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Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty quantification is to estimate the variance from an ensemble of models, which are often generated by the generally applicable bootstrap method. In this work, we demonstrate that the direct bootstrap ensemble standard deviation is not an accurate estimate of uncertainty and propose a calibration method to dramatically improve its accuracy. We demonstrate the effectiveness of this calibration method for both synthetic data and physical datasets from the field of Materials Science and Engineering. The approach is motivated by applications in physical and biological science but is quite general and should be applicable for uncertainty quantification in a wide range of machine learning regression models.
Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution. The goal o
Mass cytometry technology enables the simultaneous measurement of over 40 proteins on single cells. This has helped immunologists to increase their understanding of heterogeneity, complexity, and lineage relationships of white blood cells. Current st
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important extension of this
Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on honest random f
This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which depart