Random forests for time-dependent processes
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 801-826.

Random forests were introduced by Breiman in 2001. We study theoretical aspects of both original Breiman’s random forests and a simplified version, the centred random forests. Under the independent and identically distributed hypothesis, Scornet, Biau and Vert proved the consistency of Breiman’s random forest, while Biau studied the simplified version and obtained a rate of convergence in the sparse case. However, the i.i.d hypothesis is generally not satisfied for example when dealing with time series. We extend the previous results to the case where observations are weakly dependent, more precisely when the sequences are stationary β−mixing.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ps/2020015
Classification : 62M10
Mots-clés : Statistics, random forests, time-dependent processes 
@article{PS_2020__24_1_801_0,
     author = {Goehry, Benjamin},
     title = {Random forests for time-dependent processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {801--826},
     publisher = {EDP-Sciences},
     volume = {24},
     year = {2020},
     doi = {10.1051/ps/2020015},
     mrnumber = {4178366},
     zbl = {1455.62172},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2020015/}
}
TY  - JOUR
AU  - Goehry, Benjamin
TI  - Random forests for time-dependent processes
JO  - ESAIM: Probability and Statistics
PY  - 2020
SP  - 801
EP  - 826
VL  - 24
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps/2020015/
DO  - 10.1051/ps/2020015
LA  - en
ID  - PS_2020__24_1_801_0
ER  - 
%0 Journal Article
%A Goehry, Benjamin
%T Random forests for time-dependent processes
%J ESAIM: Probability and Statistics
%D 2020
%P 801-826
%V 24
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ps/2020015/
%R 10.1051/ps/2020015
%G en
%F PS_2020__24_1_801_0
Goehry, Benjamin. Random forests for time-dependent processes. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 801-826. doi : 10.1051/ps/2020015. http://www.numdam.org/articles/10.1051/ps/2020015/

[1] H.C.P. Berbee, Random walks with stationary increments and renewal theory. MC Tracts 112 (1979) 1–223. | MR | Zbl

[2] G. Biau, Analysis of a random forests model. J. Mach. Learn. Res. 13 (2012) 1063–1095. | MR | Zbl

[3] G. Biau and E. Scornet, A random forest guided tour. TEST 25 (2016) 197–227. | DOI | MR | Zbl

[4] R.C. Bradley, Basic properties of strong mixing conditions. a survey and some open questions. Probab. Surv. 2 (2005) 107–144. | DOI | MR | Zbl

[5] L. Breiman, Bagging predictors. Mach. Learn. 24 (1996) 123–140. | DOI | Zbl

[6] L. Breiman, Random forests. Mach. Learn. 45 (2001) 5–32. | DOI | Zbl

[7] L. Breiman, Consistency for a simple model of random forests. Technical report (2004).

[8] L. Breiman, J. Friedman, C.J. Stone and R.A. Olshen, Classification and Regression Trees. The Wadsworth and Brooks-Cole statistics-probability series. Taylor & Francis, Oxford (1984). | MR | Zbl

[9] D.R. Cutler, T.C. Edwards, K.H. Beard, A. Cutler, K.T. Hess, J. Gibson and J.J. Lawler, Random forests for classification in ecology. Ecology 88 (2007) 2783–2792. | DOI

[10] J. Dedecker, P. Doukhan, G. Lang, L.R.J. Rafael, S. Louhichi and C. Prieur, Weak dependence, in Weak Dependence: With Examples and Applications. Springer, Berlin (2007) 9–20. | MR | Zbl

[11] G. Dudek, Short-term load forecasting using random forests, in Intelligent Systems’2014. Springer International Publishing, Cham (2015) 821–828.

[12] A. Fischer, L. Montuelle, M. Mougeot and D. Picard, Statistical learning for wind power: A modeling and stability study towards forecasting. Wind Energy 20 (2017) 2037–2047. | DOI

[13] L. Györfi, M. Kohler, A. Krzyzak and H. Walk, A distribution-free theory of nonparametric regression. Springer Science & Business Media, Berlin (2006). | MR | Zbl

[14] M.J. Kane, N. Price, M. Scotch and P. Rabinowitz, Comparison of arima and random forest time series models for prediction of avian influenza h5n1 outbreaks. BMC Bioinform. 15 (2014) 276. | DOI

[15] A. Lahouar and J. Ben Hadj Slama, Random forests model for one day ahead load forecasting, in IREC2015 The Sixth International Renewable Energy Congress (2015) 1–6.

[16] A.C. Lozano, S.R. Kulkarni and R.E. Schapire, Convergence and consistency of regularized boosting with weakly dependent observations. IEEE Trans. Inf. Theory 60 (2014) 651–660. | DOI | MR | Zbl

[17] R. Meir, Nonparametric time series prediction through adaptive model selection. Mach. Learn. 39 (2000) 5–34. | DOI | Zbl

[18] L. Mentch and G. Hooker, Quantifying uncertainty in random forests via confidence intervals and hypothesis tests. J. Mach. Learn. Res. 17 (2016) 1–41. | MR | Zbl

[19] A.M. Prasad, L.R. Iverson and A. Liaw, Newer classification and regression tree techniques: bagging and random forests for ecological prediction. Ecosystems 9 (2006) 181–199. | DOI

[20] E. Rio, Inequalities and limit theorems for weakly dependent sequences. Lecture (2013).

[21] E. Scornet, On the asymptotics of random forests. J. Multivar. Anal. 146 (2016) 72–83. | DOI | MR | Zbl

[22] E. Scornet, G. Biau and J.-P. Vert, Consistency of random forests. Ann. Stat. 43 (2015) 1716–1741. | DOI | MR | Zbl

[23] J. Shotton, T. Sharp, A. Kipman, A. Fitzgibbon, M. Finocchio, A. Blake, M. Cook and R. Moore, Real-time human pose recognition in parts from single depth images. Commun. ACM 56 (2013) 116–124. | DOI

[24] V. Svetnik, A. Liaw, C. Tong, J.C. Culberson, R.P. Sheridan and B.P. Feuston, Random forest: a classification and regression tool for compound classification and qsar modeling. J. Chem. Inf. Comput. Sci. 43 (2003) 1947–1958. | DOI

[25] S. Wager and S. Athey, Estimation and inference of heterogeneous treatment effects using random forests. J. Am. Stat. Assoc. 113 (2018) 1228–1242. | DOI | MR | Zbl

[26] B. Yu, Rates of convergence for empirical processes of stationary mixing sequences. Ann. Prob. 22 (1994) 94–116. | MR | Zbl

Cité par Sources :