Analyzing Bagging

By Peter Buhlmann, Bin Yu. 2001

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Citations in the corpus

Analysis of a Random Forests Model (2010, methodology): “This subspace randomization scheme is blended with bagging ([9, 15, 16, 4]) to resample, with replacement, the training data set each time a new individual tree is grown.”
Local Linear Forests (2018, methodology): “Local linear regression has been particularly well-studied for longitudinal data, as in Li and Hsing [2010] and Yao, Muller, and Wang [2005]. Cheng, Fan, and Marron [1997] use local polynomials to estimate the value of a function at the boundary of its domain. Abadie and Imbens [2011] show how incor”
Generalized random forests (2016, background): “…forest predictions µ̂(x) are written as the average of B noisy tree-based predictors µ̂b(x), µ̂(x) = B−1 ∑B b=1 µ̂b(x); and, because individual trees µ̂b(x) have low bias but high variance, such averaging meaningfully stabilizes predictions (Bühlmann and Yu, 2002; Scornet, Biau and Vert, 2015).”
Consistency of Random Forests (2014, background): “…computationally intensive procedures to improve on unstable estimates, especially for large, high-dimensional data sets where finding a good model in one step is impossible because of the complexity and scale of the problem (Bühlmann and Yu, 2002; Kleiner et al., 2012; Wager et al., 2013).”
Uniform Convergence of Random Forests via Adaptive Concentration (2015, neutral): “1 It seems plausible, however, that all our results should still hold even if we allow for bootstrapping, since the bootstrap is thought to have a regularizing effect on the forest and should thus reduce its ability to overfit the training data [6, 11].”
Random forest predictive modeling of mineral prospectivity with small number of prospects and data with missing values in Abra (Philippines) (2015, methodology): “We did not apply pruning because, according to Breiman (1996) and Buhlmann and Yu (2002), the variance of the output error is reduced if several similar datasets (predictors and training samples) are created by bagging and if regression trees are grown without pruning and averaged.”
OBSERVATIONS ON BAGGING (2006, methodology): “, μJ) only; for example, μ = (1, 1, 2) and μ = (3, 2, 3) have the same weights, E [W 2 1W2] = E [W 2 3W2] due to exchangeability.”
How Useful is Bagging in Forecasting Economic Time Series? A Case Study of US CPI Inflation (2005, unknown): “In this subsection, we will establish that the qualitative findings of Bühlmann and Yu (2002) for the single-regressor model continue to hold in the multiple regressor model.”
A random forest guided tour (2015, methodology): “It is one of the most effective computationally intensive procedures to improve on unstable estimates, especially for large, high-dimensional data sets, where finding a good model in one step is impossible because of the complexity and scale of the problem (Bühlmann and Yu, 2002; Kleiner et al., 201”
Asymptotic Theory for Random Forests (2014, methodology): “Although Breiman originally built random forests using bootstrap aggregation or bagging [5], subsampled random forests have also been repeatedly studied and found to work well [e.g., 9, 28].”
Confidence sets for split points in decision trees (2007, background): “Ecologists have suggested that split points provide a phosphorus threshold at which biological imbalance occurs, and the lower endpoint of the confidence set may be interpreted as a level that is protective of the ecosystem.”
Robust Tree-based Causal Inference for Complex Ad Effectiveness Analysis (2015, methodology): “! of single tree-based method in Theorem 1 and the consistency of the bagging method for CART shown by Bühlmann and Yu [8].”
Leveraging Bagging for Evolving Data Streams (2010, methodology): “– Bulhman and Yu [10] proposes subagging, using resampling without replacement.”