conformal martingales. Efficiency results establish connections between randomness, exchangeability, and conformal martingales.
Original language  English 

Pages (fromto)  595611 
Number of pages  17 
Journal  Statistical Science 
Volume  36 
Issue number  4 
Early online date  11 Oct 2021 
DOIs  
Publication status  Published  Nov 2021 
Keywords
 Change detection
 Conformal prediction
 Exchangeability
 Martingale
 Online setting
 Testing randomness
Projects
 1 Finished

Conformal Martingales for ChangePoint Detection
Gammerman, A. (PI) & Vovk, V. (CoI)
1/06/20 → 31/05/21
Project: Research