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

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,...

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Vydané v:Computational statistics & data analysis Ročník 128; s. 200 - 220
Hlavní autori: Celisse, A., Marot, G., Pierre-Jean, M., Rigaill, G.J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.12.2018
Elsevier
Predmet:
Algorithms
Allele B fraction
alleles
Computer Science
DNA
DNA copy number
Dynamic programming
Gram matrix
Kernel method
Life Sciences
Mathematics
Model selection
Nonparametric change-point detection
statistical analysis
variance
Vegetal Biology
Algorithms
Model selection
DNA copy number
Allele B fraction
Nonparametric change-point detection
Dynamic programming
Kernel method
Gram matrix
ISSN:0167-9473, 1872-7352
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Shrnutí: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<104). 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≈105). 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≥106). 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.
Bibliografia:ObjectType-Article-1
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2018.07.002