Consistency of random forests

Breiman, L. (2001). Random forests. <i>Mach. Learn.</i> <b>45</b> 5–32.

Breiman, L. (1996). Bagging predictors. <i>Mach. Learn.</i> <b>24</b> 123–140.

Hastie, T. and Tibshirani, R. (1986). Generalized additive models. <i>Statist. Sci.</i> <b>1</b> 297–318.

Lin, Y. and Jeon, Y. (2006). Random forests and adaptive nearest neighbors. <i>J. Amer. Statist. Assoc.</i> <b>101</b> 578–590.

Meinshausen, N. (2006). Quantile regression forests. <i>J. Mach. Learn. Res.</i> <b>7</b> 983–999.

Geurts, P., Ernst, D. and Wehenkel, L. (2006). Extremely randomized trees. <i>Mach. Learn.</i> <b>63</b> 3–42.

Ishwaran, H., Kogalur, U. B., Blackstone, E. H. and Lauer, M. S. (2008). Random survival forests. <i>Ann. Appl. Stat.</i> <b>2</b> 841–860.

Wager, S., Hastie, T. and Efron, B. (2014). Confidence intervals for random forests: The jackknife and the infinitesimal jackknife. <i>J. Mach. Learn. Res.</i> <b>15</b> 1625–1651.

Biau, G., Devroye, L. and Lugosi, G. (2008). Consistency of random forests and other averaging classifiers. <i>J. Mach. Learn. Res.</i> <b>9</b> 2015–2033.

Bühlmann, P. and Yu, B. (2002). Analyzing bagging. <i>Ann. Statist.</i> <b>30</b> 927–961.

Díaz-Uriarte, R. and Alvarez de Andrés, S. (2006). Gene selection and classification of microarray data using random forest. <i>BMC Bioinformatics</i> <b>7</b> 1–13.

Svetnik, V., Liaw, A., Tong, C., Culberson, J. C., Sheridan, R. P. and Feuston, B. P. (2003). Random forest: A classification and regression tool for compound classification and QSAR modeling. <i>J. Chem. Inf. Comput. Sci.</i> <b>43</b> 1947–1958.

Stone, C. J. (1985). Additive regression and other nonparametric models. <i>Ann. Statist.</i> <b>13</b> 689–705.

Nobel, A. (1996). Histogram regression estimation using data-dependent partitions. <i>Ann. Statist.</i> <b>24</b> 1084–1105.

Biau, G. and Devroye, L. (2010). On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification. <i>J. Multivariate Anal.</i> <b>101</b> 2499–2518.

Stone, C. J. (1977). Consistent nonparametric regression. <i>Ann. Statist.</i> <b>5</b> 595–645.

Amaratunga, D., Cabrera, J. and Lee, Y.-S. (2008). Enriched random forests. <i>Bioinformatics</i> <b>24</b> 2010–2014.

Bai, Z.-D., Devroye, L., Hwang, H.-K. and Tsai, T.-H. (2005). Maxima in hypercubes. <i>Random Structures Algorithms</i> <b>27</b> 290–309.

Barndorff-Nielsen, O. and Sobel, M. (1966). On the distribution of the number of admissible points in a vector random sample. <i>Teor. Verojatnost. i Primenen.</i> <b>11</b> 283–305.

Biau, G. (2012). Analysis of a random forests model. <i>J. Mach. Learn. Res.</i> <b>13</b> 1063–1095.

Clémençon, S., Depecker, M. and Vayatis, N. (2013). Ranking forests. <i>J. Mach. Learn. Res.</i> <b>14</b> 39–73.

Cutler, D. R., Edwards, T. C. Jr, Beard, K. H., Cutler, A., Hess, K. T., Gibson, J. and Lawler, J. J. (2007). Random forests for classification in ecology. <i>Ecology</i> <b>88</b> 2783–2792.

Denil, M., Matheson, D. and Freitas, N. d. (2013). Consistency of online random forests. In <i>Proceedings of the ICML Conference</i>. Available at <a href="arXiv:1302.4853">arXiv:1302.4853</a>.

Efron, B. (1982). <i>The Jackknife</i>, <i>the Bootstrap and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics</i> <b>38</b>. SIAM, Philadelphia.

Genuer, R. (2012). Variance reduction in purely random forests. <i>J. Nonparametr. Stat.</i> <b>24</b> 543–562.

Ishwaran, H. and Kogalur, U. B. (2010). Consistency of random survival forests. <i>Statist. Probab. Lett.</i> <b>80</b> 1056–1064.

Kleiner, A., Talwalkar, A., Sarkar, P. and Jordan, M. I. (2014). A scalable bootstrap for massive data. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>76</b> 795–816.

Mentch, L. and Hooker, G. (2014). Ensemble trees and clts: Statistical inference for supervised learning. Available at <a href="arXiv:1404.6473">arXiv:1404.6473</a>.

Prasad, A. M., Iverson, L. R. and Liaw, A. (2006). Newer classification and regression tree techniques: Bagging and random forests for ecological prediction. <i>Ecosystems</i> <b>9</b> 181–199.

Scornet, E. (2014). On the asymptotics of random forests. Available at <a href="arXiv:1409.2090">arXiv:1409.2090</a>.

Scornet, E., Biau, G. and Vert, J. (2015). Supplement to “Consistency of random forests.” <a href="DOI:10.1214/15-AOS1321SUPP">DOI:10.1214/15-AOS1321SUPP</a>.

Shotton, J., Sharp, T., Kipman, A., Fitzgibbon, A., Finocchio, M., Blake, A., Cook, M. and Moore, R. (2013). Real-time human pose recognition in parts from single depth images. <i>Comm. ACM</i> <b>56</b> 116–124.

Wager, S. (2014). Asymptotic theory for random forests. Available at <a href="arXiv:1405.0352">arXiv:1405.0352</a>.

Politis, D. N., Romano, J. P. and Wolf, M. (1999). <i>Subsampling</i>. Springer, New York.

Devroye, L., Györfi, L. and Lugosi, G. (1996). <i>A Probabilistic Theory of Pattern Recognition. Applications of Mathematics</i> (<i>New York</i>) <b>31</b>. Springer, New York.

Hastie, T., Tibshirani, R. and Friedman, J. (2009). <i>The Elements of Statistical Learning</i>: <i>Data Mining</i>, <i>Inference</i>, <i>and Prediction</i>, 2nd ed. Springer, New York.

Breiman, L., Friedman, J. H., Olshen, R. A. and Stone, C. J. (1984). <i>Classification and Regression Trees</i>. Wadsworth Advanced Books and Software, Belmont, CA.

Boucheron, S., Lugosi, G. and Massart, P. (2013). <i>Concentration Inequalities</i>: <i>A Nonasymptotic Theory of Independence</i>. Oxford Univ. Press, Oxford.

Györfi, L., Kohler, M., Krzyżak, A. and Walk, H. (2002). <i>A Distribution-Free Theory of Nonparametric Regression</i>. Springer, New York.

Breiman, L. (2004). Consistency for a simple model of random forests. Technical Report 670, Univ. California, Berkeley, CA.

Zhu, R., Zeng, D. and Kosorok, M. R. (2012). Reinforcement learning trees. Technical report, Univ. North Carolina.