Related papers: Scalable piecewise smoothing with BART

Implicit Quantile BART (IQ-BART) posits a non-parametric Bayesian model on the conditional quantile function, acting as a model over a conditional model for $Y$ given $X$. One of the key ingredients is augmenting the observed data…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…

The paper presents Maximal Ellipsoid Backward Reachable Trees MAXELLIPSOID BRT, which is a multi-query algorithm for planning of dynamic systems under stochastic motion uncertainty and constraints on the control input. In contrast to…

Scaling regression to large datasets is a common problem in many application areas. We propose a two step approach to scaling regression to large datasets. Using a regression tree (CART) to segment the large dataset constitutes the first…

Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…

Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…

Proposed by Donoho (1997), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article we define and study Dyadic CART and…

Random Forest's performance can be matched by a single slow-growing tree (SGT), which uses a learning rate to tame CART's greedy algorithm. SGT exploits the view that CART is an extreme case of an iterative weighted least square procedure.…

To achieve the goal of providing the best possible care to each patient, physicians need to customize treatments for patients with the same diagnosis, especially when treating diseases that can progress further and require additional…

This paper extends the RRT* algorithm, a recently developed but widely-used sampling-based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often…

Machine learning models used in medical applications often face challenges due to the covariate shift, which occurs when there are discrepancies between the distributions of training and target data. This can lead to decreased predictive…

Since their inception in the 1980's, regression trees have been one of the more widely used non-parametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to…

We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble…

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP)…

Random forests are widely used in regression. However, the decision trees used as base learners are poor approximators of linear relationships. To address this limitation we propose RaFFLE (Random Forest Featuring Linear Extensions), a…

Multiple Additive Regression Trees (MART), an ensemble model of boosted regression trees, is known to deliver high prediction accuracy for diverse tasks, and it is widely used in practice. However, it suffers an issue which we call…

Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models…

The multinomial probit Bayesian additive regression trees (MPBART) framework was proposed by Kindo et al. (KD), approximating the latent utilities in the multinomial probit (MNP) model with BART (Chipman et al. 2010). Compared to…

Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…