PERT – Perfect Random Tree Ensembles

By Adele Cutler, Guohua Zhao. 2001

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Model Architectures

Citations in the corpus

Reconciling modern machine-learning practice and the classical bias–variance trade-off (2018, methodology): “To interpolate the training data, we disable the bootstrap re-sampling for results in Figure 11(a), which has been investigated under the name “Perfect random tree ensembles” by Cutler et al. [14].”
Extremely randomized trees (2006, methodology): “Cutler and Guohua (2001) propose an algorithm for classification problems that builds almost totally randomized trees.”
Variable selection using random forests (2010, background): “Purely random forests have been introduced by Cutler et al. (2001) for classiﬁcation problems and then studied by Breiman (2004), but the results are somewhat preliminary.”
Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate (2018, background): “made for other machine learning methods, including boosting [37], random forests [19], and kernel machines [12].”
SAT-based Decision Tree Learning for Large Data Sets (2021, background): “Given a class c , for all e i ; e j 2 E such that C ( e i ) = c; C ( e j ) 6 = c , we add the clauses : g i;j;w , where w = d (cid:0) d ( c ) + d min is the allowed depth in regards to the weight of c .”
Reconciling modern machine learning and the bias-variance trade-off (2018, result): “This is similar to the PERT method of Cutler and Zhao [12].”
Random Forests for Big Data (2015, methodology): “It would be of interest to use in MR-RF this RF variant, or even more randomized ones (like [29] PERT, Perfect Random Tree Ensembles, or [30, 31] PRF, Purely Random Forests).”
Encrypted statistical machine learning: new privacy preserving methods (2015, background): “It is also diﬀerent to perfectly random tree ensembles (Cutler and Zhao, 2001), where random split points are constructed between observations known to belong to diﬀerent classes.”
Consistency of Random Forests and Other Averaging Classifiers (2008, background): “Different random forests differ in how randomness is introduced in the tree building process, ranging from extreme random splitting strategies (Breiman [4], Cutler and Zhao [7]) to more involved data-dependent strategies (Amit and Geman [1], Breiman [5], Dietterich [11]).”
On the asymptotics of random forests (2014, background): “For instance, tree construction can be independent of D n (Biau, 2012), depend only on the X i ’s (Biau et al., 2008) or depend on the whole training set (Cutler and Zhao, 2001; Geurts et al., 2006; Zhu et al., 2012).”
Mondrian Forests: Efficient Online Random Forests (2014, background): “This phenomenon has been observed by others as well—for example, Cutler and Zhao [6] demonstrate that their PERT classiﬁer (which is similar to batch version of MF) achieves test accuracy comparable to Breiman-RF on many real world datasets.”
Tree‐based iterative input variable selection for hydrological modeling (2013, methodology): “Tree-based methods include both deterministic (e.g., classification and regression trees [Breiman et al., 1984], M5 [Quinlan, 1992]) and randomized methods (e.g., Bagging predictors [Breiman, 1996], Random Subspace method [Ho, 1998], Random forests [Breiman, 2001], and PERT [Cutler and Guohua, 2001]”
Understanding Random Forests: From Theory to Practice (2014, methodology): “Cutler and Zhao [2001]: With Perfect Random Tree Ensembles (PERT), Cutler and Zhao [2001] propose to grow a forest of perfectly fit decision trees in which both the (ordered) variable to split on and the discretization threshold are chosen at random.”