A Bayesian CART algorithm

By D. Denison, Bani K. Mallick, Adrian F. M. Smith. 1998

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Citations in the corpus

BART: Bayesian Additive Regression Trees (2008, methodology): “For (ii) and (iii) we use the simple defaults used by CGM98, namely the uniform prior on available variables for (ii) and the uniform prior on the discrete set of available splitting values for (iii).”
Bayesian CART – Prior Speciﬁcation and Posterior Simulation – (2006, methodology): “…actually need to restrict to trees with non-empty leaves; more generally, we may decide to require a minimum of, say, h data points in a leaf, so aim to sample from (4) The Metropolis–Hastings methods in Chipman et al. (1998) and Denison et al. (1998) are quite similar and form our starting point.”
An Introduction to MCMC for Machine Learning (2004, unknown): “Freitas, & Doucet, 2001a; Holmes & Mallick, 1998; Neal, 1996; M¨ uller & Rios Insua, 1998), Gaussian processes (Barber & Williams, 1997), CART ( Denison, Mallick, & Smith, 1998 ) and MARS (Holmes & Denison, this issue).”
Bayesian Additive Regression Trees (2006, methodology): “approaches of CGM98 and Denison et al. (1998) , where a single tree is used to”
Bayesian Treed Gaussian Process Models With an Application to Computer Modeling (2007, methodology): “The Bayesian approach is straightforward to apply to CART (Chipman et al., 1998; Denison et al., 1998), provided that one can specify a meaningful prior for the size of the tree.”
Mondrian Forests: Efficient Online Random Forests (2014, background): “Bayesian models of decision trees [4, 9] typically specify a distribution over decision trees; such distributions usually depend on X and lack the projectivity property of the Mondrian process.”
Bayesian Treed Generalized Linear Models (2003, result): “The results in this paper extend the results of Chipman, George and McCulloch (1998, 2002) (hereafter CGM 1998 and CGM 2002) and Denison, Mallick and Smith (1998) , (hereafter DMS 1998).”
REGRESSION TREES WITH UNBIASED VARIABLE SELECTION AND INTERACTION DETECTION (2002, methodology): “…Loh and Yao (1994) use a CV-based look-ahead procedure; Marshall (1995) finds non-hierarchical partitions ; Chipman, George and McCulloch (1998) and Denison, Mallick and Smith (1998) employ Bayesian methods to search among trees; Li, Lue and Chen (2000) use a stopping rule based on statistical…”
An Interpretable Stroke Prediction Model using Rules and Bayesian Analysis (2013, methodology): “5, or typical Bayesian decision tree methods (Dension et al., 1998; Chipman et al., 1998, 2002) are not particularly computationally demanding, however in practice the greediness heavily affects the quality of the solution, both in terms of accuracy and interpretability.”