Estimating Shapley effects for moderate-to-large input dimensions

Sobol' indices and Shapley effects are attractive methods of assessing how a function depends on its various inputs. The existing literature contains various estimators for these two classes of sensitivity indices, but few estimators of Sobol' indices and no estimators of Shapley effects are computationally tractable for moderate-to-large input dimensions. This article provides a Shapley-effect estimator that is computationally tractable for a moderate-to-large input dimension. The estimator uses a metamodel-based approach by first fitting a Bayesian Additive Regression Trees model which is then used to compute Shapley-effect estimates. This article also establishes posterior contraction rates on a large function class for this Shapley-effect estimator and for the analogous existing Sobol'-index estimator. Finally, this paper explores the performance of these Shapley-effect estimators on four different test functions for moderate-to-large input dimensions and number of observations.Comment: 19 pages, 3 figure

Sharded Bayesian Additive Regression Trees

In this paper we develop the randomized Sharded Bayesian Additive Regression Trees (SBT) model. We introduce a randomization auxiliary variable and a sharding tree to decide partitioning of data, and fit each partition component to a sub-model using Bayesian Additive Regression Tree (BART). By observing that the optimal design of a sharding tree can determine optimal sharding for sub-models on a product space, we introduce an intersection tree structure to completely specify both the sharding and modeling using only tree structures. In addition to experiments, we also derive the theoretical optimal weights for minimizing posterior contractions and prove the worst-case complexity of SBT.Comment: 46 pages, 10 figures (Appendix included

2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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withdrawn 2017 hrs ehra ecas aphrs solaece expert consensus statement on catheter and surgical ablation of atrial fibrillation

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Model Mixing Using Bayesian Additive Regression Trees

In modern computer experiment applications, one often encounters the situation where various models of a physical system are considered, each implemented as a simulator on a computer. An important question in such a setting is determining the best simulator, or the best combination of simulators, to use for prediction and inference. Bayesian model averaging (BMA) and stacking are two statistical approaches used to account for model uncertainty by aggregating a set of predictions through a simple linear combination or weighted average. Bayesian model mixing (BMM) extends these ideas to capture the localized behavior of each simulator by defining input-dependent weights. One possibility is to define the relationship between inputs and the weight functions using a flexible non-parametric model that learns the local strengths and weaknesses of each simulator. This paper proposes a BMM model based on Bayesian Additive Regression Trees (BART). The proposed methodology is applied to combine predictions from Effective Field Theories (EFTs) associated with a motivating nuclear physics application.Comment: 33 pages, 6 figures, additional supplementary material can be found at https://github.com/jcyannotty/OpenB

Design and Analysis of Experiments on Nonconvex Regions

<p>Modeling a response over a nonconvex design region is a common problem in diverse areas such as engineering and geophysics. The tools available to model and design for such responses are limited and have received little attention. We propose a new method for selecting design points over nonconvex regions that is based on the application of multidimensional scaling to the geodesic distance. Optimal designs for prediction are described, with special emphasis on Gaussian process models, followed by a simulation study and an application in glaciology. Supplementary materials for this article are available online.</p