Title :

New efficient algorithms for multiple change-point detection with reproducing kernels

Author(s) :

Celisse, Alain [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Briend, Guillemette [Auteur]
Evaluation des technologies de santé et des pratiques médicales - ULR 2694 [METRICS]
Male, Pierre-Jean [Auteur]
Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]
Evaluation des technologies de santé et des pratiques médicales - ULR 2694 [METRICS]
Rigaill, Guillem [Auteur]
Institut des Sciences des Plantes de Paris-Saclay [IPS2 (UMR_9213 / UMR_1403)]
Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]

Journal title :

Computational Statistics and Data Analysis

Pages :

200-220

Publisher :

Elsevier

Publication date :

2018

ISSN :

0167-9473

English keyword(s) :

Kernel method
Nonparametric change-point detection
Model selection
Algorithms
Dynamic programming
Allele B fraction
Gram matrix
DNA copy number

HAL domain(s) :

Mathématiques [math]
Informatique [cs]
Sciences du Vivant [q-bio]
Sciences du Vivant [q-bio]/Biologie végétale

English abstract : [en]

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches ...
Show more >Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, consistency). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes (n < 10(4)). This computational issue is addressed by first describing a new efficient procedure for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It is based on an exact optimization algorithm and deals with medium size signals (up to n approximate to 10(5)). Second, a faster procedure (based on an approximate optimization algorithm) is described. It relies on a low-rank approximation to the Gram matrix and is linear in time and space. The resulting procedure can be applied to large-scale signals (n >= 10(6)). These two procedures (based on the exact or approximate optimization algorithms) have been implemented in R. and C for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Calibration statistique

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL