Related papers: Risk Bounds for CART Classifiers under a Margin Co…
We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…
The standard procedure to decide on the complexity of a CART regression tree is to use cross-validation with the aim of obtaining a predictor that generalises well to unseen data. The randomness in the selection of folds implies that the…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing $\kappa$…
In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However,…
Bayesian Additive Regression Trees(BART) is a Bayesian nonparametric approach which has been shown to be competitive with the best modern predictive methods such as random forest and Gradient Boosting Decision Tree.The sum of trees…
This paper shows that decision trees constructed with Classification and Regression Trees (CART) and C4.5 methodology are consistent for regression and classification tasks, even when the number of predictor variables grows…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive…
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…
There is currently a dearth of appropriate methods to estimate the causal effects of multiple treatments when the outcome is binary. For such settings, we propose the use of nonparametric Bayesian modeling, Bayesian Additive Regression…
Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
Estimation of individualized treatment effects (ITE), also known as conditional average treatment effects (CATE), is an active area of methodology development. However, much less attention has been paid to the quantification of uncertainty…
In the era of precision medicine, genome-wide epigenetic modifications offer rich data that could inform risk prediction. However, these data are high-dimensional and exhibit complex dependence structures, which makes it difficult to…
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…
In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In…
There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian Additive Regression Trees…
Bayes additive regression trees(BART) is a nonparametric regression model which has gained wide -spread popularity in recent years due to its flexibility and high accuracy of estimation .In spatio-temporal related model,the spatio or…
In this work we study approximation algorithms for the \textit{Bounded Color Matching} problem (a.k.a. Restricted Matching problem) which is defined as follows: given a graph in which each edge $e$ has a color $c_e$ and a profit $p_e \in…